Anthology of

The Imagineer’s Chronicles

A Journey through Four Spatial Dimensions

Jeffrey O’Callaghan

 

Copyright Jeffrey O’Callaghan 2014

 

Preface

 

In Thomas S. Kuhn's book "The Structure of Scientific Revolution" he documents the doubts that precipitate a paradigm change in scientific thought.

For example, even though one could still make accurate predictions of planetary motions using Ptolemy's Epicycles it became increasing more difficult to integrate that concept with the more accurate observational data provided by the new technologies of that day.

This resulted in some scientists questioning their validity. He suggests the doubt generated by its persistent inability of to explain new data lead many scientists to adopt the simpler rules of the revolutionary heliocentric model.

Modern physics appears to be on the verge of a similar revolution because the discoveries of dark matter and dark energy are extremely difficult to integrate into its current theoretical models.

As Thomas S. Kuhn points out failure of an existing paradigm is a prelude to the search for a new one.

The Imagineer's Chronicles continues a search for a paradigm that began in its companion book "The Reality of the Fourth Spatial Dimension” which will integrate the observations of both the microscopic quantum world and the macroscopic one of Relativity into one theoretical model.

Each article will cover one aspect of the search for the "reality" it defines.

Introduction

 

Are you curious about how and why the universe of the big and small behave the way they do?  Have you even wondered why common sense does not apply to the quantum mechanical world of subatomic particles or how three-dimensional space can be undergoing a spatial expansion in universe consisting of only four dimensional space-time?

For example because quantum mechanics predicts that there is a non zero probably one can observe a particle anywhere in the universe before an observation or measurement is made, many seemly rational scientists assume that a particle simultaneously exists in at every point in space only to materialize when it is observed. 

This prompted Einstein one of the greatest thinkers of modern times to say "Do you really believe that the moon isn’t there when nobody looks?"

In other words saying that nothing exists before one looks at it does not define the "reality" most of us believe in.

Most if not all scientific advancements humankind has made have been based on concepts derived though qualitative observations of the environment 

However, modern physicists seem to have taken a different road to understanding the laws that govern our world.  They spend most if not all of their time analyzing only its quantitative or mathematical properties.

This was the motivating factor in our decision to write the series of books entitled "The Imagineer's Chronicles" because we believe a different approach to science, one based on qualitatively observing an environment can bring a more rational and logical understanding of the mechanisms that govern both the macroscopic and microscope universe.

For example Einstein's theories define the universe in terms of only four dimensional space-time.  However observations tell us that three-dimensional space is undergoing an expansion towards a higher spatial dimension.

This presents a problem for the proponents of his theories because they do not include one.

However several articles in this series show us when Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy and the constant velocity of light he gave us the ability to qualitatively and quantitatively convert it to one consisting of only four *spatial* dimensions. 

In other words by defining our universe in terms of energy/mass and the constant velocity of light he provided a qualitative and quantitative means of redefining the geometry of four dimensional space-time terms of higher fourth *spatial* dimension thereby allowing us to understand the "reality" of how three-dimensional space can be undergoing a spatial expansion.

As mentioned earlier quantum mechanics predicts that there is a non zero probably one can observe a particle anywhere in the universe before an observation or measurement is made and because of this many seemly rational scientists assume that a particle simultaneously exists in at every point in space and only materializes when it is observed. 

However one of the many articles in this series shows that if we shift the probabilistic interpretations of a quantum environment to the causality of an event instead of its outcome it would explain why particles only appear to materialize at a specific point when observed in terms of the single evolutionary path it took to get there.

For example if someone strikes a pool ball on a pool table in a dark room and cannot measure or determine the initial conditions there is an extremely high probability that he will find it on the table when he turns on the light.  However, he or she does not assume that the balls simultaneously exist on every point on its surface until the light is turned on.  Additionally one could apply Newton’s laws and the probability of the different initial conditions associated with that event to determine the most probable resting place of the pool balls after the light is turn on.  I think most would consider someone mentally deficient if he tried to convince us the pool balls simultaneous existed at every point on the surface of the pool table when the light off and only materialize when it was turn on just because he could not see how they got there.

In other words the reason why we only know where a particle is after we observe it may be because we are not sure how it got there and not because it existed everywhere before we looked for it.

We also believe our universe should be understandable to those who have a need to and are willing to work at it so each article presents the concepts in jargon free language with enough background information so that the reader will not have to do further research to understand its content.

In other words we should rely less on mathematics and more on conceptual logic and thought experiments (much like Albert Einstein did) to show how one can explain and predict all modern observations by redefining the space-time concepts of both The Special and General Theories of Relativity in terms of four spatial dimensions.


"The universe's most powerful enabling tool is not
knowledge or understanding but imagination
because it extends the reality of
one's environment." 

*************************** 

Contents

 

 

Article #

Subject

202 Can mathematics
 define reality
Dec 15, 2014

 
201 The fine tuning of the
 cosmological constant
 Dec. 1, 2014.htm

 
200 The geometry of
 quantum probabilities
 Nov. 15, 2014.htm

 
199 In the beginning
Nov. 1, 2014

 
198 A physical image of
Black Body Radiation
Oct. 15, 2014

 
197 The causality of quantum
 probabilities or why
 God must play dice
Oct. 1, 2014

 
196 Can we influence reality?
Sept. 15, 2014

 
195 The structure of our reality
Sept. 1, 2014

 
194 Fire or ice how will
our universe end?
Aug. 15, 2014

 
193 The new direction provided
by the Higgs boson
Aug. 1, 2014

 
192 The new direction provided
by Dark Energy
July 15, 2014

 
191 The reliability of our
 mathematical universes
 July 1, 2014

 
190 How could Einstein have
 explained Dark Energy
June 15, 2014

 
189 Did Einstein predict
 the Higgs mechanism in 1920?
June 1, 2014

 
188 Should measurement define "reality"
May 15, 2014

 
187 A cosmological history lesson
May 1, 2014

 
186 The reality behind
 quantum entanglement
Apr. 15, 2014

 
185 The Geometry of a particle wave
Apr. 1, 2014

 
184 The reality of quantum fields
Mar. 15, 2014

 
183 A Classical interpretation
 of quantum mechanics
Mar. 1, 2014

 
182 Mass from first
 principles
Feb. 15, 2014

 
181 Should we let our imaginations
define reality
Feb. 1, 2014

 
180 Deriving the fundamental
constants of nature
Jan. 15, 2014

 
179 The Geometry of antimatter
Jan. 1, 2014

 

178

The quantum fallacy
Dec.15,2013

 

 

 

177

The demise of the singularity
Dec. 1, 2013

 

 

 

176

The “reality” of the Higgs field
Nov. 15, 2013

 

 

 

175

The role of reality in science
Nov 1, 2013

 

 

 

174

The Geometry of Dark Matter

Oct. 15, 2013

 

 

 

173

Reformulating space-time

Oct. 1, 2013

 

 

 

172

Gravity or dark energy: which one will win?
Sept. 15, 2013

 

 

 

171

The Mysticism of a non-dimensional particle
 Sept. 1 2013

 

 

170

Can mathematics define reality?
Aug.15, 2013

 

 

 

169

Thomson’s double slit experiment in four spatial dimensions
Aug. 1, 2013

 

 

 

168

Faster than light in four *spatial* dimensions
July 15, 2013

 

 

 

167

Finding the graviton
July 1, 2013

 

 

 

166

A quantum of space-time
June 15, 2013

 

 

 

165

Plato’s lesson on quantum mechanics
June 1, 2013

 

 

164

Light and the physicality of space
May 15, 2013

 

 

 

163

The causality of motion
May 1, 2013

 

 

162

The reality of Quantum Fields
Apr. 15, 2013

 

 

 

 

161

The geometry of Quantum Mechanics

Apr 1, 2013

 

 

 

160

Will time end?
Mar. 20, 2013

 

 

 

159

The geometry of Einstein’s Aether
Mar. 15, 2013

 

 

 

158

Dark Energy in four spatial dimensions
Mar. 1, 2013

 

 

157

Particles or fields you cannot have it both ways
Feb. 15, 2013

 

 

 

156

Deriving mass without the Higgs Boson
Feb. 1, 2013

 

 

 

155

What came before the Big Bang
Jan. 15, 2013 

 

 

154

Why something rather than nothing

Jan. 1, 2013

 

 

151 Who should teach “reality”?
Nov. 15, 2012
   
150 The physical significance of Planck's constant
Nov 1, 2012
   
149 Time dilatation in four spatial dimensions
Oct. 15, 2012
   
148 Dark energy and the evolution of the universe
Oct 1, 2012
   
147 A Classical Quantum environment
Sept. 15, 2012
   
146 The Illusion that is time
Sept. 1, 2012
   
145 The fabric of the cosmos
Aug 15, 2012
   
144 Putting the Chromo in Quantum Chromodynamics
Aug. 1, 2012
   
143 A verifiable alternative to the Higgs Boson
July 15, 2012
   
142 The “reality” of Faraday’s fields
July 1, 2012
   
141 Is time eternal?
June 15, 2012
   
140 The "reality" behind wave-particle duality
June 1, 2012
   
139 Curious as to why yellow is yellow?
May 15, 2012
   
138 Unification in four *spatial* dimensions
May 1, 2012
   
137 Quantum numbers: a classical interpretation
Apr. 15 2012
   
136 Dark matter and the evolution of the universe
April 1, 2012
   
135 Linking gravitational  and electrical forces
Mar. 15, 2012
 
134 Solving the Measurement Problem
Mar. 1, 2012
 
133 Pauli's Exclusion Principal: a classical interpretation
Feb. 15, 2012
 
132 Dark matter and energy linked to Quantum mechanics
Feb 1, 2012
 
131 The Hunt for the Graviton
Jan. 23, 2012
   
130 Compton scattering  a classical approach
Jan. 15, 2012
   
129 Absolute verses relative size
Jan. 1, 2012
   
128 Defining objective reality
Dec. 15, 2011
   
127 Mass, inertia, and the Higgs Boson
Dec. 1, 2011
   
126 The reality of quantum superposition
Nov. 15, 2011
   
125 The Geometry of Dark Matter
Nov. 1, 2011
   
124 Mathematical verses observational Reality
Oct 15, 2011
   
123 Quantum entanglement: A Classical non-locality
Nov. 1 2011
   
122 Deriving the causality of time
Sept 15, 2011
   
121 Linking gravity to the strong and weak forces
Sept. 1, 2011
   
120 Newtonian verses Planck’s or Quantum time
Aug. 15, 2011
   
119 The Relativity of a four dimensional Newtonian universe
Aug. 1, 2011
   
118 Gravity, quarks and Pauli's exclusion principle
July 15, 2011
   
117 The Reality of illusions
July 01, 2011
   
116 Evolution of the universe in four *spatial* dimensions
 06-15-2011
   
115 The physics of reality
June 1, 2011
   
114 The relative masses of the proton and electron
May 15, 2011
   
113 The trouble with Physics
May 1, 2011
   
112 A sensible solution to the Horizon Problem
Apr. 15, 2011
   
111 The *reality* of quantum probabilities
Apr. 1, 2011
   
110 Reality and the EPR Paradox
Mar. 20, 2011
   
109 The Strong force in four spatial dimensions
Mar. 10, 2011
   
108 The weak force in four *spatial* dimensions
Mar. 1, 2011
   
107 Gravitational lensing
Feb. 15, 2011
   
106 The Geometry of antimatter
Feb. 01, 2011
   
105 The conflict between the photoelectric effect and Maxwell’s field equations
Jan, 15, 2011
   
104 Supersymmetry and four spatial dimensions
Jan. 1, 2011
103 A quantum Gravity field
Dec. 15, 2010
 
102 The reality of the fourth spatial dimension
Dec. 1, 2010
 
101 Gravity verses entropy
Nov. 15, 2010
 
100 The geometry of a positron
Nov. 1, 2010
 
99 Maxwell's equations in four spatial dimensions
Oct. 15, 2010
 
98 Quantum polarization the measurement problem
Oct. 1, 2010
 
97 Entropy and the Big Crunch
Sept 15, 2010
 
96 Heisenberg uncertainty principal: A Classical explanation
Sept 1, 2010
 
95 The Fundamental Quantum Particles
Aug. 15, 2010
 
94 The inertia of dimensional interactions
Aug. 1, 2010
 
93 Why the universe must be flat
July 15, 2010
 
92 An alternative to Dark Matter
July 1, 2010
 
90 Discovering Quantum gravity
Jun. 15, 2010
 
89 Defining the "reality" of a Quantum Vacuum
Jun 1, 2010
 
88 A new paradigm
May 20, 2010
 
87 Entropy and the arrow of time
May 10, 2010
 
86 Quantum boundaries
May 1, 2010
 
85 The Hubble Deep Field
Apr. 20, 2010
 
84 A Quantum Enigma: the wave particle duality of
existence
Apr. 10, 2010
 
83 A background independent quantum gravity
Apr. 01, 2010
 
82 What is the universe expanding into
Mar. 21, 2010
 
81 A Classical Schrödinger's equation
Mar. 15, 2010
 
80 What are Quantum ”fields”
Mar. 01, 2010
 
79 The Anthropic principle
Feb.15, 2010
 
78 How is space expanding
Feb. 01, 2010
 
77 The geometry of Quantum Mechanics
Jan. 20, 2010
 
76 The origin of Dark energy
Jan. 10, 2010
 
75 The Geometry of Young's Double Slit Experiment
Jan. 01, 2010
 
74 Occam's Razor
Dec, 15, 2009
 
73 The Flatness problem
Dec. 01, 2009
 
72 How many dimensions do we need?
Nov. 15, 2009
 
71 The Geometry of Dark energy
Nov. 01. 2009
 
70 Vacuum or zero point energy and quantum fluctuations
Oct. 22, 2009
 
69 Quantum gravity
Oct. 15, 2009
 
68 Black body radiation the Ultraviolet Catastrophe
Oct. 01, 2009
 
67 Falsifiability
Sept. 15, 2009
 
66 Defining the causality of inertia
Sept. 01, 2009
 
65 Cosmic background radiation an alternative
Aug. 15, 2009
 
64 Quantum fields
Aug. 1, 2009
 
63 The geometry of mass
July 15, 2009
 
62 Does anti-matter fall up?
July 01, 2009
 
61 The geometry of a stable particle
Jun. 15, 2009
 
60 Gravity in four *spatial* dimensions
Jun. 01, 2009
 
59 Matter verses antimatter
May 15, 2009
 
58 The Big Picture
May 01, 2009
 
57 Who I am
Apr. 15, 2009
 
56 Seeing the invisible
Apr. 01, 2009
 
55 The geometry of quarks
Mar.15, 2009
 
54 Spaceship Spitzer and the black hole
Mar. 01-2009
 
53 A Comparison
Feb.-15-2009
 
51 Dark energy and the cosmological constant
Jan. 15, 2009
 
50 Black holes Just two numbers is all you need
Jan. 01, 2009
 
49 Quantum tunneling A classical Interpretation
Dec. 15 2008
 
48 Black Hole Mysteries and Myths
Dec. 01, 2008
 
47 Why four spatial dimensions
Nov. 15, 2008
 
46 Causality explanation and deductions of predictions
Nov. 01, 2008
 
45 The Casimir effect
Oct. 15, 2008
 
44 The science of Physics
Oct. 01, 2008
 
43 Solving the Mystery of Dark Matter
Sept-15-08
 
42 Common Sense
Sept. 01, 2008
 
41 An alternative to a singularity
Aug. 15, 2008
 
40 Gravitational Quantumelectrodynamics
Aug. 01, 2008
 
39 The Principal of Equivalence
Jul. 15, 2008
 
38 Reference frames
Jul. 01, 2008
 
37 What is the universe expanding towards
Jun. 15, 2008
 
36 Defining causality
Jun. 01, 2008
 
35 The unification of gravitational and electrical forces
May 15, 2008
 
34 Why a continuous non-quantized form of mass
May 01, 2008
 
33 A deterministic Quantum Mechanics
Apr. 15, 2008
 
32 A Quantum Paradox
Apr. 01, 2008
 
31 Beyond the Standard Model
Mar. 15, 2008
 
30 The cosmological redshift
Mar. 01, 2008
 
29 A Theory of Everything
Feb. 15, 2008
 
28 Unifying Quantum Mechanics with the
 velocity of light
Feb. 01, 2008
 
27 Return of the Big Bang
Jan. 15, 2008
 
26 Should mathematics define observations
Jan. 01, 2008
 
25 Gravity and electromagnetism in four spatial dimensions
Dec. 15, 2007
 
24 The "relativity" of four spatial dimensions
Dec. 01, 2007
 
23 Defining potential and kinetic energy
Nov. 26, 2007
 
22 Dark matter and the Pioneer anomalies
Nov. 19, 2007
 
21 Defining reality
Nov. 12, 2007
 
20 Quantum Puzzles
Nov. 05, 2007
 
18 Black Holes where are they now
Oct. 29, 2007
 
17 Embedded Dimensions
Oct. 22, 2007
16 What is dark energy
Oct. 15, 2007
 
15 Is the solution the answer
0ct. 08, 2007
 
14 Why is energy/mass quantized
Oct. 04, 2007
 
13 The Photon; a matter wave
Oct. 01, 2007
 
12 The casualty of electromagnetic energy
Sept. 27, 2007
 
11 Why space time
Sept. 27, 2007
 
10 Defining what time is
Sept. 20, 2007
 
9 A Wider View
Sept. 17, 2007
 
8 Defining Space
Sept. 13, 2007
 
7 What is Dark Matter
Sept. 10, 2007
 
6 The Causality of mass and energy
Sept. 06, 2007
 
5 A theory of Everything
Sept. 03, 2007
 
4 The architect
Aug. 30, 2007
 
3 The Role of imagination in science
Aug. 27, 2007
 
2 Experiences
Aug. 24, 2007
 
1 The State of the Universe
Aug. 20, 2007
 

 

202
 Can mathematics
 define reality
Dec 15, 201

Mathematics is the primary tool many of today's science use to define the causality of the physical laws governing of our observable universe.

However it is by definition is an abstract creation of the mind and therefore is not physically connected to the observable real world, most of us believe we live in.

Therefore, we can never be sure the equations developed by science accurately define the physicality of those laws or the real world they are describing.

This is true even though they make accurate predictions because unless there is a way of physically connecting the mathematical worlds create by the intellect to the observable world we live in science cannot be sure that is has chosen the correct set of facts that defines its existence.

Granted the mind can systematical quantify the natural world as the mathematics of quantum mechanics does with great accuracy but that does not necessarily mean it tell us anything about the reality of how or why that quantification takes place.

For example there are an infinite number of ways one can mathematically describe the fact that there are two apples on a table. One can predict why based on the assumption that there were originally four apples and two were taken away or assume that originally there were six and four were taken away.  However if there were only four apples to begin with the mathematical description using six apples even though accurately quantifies the existence of two apples it does not describe their world because in "reality' that world did not contain six apples.

Similarly just because the mathematics of quantum mechanics can very accurately predict the quantitative observation of the particle world does not mean that it defines why it is that way.

Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

He realized for science to make a claim that they have organized the natural world into a single set of patterns or laws that describe why we perceive its  "reality" the way we do they must be able to conceptually connect the independent models developed by our minds to the reality of natural world that exists outside of it.

For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

However Einstein realized by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a four dimensional space-time manifold one could explain how gravity "may act upon another at a distance through a vacuum" in terms of a curvature in space and time.   This enables one to understand gravity based on a physical image formed by the "reality" of what we can see and touch in our three-dimension world.

In other words he was able to connect the observable reality of our three dimensional world to the mathematical one he had created in his mind to explain gravity in terms of a physical imaged form in our three dimensional world.

Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Einstein.  They chose to look for reality only in terms of abstract mathematics instead of the physical imagery given to us by the "reality" of what we can see and touch.

The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency than it is to alter one based on physical imagery.

For example Quantum theory makes predictions based on the random properties of a probability function.  However because the abstract properties of probabilities which are not physically connected to our world, all its predictions no matter how inconsistent they are with the world they are describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in our three-dimensional environment physically connects it to a four-dimensional space time-environment

For example a single instance of a mass being gravitational repelled instead of attracted would contradict the physical imagery define by Einstein and would be extremely if not impossible to explain because no one has ever observe objects rolling up hill in our three-dimensional environment.  In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses gravitational repelling each other virtually impossible to incorporate into it.

However because quantum mechanics is based on probabilities anything that can happen eventually will.  Therefore it is virtually impossible to find any observation in the real world that contradicts it.  However this can only happen in an abstract environment which is not bound by the physicality of our observational world.

As mentioned earlier unless science can conceptually connect the mathematical worlds created by the intellect to the observable world we live in we cannot say that we know or understand anything physical laws that we assume define its reality.

But why should science put in the effort to understanding our theoretical models in terms of the physical "reality" of our world when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein's theories make very accurate predictions of future events.

Because the mission of a science is to define the real world in terms of what we perceive in our environment not to perceive an abstract mathematical environment to define what we want it to be.

201
The fine tuning of the
 cosmological constant
 Dec. 1, 2014

"Einstein once said, “What really interests me is whether God had any choice in the creation of the world. This is a fundamental question.  Compared to this question, all others seem trivial. Yes, God would have had many choices if He had wanted to create a barren universe. However, in order to create a universe where life is possible, with the same set of natural laws as ours, it seems that He had only limited choices. According to recent findings, the values of physical constants should have been fine-tuned to make the emergence of life in the universe possible." Taeil Albert Bai Stanford University.

However one may be able to understand why they are what they by observing them in terms of the laws of causality that govern our present universe.  In other words God may not have a choice in the creation of our world once those laws had been set.

For example one of the most puzzling questions facing cosmology today is why the density of matter and energy are so close to that required to create a flat universe.

The universe will be flat if and only if the attractive gravitational potential of its matter just equals the expansive energy of the big bang. This will result in the expansion slowing and only stopping after an infinite amount of time has passed.

This is important to life because the physical laws that govern our universe tell us if its expansion was much faster than its present value stars and galaxies would not have been able to form while the gravitational force of too much matter would have cause it to clump together more rapidly and thereby not giving enough time for life to evolve.

But why the universe appears to be flat even after 14 billion years of expansion is still a mystery because a flat universe is like the top of a hill.  If you are a little away from it the expansion of the universe soon drives you far away from this value, just as a ball that is a short distance from a hilltop will roll down to the bottom. Therefore, when the Universe was one second old, it must have deviated from flatness by less than one part in ten-thousand-trillion. This is a problem because it is hard to understand how the amount of mass and the energy associated with the expansion could have been adjusted to such precision.

However as mentioned earlier one may be able to explain the reason by observing how matter and energy interact and apply the laws of causality that govern those interactions in our present universe to its formation. 

For example recent observations tell us that space is not only expanding but accelerating towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain how the universe is expanding and accelerating towards higher spatial dimension one would have to assume the existence of another one in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he defined the geometric properties of a space-time universe in terms of the balance between mass and energy defined by the equation E=mc^2 and the constant velocity of light because that provided a method of converting the displacement in space-time he associated with energy to its equivalent displacement in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time manifold.

However doing so can add significantly to our understanding how and why the forces of gravity and Dark Energy interact to cause the universe to be flat because it would allow one to derive them and the kinetic energy of its expansion in terms in terms of the common geometry of oppositely directed displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example, one can understand why Dark Energy is causing the accelerated expansion of our universe by extrapolating that fact that if the walls of an above ground pool filled with water collapse the molecules on the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.  Therefore similar to the water molecules occupying the elevated two dimensional surface of the water, the particles occupying an "elevated' region of three-dimensional space will flow and accelerate outward in the four dimensional environment surrounding it and, as it was with the water molecules in pool their acceleration will decrease as they expand outward towards four dimensional space.

Yet deriving both gravity and the forces involved with the universes expansion in terms of a common geometry as was done above can not only explain why Dark Energy is causing it to accelerate but it can also add significantly, as mentioned earlier to our understanding of why it is flat in terms of the laws that govern our current universe.

This is because the fact that the universe is by definition is a closed system the law of conservation of energy/mass means there must a dynamic balance between the curvature created by the gravitational potential of the its energy/mass and the oppositely directed kinetic energy associated with its expansion.

This means as was shown in the article "Defining energy" the "downward" directed displacement in a "surface" of three-dimension space with respect to a fourth "spatial* dimension it associates with the total gravitational potential of the universe would be offset by the "upwardly" directed one associated with its Kinetic energy.

This would allow one to understand why the universe is flat in terms of the observations of the three-dimensional environment occupied by a piece of paper.  They show us that if one crumples one that was original flat and views its entire surface from its three dimensional center the overall magnitude of the displacement caused by that crumpling would be zero because the height above its surface would be offset by an oppositely directed one below its surface.  (This would be true even if one folded it in half because there would be an equal amount of paper above and below its center.)  Therefore, if one views its overall surface only with respect to its height, its curvature would appear to be flat.  In other words flatness is an intrinsic property of a flat piece of paper that has been crumpled.

Similarly, if the energy density associated with the momentum of the universe's expansion is a result of oppositely directed displacements in a "surface" of a three-dimensional space manifold with respect to that associated with its matter component their overall density would appear to be flat with respect to its four dimensional center because, similar to a crumpled piece of paper the "depth" of the displacement below its "surface" caused by matter would offset by the "height" of the displacement above it caused by its Kinetic energy.

However this would be true only if only if the matter and energy in our universe was "flat" or equally disturbed in the beginning.

Many proponents of the Big Bang Model assume it began from the expansion of mass and energy around a one-dimensional point.  However, if we are correct in assuming that density of the mass and energy components of our universe are a result of oppositely directed curvatures in a "surface" of a three-dimensional space manifold, the universe must have been "flat" with respect to their density at the time of the Big Bang.  This is because a one-dimensional point would have no "vertical" component with respect to a fourth *spatial* dimension and therefore the "surface" of three-dimensional space originating from it would be "flat" with respect to that dimension.

However, if the universe was flat with respect to the density of its energy/mass in the beginning it would remain flat throughout its entire expansive history because as was shown above its expansion would result in a proportional reduction in the displacements above and below its three-dimensional "surface" as it expanded.

Another advantage to viewing our universe in terms of four *spatial* dimensions instead of four dimensional space-time is that it allows one to not only understand why it appears to be fine-tuned for flatness but also why the values of many of the other fundamental constants are what they are in terms of their evolution history.

We know from observations the equation E=mc^2 defines the equivalence between mass and energy and since mass is associated with the attractive properties of gravity it also tells us, because of that equivalence, the kinetic energy associated with the universe's expansion also possess those attractive properties.  However the law of conservation of energy/mass tells us that in a closed system the creation of kinetic energy cannot exceed the gravitational energy associated with the total energy/mass in the universe and that a reduction in one must be compensated for by an increase in the other.

This means the total gravitation potential of the universe must increase as it expands and cools approaching a maximum value at absolute "0" while at the same time the kinetic energy of its expansive components must decrease.  Therefore, at some point in time, the universe MUST enter a contractive phase because the total gravitational potential must eventually exceed the kinetic energy of its expansion.  This is would be true even though the gravitational potential of its kinetic energy components would be disturbed or "diluted" by a factor of c^2.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate. Therefore they believe that its expansion will continue forever.  However, as was shown in the article "Dark Energy and the evolution of the universe" Oct. 1, 2012 if one assumes the law of conservation of mass/energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent will eventually have to exceed its expansive energy because as mentioned earlier kinetic energy also possess gravitational potential therefore as the universe cools there be an ever increasing force opposing its accelerated expansion. Therefore the increasing gravitational potential due to the cooling of the universe will slow the rate of the acceleration and eventually allow gravity to take over and cause the universe to enter a contractive phase.  There can be no other conclusion if one accepts the validity of the laws of thermodynamics and Einstein General Theory of Relativity.)

The rate of contraction will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of that contraction.

At some point in time the total kinetic energy of the universe would be equal to the total mass equivalent of that energy or E=mc^2.  From this point on the velocity of the contraction will slow due to the radiation pressure generated by the heat of its contraction and be maintained by the momentum associated with the remaining mass component of the universe.

However after a certain point in time the heat and radiation pressure generated by it collapse will become great enough to fully ionize its mass component and to cause it to reexpand.

Yet at some point in future the contraction phase will begin again because as mentioned earlier its kinetic energy can never exceed the gravitational energy associated with its mass/energy equivalent.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates that in a closed system energy/mass cannot be created or destroyed.

This results in the universe experiencing in a never-ending cycle of expansions and contractions.

Many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore it could not re-expand.

However, according to the first law of thermodynamics the universe would have to begin expanding before it reached a singularity because that law states that energy/mass in an isolated system can neither be created nor destroyed

Therefore, because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it.  This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase.  This will result the energy/mass of the universe will oscillate around a point in space because its momentum will carry it beyond the equilibrium point were the radiation pressure was equal to its gravitational contractive component. 

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it. 

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of the universe is defined by the mass and the momentum of its components.  Therefore, when one decreases the other must increase which means the universe must oscillate around a fixed point in four-dimensional space.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space.  Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

In other words if this theatrical model is correct our universe will osculate between a very dense hot dense environment and a cold dark one. 

However the mechanism outlined above provides a negative feedback loop in terms of universe's total mass because if it is to great the speed of its collapse will be faster due to its greater gravitational potential thereby causing the next cycle to begin at a higher temperature.  This will result in a faster expansion rate and therefore less time for mass to clump together to form stars and galaxies. While if its mass component is too small it would expand to a larger volume resulting a slower contraction resulting in the next cycle beginning at a lower temperature which means its expansion will be slower allowing for the creation of more mass.

This would result in the universe's  fundamental constants that have a positive effect on the creation of mass to have a very specific values. This is because if they caused to much mass to form the feedback loop describe above would result in a new value that would reduce the total amount of mass created in the next cycle.  Therefore after a few cycles they would approach an optimal value that is solely dependent on the ratio on the expansive and gravitational properties of the universe.

In other words after the laws that govern the expansion and contraction of our universe were established God may not have had a choice whether or not to create it with the fundamental constants required to sustain life because as was just shown their values would depend on those laws.

It should be noted that this conclusion is based solely on observing of how matter and energy interact and the laws of causality associated with the environment they are currently occupying

200
 The geometry of quantum probabilities
 Nov. 15, 2014.htm

There can be no doubt the probabilistic interpretation of Schrödinger's wave equation predicts with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it.

However this interpretation is at odds with the reality of the classical or deterministic world most of us appear to live in because it assumes that for a given set of initial conditions there can only be one outcome while the probabilistic interpretations of quantum mechanics assumes there can be an infinite number.

However many of the standard interpretations of quantum mechanics assume that probability is the fundamental property of the universe, while alternative interpretations explain it as an emergent or a second-order consequence of various limitations of the observer or the environment he or she is occupying when making an observation.

Determining which is the correct way of interpreting it is difficult because due to the limitation imposed on observers by uncertainty principle we can never be sure what is happening on the quantum scale when an observation is made.

Yet that does not mean that we cannot extrapolate what we can learn from observing our four dimensional space-time environment to the quantum world to help us understand what happens when we make an observation.

However we will find it beneficial to redefine Einstein space-time model of the universe into its equivalent in four spatial dimensions.

(The reason for this will become obvious later on)

Einstein gave us the ability to do this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 and used the constant velocity of light to define it because it provided a method of converting a unit of space-time he associated with energy to unit of space we feel he would have associated with mass.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

As mentioned earlier Quantum mechanics assumes one can only determine the future evolution of a particle in terms of the probabilistic values associated with its wave function which is in stark contrast to the Classical "Newtonian" assumption that one can assign precise values of future events based on the knowledge of their past. 

In other words in a quantum system Schrödinger's wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution.

This accentuates the fundamental difference between quantum and classical mechanics because the latter defines the reality of future events in terms of pervious events whereas quantum mechanics defines them based on the "non-classical" reality of the sum total of all possible events that can occur.  

However as mentioned earlier one may be able to understand the physical reason why these two theories define the reality of events differently if, as was done earlier one redefine Einstein's space-time concepts in terms of four spatial dimensions.

In the article #14 “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can understand the physicality of quantum properties energy/mass by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to  a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established space.

Therefore, these oscillations in a "surface" of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or "structure" in four-dimensional space if one extrapolated them to that environment. 

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with it fundamental or a harmonic of its fundamental frequency.

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.

(In the article #55 "The geometry of quarks" Mar. 15, 2009  the internal structure of quarks, a fundament component of particles was derived in terms of a resonant interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions.)

However, if a quantum mechanical properties of particle is a result of a matter wave on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension, as this suggests one should be able to show that it is responsible for the uncertainties and probabilistic predictions made by Schrödinger and his wave equation regarding the position and momentum of particles.

Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle could be only be defined at the “peaks” and “valleys” of the matter wave responsible for its resonant structure because those points are the only place where its energy or “position” is stationary with respect to a fourth *spatial* dimension.  Whereas it's precise momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360-degree points of that wave.  All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or “drain” all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum left to be observed by another instrument.  Therefore, if one was able to precisely determine position of a particle he could not determine anything about its momentum.  Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position energy left to for an instrument which was attempting to measure its position.  Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended wave is because, as mentioned earlier the

#14 “Why is energy/mass quantized?“ showed energy must be packaged in terms of its discrete resonant properties.  Therefore, when we observe or “drain” the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point” source with respect the extended volume of water in the sink.

As mentioned earlier, all points in-between are a dynamic combination of both position and momentum.  Therefore, the degree of accuracy one chooses to measure one will affect the other. 

For example, if one wants to measure the position of a particle to within a certain predefined distance “m” its wave energy or momentum will have to pass through that opening.  However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area thereby making its momentum harder to determine.  Summarily, to measure its momentum “m”kg / s one must observe a portion the wavelength associated with its momentum.  However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum.  But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.

However, this dynamic interaction between the position and momentum component of the matter wave would be responsible for the uncertainty Heisenberg associated with their measurement because it shows the measurement of one would affect the other by the product of those factors or m^2 kg / s.

Yet because of the time varying nature of a matter wave one could only define its specific position or momentum of a particle based on the amplitude or more precisely the square of the amplitude of its matter wave component.

This defines the physical reason in terms of four *spatial* dimensions for why we are unable to measure the exact position and moment of a quantum system.

However it also defines the reason why the probably functions of quantum mechanics are an emergent or a second-order consequence of various limitations of the observer or the environment and not a fundamental property of our universe because as was just shown the physicality of four *spatial* dimension places limitations on our ability to define the initial conditions or momentum and position of a quantum system we are measuring. 

In other words the reason quantum mechanics can only predict the probability of an event occurring is because of the limitations the physical properties of four *spatial* dimension places on an observer.

This shows why we should view the probabilistic properties of quantum mechanics as an emergent or a second-order consequence of the limitations of the four *spatial dimension or space-time environment he or she is occupying when making an observation and not a fundamental property of the universe.

199
In the beginning
Nov. 1, 201`4

One of the most fundamental questions science can ask is "How did our unversed begin?"

For example The Big Bang theory, the prevailing cosmological model for the early development of the Universe assumes that in the beginning it was in an extremely hot and dense state which began expanding and after cooling sufficiently, energy was converted into subatomic particles, including protons, neutrons, and electrons.

It offers a one of the most comprehensive explanations we have for most observed phenomena, including the abundance of light elements, the cosmic microwave background, large scale structure, and the Hubble expansion with two notable exceptions which have been given the name the Flatness and Horizon problem.

The first or the Flatness problem addresses the apparent fine-tuning of the density of matter and energy in the universe. The problem is that the current density of the universe is observed to be very close to the critical value required to make it flat.  Since the total density departs rapidly from this critical value over cosmic time, the early universe must have had a density even closer to the critical density, departing from it by one part in 1062 or less.  This leads cosmologists to question how the initial density came to be so closely fine-tuned to this "special" value

The other or the Horizon problem is address the fact that different regions of the universe which have not been able to interact with each other have the same temperature and other physical properties. 

To resolve these issues physicist Alan Guth proposed the universe underwent a very rapid period of expansion (called inflation) increasing its size by more than a trillion in the first few nano-seconds after its birth.  This resolves the Flatness problem because its size is magnified so much by the inflation factor that locally it appears flat.

The reason for this can be understood by imagining what a two-dimensional creature who was living on a surface of a balloon would observe regarding the curvature of its surface.  If the size of the balloon were small compared to his field of vision he would notice that it surface was curved while if its size was very large, again compared to his field of vision it would appear to her or him to be flat. 

Similarly if the universe underwent a very rapid exponential expansion early in its history it would have become so large that it would appear to be flat with respect to our field of vision. 

However adding an inflationary period to the big bang models also solves the Horizon problem because prior to the inflationary period the entire universe would have been extremely small and therefore each point could be causally connected.  It was during this period, according to its proponents the physical properties of the universe evened out.  Inflation then caused its volume to increase to the point where different parts were too far apart to allow their properties to interact.  This essentially froze any irregularities and prevented them from being “smoothed out” which according to this theoretical model explains why the universe appears to be almost, but not perfectly homogeneous.  In other words they assume the solution to the Horizon problem is the fact that in the modern era distant areas in the sky which appear to be unconnected causally were in the past because they were much closer together.

However the science of physics is devoted to answering questions regarding the outcome of experiments based on observing the environment in which they occur.  Unfortunately we cannot nor will we ever able to directly observe the origins of our universe.

Even so most scientists would agree that a valid theoretical model of the beginnings of our universe must consist of two parts.  The first part must allow one to accurately predict its properties based on the outcome of experiments or observations that we can perform in today's environment while the second is to provide a logically consistent explanation for their origins in terms of the currently accepted laws of physics that govern that environment.

However the inflationary model fails to satisfy that requirement because it cannot logically explain where the energy to power the inflationary period originated from in terms of any observable processes even though some cleaver physicists have convinced themselves that they have in terms of a mathematical model which says it originated in what is call vacuum energy.  Unfortunately there is very little or no observational evidence to support its existence. 

Yet what is even more damaging to the inflationary model is that it is possible to develop a theoretical model of our beginnings using only our ability to observe our present environment and the laws that govern it if one views it in terms of four *spatial* dimensions instead of four dimensional space time.

(The reason will become obvious latter.)

Einstein provided a way of doing this when he defined the geometric properties of space-time in terms energy/mass, the constant velocity of light and equation E=mc^2 because that  provided a method of converting a unit of space-time he associated with energy to unit of space we think he would have associated with mass.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between the time related properties of a space-time universe with the spatial properties of one made up of four *spatial* dimensions.

In other words it allow one to define energy/mass in terms of a curvature or displacement  in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension as well as a curvature in a space-time manifold.

However the fact that one can use Einstein's equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This differs from Einstein's theory in that it defines only gravitational energy in terms of a displacement in a surface of a space-time manifold while using the above concepts one can define both it and kinetic energy in terms of oppositely directed displacements in a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension. 

Yet having the ability to define both gravity and kinetic energy in terms of a common geometry can add significantly to our understanding of the shape of our universe because its geometry is related to the ratio of total gravitational potential of its energy/mass to the total kinetic energy associated with its expansion.  This would allow one to theoretically derive the energy density of the universe's kinetic energy in terms of an oppositely directed displacement in a "surface" of a three-dimensional space manifold with respect to the energy density of its matter component.  This means that the "flatness" of our universe would be an intrinsic property of its existence and would not require the fine-tuning of any of its components to explain it.

This is because the universe, by definition is a closed system the law of conservation of energy/mass tells us there must a dynamic balance between the curvature created by the gravitational potential of the its energy/mass and the oppositely directed kinetic energy associated with its expansion.

However, as was shown in the article #23 “Defining energy?” Nov 27, 2007" this means the "downward" directed displacement in a "surface" of three-dimension space with respect to a fourth "spatial* dimension it associates with the total gravitational potential of the universe would be offset by the "upwardly" directed one associated with its Kinetic energy.

For example observations of the three-dimension environment occupied by a piece of paper shows us that if one crumples a piece that was original flat and views its entire surface the overall magnitude of the displacement caused by that crumpling would be zero because the height of it above its surface would be offset by an oppositely directed one below its surface.  Therefore, if one views its overall surface only with respect to its height, its curvature would appear to be flat.  In other words flatness is an intrinsic property of a piece of paper that has been crumpled.

Similarly, if the energy density associated with the momentum of the universe's expansion is a result of oppositely directed displacements in a "surface" of a three-dimensional space manifold with respect to that associated with its matter component their overall density would appear to be flat because, similar to a crumpled piece of paper the "depth" of the displacement below its "surface" caused by matter would offset by the "height" of the displacement above it caused by its Kinetic energy.

However this would be true only if only if the matter and energy in our universe was "flat" or equally disturbed in the beginning.

Many proponents of the Big Bang Model assume it began from the expansion of mass and energy around a one-dimensional point.  However, if we are correct in assuming that density of the mass and energy components of our universe are a result of oppositely directed curvatures in a "surface" of a three-dimensional space manifold, the universe must have been "flat" with respect to their density at the time of the Big Bang.  This is because a one-dimensional point would have no "vertical" component with respect to a fourth *spatial* dimension and therefore the "surface" of three-dimensional space originating from it would be "flat" with respect to that dimension.

However, if the universe was flat with respect to the density of its energy/mass in the beginning it would remain flat throughout its entire expansive history because as was shown above its expansion would result in a proportional reduction in the displacements above and below its three-dimensional "surface" as it expanded.

This unlike, Alan Guth's inflationary model, which does not have any observational support provides a logically consistent and verifiably explanation of why our universe appears flat and remains flat throughout its evolution in terms of its observable properties and the currently accepted laws of physics that govern that it.

The other reason physicists have for proposing the inflationary model was to solve the other inconsistency with the big bang theory or the Horizon problem which is related to the fact that different regions of the universe which have not been able to interact with each other have the same temperature and other physical properties.  This should not be possible, given that the transfer of information (or energy, heat, etc.) can occur, at most, at the speed of light.

As mentioned earlier Alan Guth Inflationary model also solves the Horizon problem because it assumes that the early universe was extremely small and therefore each point was causally connected Unfortunate as mentioned earlier there is not observational evidence to support this hypothesis.

However similar to the solution of the Flatness problem, defined earlier it is possible to develop a theoretical model of our beginnings that solves the Horizon problem in a manner that is consistent with observable properties of our universe if one views it in terms of four *spatial* dimensions instead of four dimensional space time.

We know from observations the equation E=mc^2 defines the equivalence between mass and energy in an environment and since mass is associated with the attractive properties of gravity it also tells us, because of this equivalence, the kinetic energy associated with the universe's expansion also possess those attractive properties.  However the law of conservation of energy/mass tells us that in a closed system the creation of kinetic energy cannot exceed the gravitational energy associated with the total energy/mass in the universe and that a reduction in one must be compensated for by an increase in the other.

This means the total gravitation potential of the universe must increase as it expands and cools approaching a maximum value at absolute "0" while at the same time the kinetic energy of its expansive components must decrease.  Therefore, at some point in time, the universe it will enter a contractive phase because the total gravitational potential must eventually exceed the kinetic energy of its expansion.  This is would be true even though the gravitational potential of its Kinetic energy components would be disturbed or "diluted" by a factor of c^2.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate. Therefore they believe that its expansion will continue forever.  However, as was shown in the article #148 “Dark Energy and the evolution of the universe” Oct. 1, 2012 if one assumes the law of conservation of mass/energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent will eventually have to exceed its expansive energy because as mentioned earlier kinetic energy also possess gravitational potential therefore there will be constant force opposing this accelerated expansion. Therefore the gravitational potential of Dark Energy must slow the rate of the acceleration and eventually allow gravity to take over and cause the universe to enter a contractive phase.  There can be no other conclusion if one accepts the validity of the laws of thermodynamics and Einstein General Theory of Relativity.)

The rate of contraction will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of that contraction.

At some point in time the total kinetic energy of the universe would be equal to the total mass equivalent of that energy or E=mc^2.  From this point on the velocity of the contraction will slow due to the radiation pressure generated by the heat of its contraction and be maintained by the momentum associated with the remaining mass component of the universe.

However after a certain point in time the radiation pressure generated by it will become great enough to fully ionize its mass component and to cause it to reexpand.

Yet at some point in future the contraction phase will begin again because as mentioned earlier its kinetic energy can never exceed the gravitational energy associated with its mass/energy equivalent.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates that in a closed system energy/mass cannot be created or destroyed.

This results in the universe experiencing in a never-ending cycle of expansions and contractions.

This would solve the Horizon problem because the repeated cycles would allow different regions of the universe to mix and equalize thereby explaining why their temperature and other physical properties are almost identical.

This would be analogous to mixing the content of two cans of paint by pouring one into the other.  The evenness of the mixture would increase in proportion to the number of times one pored one can into the other.

Similarly the evenness of the temperature distribution and physical properties of the universe would increase in proportion to the number of cycles it had gone through.

However it also explains why there are small temperature and other physical irregularities in the large-scale structure of the universe.

For example one cannot completely mix two different colors of paint no matter how many times they pour one can into another because the random motion of the different colored paint molecules means that some regions will have more of one color than the other.

Similarly the random condensation of baryonic matter in the universe during its expansive phase means that some regions will have more matter or be denser that others no matter how many cycles of expansion or contraction it has undergone.

This explains why the large-scale structures such as galactic clusters exist.

Many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy/mass in an isolated system can neither be created nor destroyed

Therefore, because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it.  This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase.  This will result the energy/mass of the universe will oscillate around a point in space because its momentum will carry it beyond the equilibrium point were the radiation pressure was equal to its gravitational contractive component. 

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it. 

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of the universe is defined by the mass and the momentum of its components.  Therefore, when one decreases the other must increase which means the universe must oscillate around a fixed point in four-dimensional space.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space.  Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

However this theoretical model provides, unlike the inflation model a logically consistent explanation based on the currently accepted laws of physics where the energy to power the current expansion of our universe came from because, as was shown above one can use the conservation laws to show that the kinetic energy of its expansion originated in the Gravitational energy of its mass.

One could verify this scenario by observing our current universe and using Einstein General Theory of Relativity and the law of conservation of energy/mass to calculate the how long it would take for the radiation pressure generated by its gravitational collapse to become large enough to cause it to expand and determine if it would allow enough time for different regions to be causally connected to the point where it could explain Horizon Problem and why there are small variations homogeneous structure.  Additionally one could determine if the heat generated by that collapse would be great enough to ionize its mass component enough to explain the properties of the cosmic background radiation.

It should be noted that this derivation of the universe's origin, its geometry and matter distribution does provide an observational method for verification or falsification because it relies exclusively on the interoperation of physical observations and the accepted laws of physics, not, as is the case with the inflation model on abstract creations of human intellect.

198
A physical image of
Black Body Radiation
Oct. 15, 2014

Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

For example one can easily understand how a curvature in space-time can be the causality of gradational forces in terms of the physical image of a marble on a curved surface of a rubber diaphragm.  The marble follows a circular pattern around the deformity in the surface of the diaphragm. Similarly planets revolve around the sun because they follow a curved path in the deformed "surface" of space-time.

However the same cannot be said about black body radiation.

This is because classical physics suggests that all modes have an equal chance of being produced even when the number of modes goes up proportional to the square of the frequency.  However this classical concept works reasonably well at low frequency yet it begins to diverge at higher frequencies so much so that the energy content of black body approaches infinity.  This discrepancy between the classical description of a black body and its reality has come to be called the Ultraviolet Catastrophe.

However Einstein realized it could be explained by assuming, as Planck had done that energy is not continuous but comes in discreet packaged define by the equation E=hv.  Their observation that the energy in a black box is quantized was the basis for the development of Quantum theory.

Yet no one, up until now has been able to provide a physical image of how and why this should be so.

Up until now because in the article #13 “The Photon: a matter wave?" Oct. 1, 2007 it was shown that one can use the observed wave properties of electromagnetic radiation and Einstein Theory of Relativity to form a physical image of how energy is disturbed in a black body.

However it is easier if one converts or transposes Einstein space-time universe to one consisting of only four *spatial* dimensions.

(The reason will become obvious later.)

Einstein gave us the ability to do this when used the constant velocity of light to define the geometric properties of space-time because it provided a method of converting the space-time displacement he associated with energy in a space-time universe to a spatial one in a universe consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming, as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy including electromagnetic can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier the article “The Photon: a matter wave?" Oct. 1, 2007 shows how one can understand properties of electromagnetic energy and how it is disturbed in space and a black body in terms of a physical image based on the classical properties of wave motion if one assume that space is composed of four *spatial* dimensions instead of four dimensional space-time.

For example a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by this displacement, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the undisturbed surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

However, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become "attracted" to each other.

This would define in terms, of a physical image the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.  This is because classical mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement.

This provides a physical image that would allow on to understand the electromagnetic wave component of black body radiation 

However its quantum mechanical or particle properties can also be derived in terms of a physical image by extrapolating the laws of classical resonance to that same wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example as the article #14 “Why is energy/mass quantized?” Oct. 4 2007 showed one could derive a physical image of the particle or photonic properties electromagnetic energy by extrapolating the laws of classical wave to a fourth *spatial* dimension.

Briefly, it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four *spatial* dimensions.

The existence of four *spatial* dimensions would give space (the substance) the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space to oscillate with the frequency associated with the energy of that event.

However, these oscillations in a continuous non-quantized field of energy/mass caused by such an event would cause a resonant system or "structure" to be established in it. 

Classical mechanics tells us the energy of a resonant system can only take on the discreet quantized values associated with its resonant or a harmonic of its resonant frequency.

However, one can also use the above concepts of four *spatial* dimensions to develop a physical image of the particle or photonic properties Max Planck, as was mentioned earlier associated with black body radiation.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article #14 “Why is energy/mass quantized?

These resonant systems in a continuous non-quantized field of energy/mass are responsible for the discrete or incremental energies associated with the quantum component of black body radiation.

However, these two articles also provide a physical image of why the energy distribution in a black body is what it is in terms of the concepts of classical physics.

A black body is an idealized object that absorbs all electromagnetic radiation that falls on it.  Because no light is reflected or transmitted, the object appears black when it is cold.  However, a black body emits a temperature-dependent spectrum of light.  This thermal radiation from a black body is termed black body radiation.

At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature.  By the time an object is white, it is emitting substantial ultraviolet radiation.

The problem is, as was mentioned earlier the laws of classical mechanics, specifically the equipartition theorem, states that black-bodies which have achieved thermodynamic equilibrium are mathematically obligated (by classical, pre-quantum, laws) to radiate energy in the form of ultraviolet light, gamma rays and x-rays at a certain level, depending on the frequency of emitted light.

However, as mentioned earlier observations of black body radiation indicate that there was less and less energy given off at high end of the spectrum.

Einstein pointed out this difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck.  He had hypothesized that electromagnetic energy did not follow classical laws, but could only oscillate or be emitted only in discrete packets of energy proportional to the frequency, as given by Planck's law.  In other words, the light waves of each frequency in a black body could not have any energy but are limited to a few discrete values.

However, as mentioned earlier the article #14 “Why is energy/mass quantized?” Showed the quantity of energy of a photon at each frequency could be understood by extrapolating a physical image of a resonant system in three-dimensional space to a fourth *spatial* dimension similar to how Einstein was able to from a physical image of gravity.

For example as the above theoretical model showed using only the concepts of classical physics and Einstein's theory of  Relativity a photon could only have the discrete energies or frequencies that are a fundamental or harmonic of the energy of an environment which would be determined by the temperature of the one it was occupying. Therefore, according to the above theoretical model any frequency other than that would be irregular and non-repeating and would be absorbed into the fundamental or harmonic frequency of that environment.

In other words it explains in terms of a physical image based on our classical reality why black-bodies which have achieved thermodynamic equilibrium are mathematically obligated by (classical, pre-quantum, laws) to radiate energy in the form of ultraviolet light, gamma rays and x-rays at a certain discrete levels, depending on the frequency of emitted light.

It should be remember Einstein’s genius allows us to choose if we want to view the physical properties of electromagnetic energy and black body radiation in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the sensory as well as the non-sensory time properties of our universe thereby giving us a new perspective on the physical relationship between particles and waves.

197
The causality of
 quantum probabilities or why
God must play dice
Oct. 1, 2014

Is it possible to define the “reality” behind the quantum world of probabilities in terms of the physical concepts of causality in the space-time environment defined by Einstein? 

Quantum theory defines the existence of particles in terms of a mathematically generated probability function created by Schrödinger's wave equation and assumes that particles do not exist until a conscience observer looks at it.  In other words it assumes the act of observation or measurement creates their reality.

However because it is based on probabilities it also assumes that the predictability associated with the laws of causality that govern our macroscopic universe do not apply to a quantum world.

In other words in quantum theory, everything is unpredictable.

Einstein hated this uncertainty, famously dismissing it when he said "God does not play dice with the universe" even though he was unable to give a reason.

However he gave us a clue as to why God must play dice when he said "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless"

In other words we may be able to understand why a quantum environment lacks causality if we can transform the abstract or non-physical aspects or the probabilities associated with Schrödinger's wave equation to one that more closely resembles the physical properties of our classical world.

For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.

Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.

Granted Einstein's theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the "reality" of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.

For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional "surface" in a three dimensional environment to four dimensional space-time.  However this image only contains reference only to the sensory reality of the spatial dimensions and not a time or space-time dimension.

Yet, the fact that most humans define our physical "reality" in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of space-time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions allows one to form an image of its causality in terms of the physical properties of the spatial dimension instead of the non-physical ones most of us associate with time or a space-time dimension. 

As was mentioned earlier one of the advantage to redefining Einstein space-time concepts in terms of four *spatial* dimensions is that it not only allows one to understand gravitational energy in more direct terms but also allows on to form a physical image in terms of a classical environment for the unpredictability of the quantum world.

For example in the article #14 “Why is energy/mass quantized?” Oct 4, 2007 it was shown one can derive the quantum mechanical properties of a particle by extrapolating the laws governing resonance in a classically three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally, it was showed why all energy exists in these resonant systems and therefore must be quantized.

Briefly it was showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would also be found in one consisting of four.

The existence of four *spatial* dimensions would give three-dimensional space (the substance with a natural frequency) the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, these oscillations in a “surface” of a three-dimensional space manifold, according to classical mechanics would generate a resonant system or “structure” in space.  These resonant systems are known as particles.

(In an earlier article #55 “The geometry of quarks” Mar. 2009 it will be shown how and why they join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The energy in a classically resonating system is discontinuous and can only take on the discrete values associated with its fundamental or a harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass.  This is the basis for assuming, as was done in the article #14 “Why is energy/mass quantized?” that its quantum mechanical properties are a result of a resonant system in four *spatial* dimensions.

The reason why we do not observe energy in its extended wave form is that, as mentioned earlier all energy is propagated through space in discrete components associated with its resonant structure.  Therefore, its energy appears to originate from a specific point in space associated with where an observer samples or observes that that energy.

This is analogous to how the energy of water in a sink is release by allowing it to go down the drain.  If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain.  However, in reality the water occupies a much larger region.

However, treating the quantum mechanical properties of energy/mass in terms of a resonant system generated by a matter wave also allows one to form a physical image of its unpredictability by extrapolating the laws of our classical three-dimensional world to a fourth *spatial* dimension.

Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle quantum mechanics associates Schrödinger's wave equation with could be only be defined in terms of the peaks and valleys of the matter wave responsible for its resonant structure because those points are the only places where its energy or “position” is stationary with respect to a fourth *spatial* dimension.  Whereas it's precise momentum would only be definable with respect to where its energy change or velocity is maximum at the 180 and 360-degree points of that wave.  All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or “drain” all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum to be observed by another instrument.  Therefore, if one was able to determine precise position of a particle he or she could not determine anything about its momentum.  Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position information left to for an instrument which was attempting to measure it.  Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended object is because, as mentioned earlier the article #14 “Why is energy/mass quantized?” showed its energy/mass must be packaged in terms of a resonant system.  Therefore, when we observe or “drain” the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point” source with respect the extended volume of water in the sink.

However, this allows one to form a physical image of the unpredictability of a quantum environment because it give us a Classical reason why we cannot precisely measure the both the momentum or position of a quantum object because the measurement of one effects the measurement of the other. 

For example, if one wants to measure the position of a particle to within a certain predefined distance “m” its wave energy or momentum will have to pass through that opening.  However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area.  Similarly, to measure its momentum one must observe a portion the wavelength associated with its momentum.  However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum.  But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.

However, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article  #14 “Why is energy/mass quantized?” the change or uncertainty of one with respect to the other would be defined by the product of those factors.

Another way of looking at this would be to allow a particle to pass through a slit and observe where it struck a screen on the other side.  One could get a more precise measurement of its position by narrowing the slit however classical wave mechanics tell us this will increase the interference of the wave properties associated with its resonant structure.  However this will cause the interference pattern defining its momentum to become more spread out and therefore make it more difficult to accurately determine its value.

Therefore, Classical wave mechanics, when extrapolated to Schrödinger's wave equation in an environment consisting a fourth *spatial* dimension tells us the more precisely the momentum of a particle is known, the less precisely its position can be known while the more precisely its position is known, the less precisely its momentum can be determined.  In other words it tells us in terms of a physical image based on a classical environment the reason why God must play dice is because the physicality of a quantum environment prevents us from precisely determining the initial condition of a particle through observation.

196
The structure of “OUR reality”
Sept.1, 2014

Truth can only be found through the window of observation while "OUR reality" is determined by what we see in that window.

But some say what we see in it does not define "THE reality" because of the limitation of our senses.  For example humans can only see a very small portion of the electromagnetic spectrum therefore; because of those limitations they say that our senses should not be the only arbiters of "THE reality".

In other words because our instruments tell us that reality extends far, far beyond what our senses see, many feel the only way to find it is through the window they provide instead the one provided by our senses.

However, our impression of "THE reality" is made up of a combination of what our senses see around us and what our instruments tell us about that world.

In other words each is an integral part of how we and science views "THE reality" and therefore the different realities they show us cannot be treated as separate.

For example the instruments we use to observe it tell us that a fundament component of a quantum environment is that all objects exist simultaneously as both particles and waves.

However, our senses tell us objects cannot be both a particle and wave at the same time.

But how can we merge or integrate these two realities and determine their fundamental component when what our instruments "tell" us about our world appears to conflict with what our senses see in it.

Einstein gave us a clue when he said "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

Yet how can we form a physical image of the quantum world when its fundamental component, the wave particle duality of objects is contradictory to the physicality of our sensory environment.

We can start by reexamining how we define our sensory environment.

For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.

Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.

Granted Einstein's theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the "reality" of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.

For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional "surface" in a three dimensional environment to four dimensional space-time.  However this image only contains reference only to our sensory reality of the spatial dimensions and not a time or space-time dimension.

However, the fact that most humans define our physical "reality" in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.

On pages 17 thru 23 of Richard P Feynman book "QED The Strange Theory of Light and Matter" he address the conflict between our sensory world and the particle wave reality of a quantum environment by describing what happens when light when it is partially reflected by two surfaces,

On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

The fact that the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass indicates that their energy is not transmitted by a wave but by a particle.

This shows that in a quantum environment a photon can either be a particle or a wave. However, our senses tell us objects such as photons cannot be both a particle and wave at the same time.

Yet as mentioned earlier we may be able to merge or integrate these two realities and determine the fundamental component of "THE reality"  by viewing them, as mentioned earlier in terms four *spatial* dimension instead of four dimensions space-time.

For example in the article #14 “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of objects and a photon by extrapolating the physical image of a wave in a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it showed that all energy must be propagated in these resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore if one extrapolates the physical image of a wave in a three dimensional environment to a fourth *spatial* dimension one could understand how these oscillations in a "surface" of a three-dimensional space manifold would generate the wave properties of objects in a quantum environment.

However we know from observations that tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency. Similarly the incremental or discrete energies associated with individual photons in Richard Feynman's experiment could be understood in terms of the physical image of the resonate properties of wave in four *spatial* dimensions. However, one can also describe the physical boundaries of a particle in terms of the wave properties of its resonant structure.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article #14 “Why is energy/mass quantized?"

This would allow one to merge or integrate the wave particle duality of a quantum environment into our sensory world by extrapolating, as was show earlier the physical image of wave moving on water to a matter wave moving on the "surface" of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was also show earlier they are equivalent.  

For example, the wave like interference of photons Richard Feynman's experiment observed in his experiment would be due to the wave properties of the resonant "system" defined in the article #14 “Why is energy/mass quantized?".

If the distance between the two glass surfaces was equal to half of the wavelength of the resonant "system" associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.

 If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.

However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article #14 “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy must be propagated through space in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying.

Yet this also defines reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because in our sensory environment when two waves in phase interact they will reinforce each other.  Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.

This demonstrates how one can project the "structure" of "OUR reality" beyond our sensory environment to explain and understand the quantum world.   It also demonstrates why forming a physical image of a process is so valuable to science because it shows that one can integrate or merge the reality shown to us by our instruments into our sensory reality in terms of "THE reality" of four *spatial* dimension or four dimensional space-time.

It should be remember Einstein’s genius allows us to choose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the sensory as well as the non-sensory time properties of our universe thereby giving us a new perspective on the physical relationship between particles and waves

195
The structure of our reality
Sept. 1, 2014

Truth can only be found through the window of observation while "OUR reality" is determined by what we see in that window.

But some say what we see in it does not define "THE reality" because of the limitation of our senses.  For example humans can only see a very small portion of the electromagnetic spectrum therefore; because of those limitations they say that our senses should not be the only arbiters of "THE reality".

In other words because our instruments tell us that reality extends far, far beyond what our senses see, many feel the only way to find it is through the window they provide instead the one provided by our senses.

However, our impression of "THE reality" is made up of a combination of what our senses see around us and what our instruments tell us about that world.

In other words each is an integral part of how we and science views "THE reality" and therefore the different realities they show us cannot be treated as separate.

For example the instruments we use to observe it tell us that a fundament component of a quantum environment is that all objects exist simultaneously as both particles and waves.

However, our senses tell us objects cannot be both a particle and wave at the same time.

But how can we merge or integrate these two realities and determine their fundamental component when what our instruments "tell" us about our world appears to conflict with what our senses see in it.

Einstein gave us a clue when he said "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

Yet how can we form a physical image of the quantum world when its fundamental component, the wave particle duality of objects is contradictory to the physicality of our sensory environment.

We can start by reexamining how we define our sensory environment.

For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.

Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.

Granted Einstein's theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the "reality" of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.

For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional "surface" in a three dimensional environment to four dimensional space-time.  However this image only contains reference only to our sensory reality of the spatial dimensions and not a time or space-time dimension.

However, the fact that most humans define our physical "reality" in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.

On pages 17 thru 23 of Richard P Feynman book "QED The Strange Theory of Light and Matter" he address the conflict between our sensory world and the particle wave reality of a quantum environment by describing what happens when light when it is partially reflected by two surfaces,

On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

The fact that the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass indicates that their energy is not transmitted by a wave but by a particle.

This shows that in a quantum environment a photon can either be a particle or a wave. However, our senses tell us objects such as photons cannot be both a particle and wave at the same time.

Yet as mentioned earlier we may be able to merge or integrate these two realities and determine the fundamental component of "THE reality"  by viewing them, as mentioned earlier in terms four *spatial* dimension instead of four dimensions space-time.

For example in the article #14 “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of objects and a photon by extrapolating the physical image of a wave in a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it showed that all energy must be propagated in these resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore if one extrapolates the physical image of a wave in a three dimensional environment to a fourth *spatial* dimension one could understand how these oscillations in a "surface" of a three-dimensional space manifold would generate the wave properties of objects in a quantum environment.

However we know from observations that tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency. Similarly the incremental or discrete energies associated with individual photons in Richard Feynman's experiment could be understood in terms of the physical image of the resonate properties of wave in four *spatial* dimensions. However, one can also describe the physical boundaries of a particle in terms of the wave properties of its resonant structure.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article #14 “Why is energy/mass quantized?"

This would allow one to merge or integrate the wave particle duality of a quantum environment into our sensory world by extrapolating, as was show earlier the physical image of wave moving on water to a matter wave moving on the "surface" of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was also show earlier they are equivalent.  

For example, the wave like interference of photons Richard Feynman's experiment observed in his experiment would be due to the wave properties of the resonant "system" defined in the article #14 “Why is energy/mass quantized?".

If the distance between the two glass surfaces was equal to half of the wavelength of the resonant "system" associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.

 If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.

However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article #14 “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy must be propagated through space in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying. 

Yet this also defines reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because in our sensory environment when two waves in phase interact they will reinforce each other.  Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.

This demonstrates how one can project the "structure" of "OUR reality" beyond our sensory environment to explain and understand the quantum world.   It also demonstrates why forming a physical image of a process is so valuable to science because it shows that one can integrate or merge the reality shown to us by our instruments into our sensory reality in terms of "THE reality" of four *spatial* dimension or four dimensional space-time.

It should be remember Einstein’s genius allows us to choose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the sensory as well as the non sensory time properties of our universe thereby giving us a new perspective on the physical relationship between particles and waves.

194
Fire or ice how will
 our universe end?
Aug 15, 2014

Before the discovery of Dark Energy cosmologists had two models of how the universe's expansion would end.

In first scenario, there would be enough matter in the universe to slow the expansion to the point it would come to a halt and gravitational forces would cause it to begin contracting which eventually would result in a fiery death called the "Big Crunch.

In the other scenario, there would be too little matter to stop the expansion and everything would drift on forever, always slowing but never stopping. This would end in a vast, dark, and cold state: a "Big Chill," as the stars faded and died out.

However the discovery of a force causing the expansion of the universe to accelerate called Dark Energy opened up the possibility that the galaxies, solar system, stars, planets, and even molecules and atoms could be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.

Most scientists would agree that the best way of determining which one these scenarios defines its ultimate fate would be to understand the forces involved based on the most successful theories we have regarding the macroscopic properties of the universe.

However modern theories only address two of them.  For example the laws of thermodynamics which defines the forces associated with heat early in the universe and Einstein General Theory of Relativity which defines the gravitational forces which affect its evolution are two of the most success theories we have.  Unfortunately neither of them, in their present form addresses the expansive force called Dark Energy.

This is true even though Einstein foresaw the existence of Dark Energy when he added a cosmological constant to his General Theory of Relativity to make it conform to his belief in a static universe. 

Granted he added it in an "adhoc" manner to force it, in keeping with physicists thinking at the time to predict a stationary universe.  However when it became clear that the universe wasn't static, but was expanding Einstein abandoned the constant, calling it the '"biggest blunder" of his life.

But lately scientists have revived Einstein's cosmological constant (denoted by the Greek capital letter lambda) to explain this mysterious force which as mentioned earlier is causing the expansion of our universe to accelerate even though they have been unable to Einstein integrate it into the theoretical structure of his General Theory of Relativity.

However we may find clue as to why by observing how our universe is expanding.

For example observations of the universe's expansion tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the how the expansive force called dark energy is accelerating the spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 and the constant velocity of light because that provided a method of converting the displacement in space-time manifold he associated with energy to its equivalent displacement in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space time manifold.

As mentioned earlier one reason why it is difficult to integrate the accelerated special expansion of three-dimensional space towards a higher space dimension into Einstein space-time universe because it does not define one. 

However it is easy to do if one redefined it, as was done above in terms of four *spatial* dimension because that higher spatial dimension would become an integral part of its theoretical structure.

Yet it also allows one to understand how and why Dark Energy is causing the accelerated spatial expansion of the universe and what its ultimate fate will be in terms the laws of thermodynamics and the concepts of Einstein's theories.

We know from the study of thermodynamics that energy flows from areas of high density to one of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the molecules on the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Additionally we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool the particles that occupy that elevated region of three-dimensional space and the space they occupy will accelerate and flow or expand outward in the four dimensional environment surrounding it and that the force associated with that expansion will decline as it expands.

This shows how reformulating Einstein's theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of those theories.

Many feel that because space is everywhere, the force called Dark Energy is everywhere, and its effects increase as space expands. In contrast, gravity's force is stronger when things are close together and weaker when they are far apart.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because similar to the water in a collapsed pool the accelerative forces associated with it will decline as it expands. Yet because the mass of the universe remains constant throughout its history the gravitational potential associated with it will also. 

Therefore the gravitational contractive forces associated with it will exceed the expansive forces associated with Dark Energy even though its components may be separated by extremely large distances because as just mentioned the force associated with dark energy will decease relative to gravity as time goes by.

However the equivalence between mass and energy defined by Einstein tells us that energy also possesses gravitational potential.

Therefore, just after the big bang when the concentration of energy and mass was high, gravitational force would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands the gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe. 

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.

This means that eventually gravitational forces will overcome those of Dark energy because, as mentioned earlier the laws of thermodynamics tells us the total accelerative forces associated with it will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

However this is not the end of the story for our universe because after a certain point in time the heat generated by its gravitational collapse will raise its temperature to the point where its expansive properties will exceed gravitational forces causing it to reexpand.

Yet many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed

Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it. This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and therefore it would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass. This will cause the mass/energy of our three-dimensional universe to oscillate around a point in the fourth *spatial* dimension.

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space. Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

In other words if this theoretical model is correct our universe has never ending future which exists between an icy death caused by Dark Energy and a fiery rebirth created by gravity.

There can be no other conclusion if one accepts the validity of Einstein's theories and the laws of thermodynamics because the theoretical arguments presented are a base solely on their validity.

193
The new direction provided
by the Higgs boson
Aug 1, 2014

The Higgs Boson which was tentatively confirmed to exist on 14 March 2013 appears to confirm the existence of the Higgs field.  Its discovery is pivotal to the Standard Model and other theories within particle physics because it explains, in terms of an asymmetry created by it why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless.  Many feel this discovery will allow physicists to finally validate the last untested area of the Standard Model's approach to fundamental particles and forces, guide other theories and discoveries in particle physics, and potentially lead to developments in New Physics.

However it may also provide a way of integrating gravity into the Standard Model because it would allow one to physically connect its particle concept of mass associated with the Higgs field to the field properties Einstein associated with gravity. 

This is true because even though Einstein was only able tell us how mass interacts with the field properties of space-time not what it was.

As Steven Weinberg said "Mass tells space-time how to curve while space-time tells mass how to move".

In other words Einstein was only able to explain how the field properties of space interact to create gravity while the Standard Model defines how the asymmetry of those fields gives particles their mass.

However this suggests that one may be able to integrate Einstein's concept of gravity into the Standard Model if one can define a common physical mechanism responsible for how particles break the symmetry of space-time to create mass while at the same time explaining how and why its field properties interact to create gravity.

Einstein gave us a method for accomplishing this when he said "If a new theory (such as that associated with the Higgs boson) was not based on a physical image simple enough for a child to understand, it was probably worthless."

For example Newton was troubled by the fact that that his gravitational theory meant ." that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

However Einstein realized that one can understand how gravity "may act upon another at a distance through a vacuum" by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension environment.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why "one body may act upon another at a distance" by physically connecting it to the reality of what we can see and touch.

However, as mentioned earlier he was unable to tell us what mass is, he was only able tell us how mass interacts with space-time.

Similarly the Standard Model is able to define mass in terms of the symmetry breaking properties of the Higgs field however it is unable to define in terms of a physical image of how it interacts with the field properties of space-time to create gravity or the forces associated with mass.

This fact is difficult to understand because the Standard model is based on a Relativistic Quantum Field theory which has its foundation in Einstein's Theories.  Therefore one would think that it would be easy to integrate it into them.

However Einstein's and modern scientist's inability to connect the Standard Models explanation for mass to Einstein's explanation of gravity can be traced to the fact that they chose to define the universe in terms of energy instead of mass.

Einstein told us that a curvature in the filed properties of space-time is responsible for gravitational energy and because of the equivalence between energy and mass defined by his equation E=mc^2 one must also assume that it is responsible for mass.

This suggest that one may be able to incorporate Einstein's explanation of the gravity into the Standard Model if one converts or transposes the his space-time universe which defines field properties of energy in terms of geometry of space-time to one that defines mass of in terms of its field properties.

Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass and energy because that provided a method of converting the space-time displacement he associated with energy in a space-time universe to one we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also allows us to defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to both qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of its spatial properties in four *spatial* dimensions is the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy/mass, including that associated with the Higgs field can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which the Higgs Field or the field properties of four *spatial* dimensions interacts with particles to create mass and why they are quantized in terms of a physical image formed in our three-dimensional environment.

For example one can form a physical image of why mass is quantized, as was done in the article #14 “Why is energy/mass quantized?” Oct. 4, 2007" by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions.

This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move on a curved surface of three-dimension space to one consisting of four dimensional space-time.

(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).

Briefly that article showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension at a frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Physical observations of our three dimensional environment tell us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

However one can also understand in terms of a "physical image" of the boundaries of the point particles of the Standard Model using the above concepts.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the "box" containing the resonant system the article #14 “Why is energy/mass quantized?” associated with a particle. 

(The reasons why particles can be treated as a mathematical points in the Standard Model is because according to the above theoretical model the components of their energy/mass and forces associated with them would be evenly distributed around a point located at it center.)

This suggest the symmetry breaking properties the standard model associate with the Higgs field may be related to the geometric properties of four *spatial* dimensions.

If true one should be able to use those field concepts to explain how it interacts with particles to give them mass and why the mass of the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below grows larger in each successive family.

Family 1

Family 2

Family 3

Particle

Mass

Particle

Mass

Particle

Mass

Electron

.00054

Muon

.11

Tau

1.9

Electron
Neutrino

< 10^-8

Muon
Neutrino

< .0003

Tau
Neutrino

< .033

Up Quark

.0047

Charm Quark

1.6

Top Quark

189

Down Quark

.0074

Strange Quark

.16

Bottom Quark

5.2

As mentioned earlier the article #14 “Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy" showed that one can derive the energy or temperature of an environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the "surface" of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article #14 “Why is energy/mass quantized?” but also on temperature or energy of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families in the Standard Model have identical properties except for their mass, which grows larger in each successive family." is because of an interaction between the resonant properties defined in the article #14 “Why is energy/mass quantized?” and the mass content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative "separation" in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "separation", with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the "separation" associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial "separation" associated with the second family.

Additionally the corresponding particle types across the three families have "identical properties" because as shown in the article # 55 "The geometry of quarks" Mar. 15, 2009 they are related to the orientation of the "W" axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the "W" axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why "The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the asymmetrical field of four *spatial* dimensions.

However it also shows how one can use the asymmetrical field properties of four *spatial* dimensions or the Higgs Field to understand the causality of the masses of the fundamental particles in the Standard model in terms of a physical image based on the "reality" of what we can see and touch in our three dimensional environment.  This is similar to how Einstein, as mentioned earlier was able to shown that a mass "may act upon another at a distance through a vacuum" by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold.

As mentioned earlier the article #14 “Why is energy/mass quantized?” showed that one can derive the total mass of all particles in terms of the sum of energy contained within a resonant system generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the energy associated with displacement in the "surface" of three-dimensional space associated the environment it is occupying.

However if one assumes, as was done above the Higgs field is created by a spatial displacement in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can also understand how its asymmetric properties interacts with particles to create their mass in terms of the physical image formed by water in a dam.

This is because the potential energy of water molecule in a dam is defined by its asymmetrical spatial separation with respect to the bottom of the dam.

Similarly, according to the above theoretical model, the potential energy or mass contained in particles would be defined by an asymmetrical displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words it gives one the ability to define the asymmetrical properties the Standard Model associates with the Higgs field in terms of a physical image of water in a dam because as mentioned earlier its potential energy is in part dependent on the height of the dam while that of a particle would be dependent on magnitude of the spatial separation or the "height" of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.

However, as was mentioned earlier Einstein also defined gravity in terms of an asymmetrical displacement or curvature or a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension or a space-time manifold.

This suggest that one may be able to unite Einstein's concept of gravity with the Standard Model if one can find a way of integrating the effects an asymmetrical curvature in "surface" of a three-dimensional manifold with respect to either space-time or a higher or fourth *spatial* dimension would have on a particle with the asymmetrical properties of the Higgs field.

It should be remember that Einstein's genius allows us to choose whether to view the reality of the Higgs Field in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

192
The new direction provided
by Dark Energy
July 15, 2014

Recently there have been many observations that are extremely difficult to integrate into the currently accepted theoretical models.

Particularly the force called Dark Energy has eluded any attempt make it a part of the "The Standard Model of Particle Physics" one of the most successful theories ever created. 

However what makes this even more troubling is that the Standard model is based on two other very successful theories, that of Einstein Special Theory of Relativity and Quantum Field Theory.

Therefore if, despite continued efforts to developed a theoretical understanding of Dark Energy in terms of these theories we still cannot succeed, should we assume that, due to how interconnected these theories are we must discard them and look in a new direction.

Not necessarily because we may be able to understand its causality in terms of our current theories if instead of trying to make Dark Energy conform to them we allow its observed properties to guide us to a more complete understanding their validly.

Most scientists would agree that the best way of determining how one should interpret a theoretical model would be to list all observations regarding the forces in its domain and try to define them in terms of the rules it lays out.

For example observations of the expansive force called Dark Energy tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three-spatial dimensions and one time dimension that Einstein's theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass and energy responsible for geometric properties of space-time because it provided a method of converting the space-time displacement he associated with energy in a space-time universe to a spatial one in a universe consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to both qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy, including that associated with the Higgs field can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier it is difficult to integrate the causality of how three-dimensional space can be expanding towards a higher *spatial" dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy if one redefines Einstein's space-time universe, as was done above in terms of four *spatial* dimensions because a higher or fourth *spatial* dimension would be an integral part of its theoretical structure.

Yet it also allows one use Einstein theories and the laws of thermodynamics to understand how and why the expansive force called Dark Energy is causing the spatial expansion of our universe because it gives one the ability to qualitatively and quantitatively define energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space-time environment.

We know from the study of thermodynamics that energy flows from areas of high to one of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the water molecules on the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However according to concepts developed in the article “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the water molecules occupying the elevated two dimensional surface of the water in the pool, the particles occupying a region of three-dimensional space that is elevated because of its 3.7 degree temperature will flow and accelerate outward in the four dimensional environment surrounding it.

This shows how reformulating Einstein's theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of the Einstein's theories.

Many feel that because space is everywhere, the force called Dark Energy is everywhere so therefore its effects will increase as space expands.  In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart. Therefore they feel the rate at which the universe expands will increase as time go by resulting in galaxies, stars, the solar system, planets, and even molecules and atoms could be shredded by the ever-faster expansion. In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because, similar to the water in a collapsed pool the accelerative forces associated with it will decline as it expands and yet because the quantity of energy/mass of the universe remains constant through its history its gravitational potential will also.

Therefore in the future the gravitational contractive forces associated with it will exceed the expansive forces associated with Dark Energy because, as mentioned earlier according to this theoretical model its accelerative forces should decrease as the universe expands. This would be true even though its components may be separated by extremely large distances because, as just mentioned if the above theoretical scenario is correct the force associated with dark energy will decease relative to gravity as time goes by.

Recent observations also suggest that early in the universe evolution the gravitational forces exceeded the expansive forces of Dark Energy.

The reason is according the above theoretical model, just after the big bang when the concentration of energy and mass was high; the gravitational forces of the universe’s energy/mass would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands its gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe.

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.

This means that eventually gravitational forces will win because, as mentioned earlier the laws of thermodynamics tells us the total accelerative forces associated with Dark Energy will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

Therefore gravity will eventually win the battle with dark Energy because as was just mentioned the forces associated with it approach zero as the expansion progress while those of gravity remain constant.

There can be no other conclusion if one accepts the validity of Einstein’s theories and the laws of thermodynamics because the theoretical arguments presented are a base solely on their validity.

This shows how one can fully integrate the observed properties of Dark Energy into Einstein Special Theory of Relativity while at the same time demonstrating the advantages of allowing observations guide our understanding of our theoretical model instead of forcing them to be subservient to our preconceive theoretical ideas.

However this may also allow gravity to be integrated into the Standard Model if one can reformulate its space-time equations to their equivalent in four *spatial* dimensions as was shown above to be possible.

It should be remember that Einstein’s genius allows us to choose whether to view Dark Energy and the mathematical equations in the Standard Model in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

191
The reliability of our
 mathematical universes
 July 1, 2014

How can we be sure that the mathematical universes we create actually exist in nature?

Paul Adrien Maurice Dirac addressed this issue in a lecture he delivered on February 6, 1939 regarding "The Relation between Mathematics and Physics".

"The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed (or cannot be performed). There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success. This must be ascribed to some mathematical quality in Nature, a quality which the casual observer of Nature would not suspect, but which nevertheless plays an important role in Nature's scheme.

One might describe the mathematical quality in Nature by saying that the universe is so constituted that mathematics is a useful tool in its description. However, recent advances in physical science show that this statement of the case is too trivial. The connection between mathematics and the description of the universe goes far deeper than this, and one can get an appreciation of it only from a thorough examination of the various facts that make it up."

But exactly how deep is the connection between the mathematical reasoning we use to predict nature to its reality.  In other words how can be sure the equations we use to "infer the results of experiments that have not been performed" (or cannot be performed) actually defines the reality of the environment that encompasses them

Unfortunately we cannot because, as was just mentioned we have not or never will be able to observe them.

Therefore we must be very sure that the equations we use to predict a "quality of Nature" that is unobservable have a "factual" foundation in the theoretical models they are derived from because it is only way in which we can be connect to true "Nature" of reality defined by that theoretical model.

This is especially true when we use the mathematics of an established paradigm such as the General Theory of Relativity to predict the existence of objects or things such as a singularity which, by definition can never be observed.

For example ESA, at its HubbleSite tells us using Newton’s Laws in the late 1790s, John Michell of England and Pierre-Simon Laplace of France independently suggested the existence of an "invisible star." Michell and Laplace calculated the mass and size – which is now called the "event horizon" – which an object needs in order to have an escape velocity greater than the speed of light. While n 1915, Einstein's gave us a conceptual basis for their existence when he publish his General Theory Relativity was able to gives for their predicted the existence of black holes.

Later Karl Schwarzschild, when quantified their existence using mathematics based on Einstein General Theory of Relativity discovered that the gravitational field of a star greater than approximately 2.0 times a solar mass would collapse form an "invisible star" of black hole, as it is now called. Additionally he showed those same equation indicated that the mass would continue to collapse even after its formation to a singularity or one dimensional point. 

He was also able to mathematically quantify the critical circumference or boundary in space around it where the strength of a gravitational field will become strong enough to prevent light from escaping and time being infinitely dilated or slowing to a stop.

In other words, as a star contacts and its circumference decreases, the time dilation on its surface will increase.  At a certain point the contraction of that star will produce a gravitational field strong enough to stop the movement of time.  Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

However unlike a black hole which have been observationally confirmed through the gravitational effects they have on companion stars the singularity which Schwarzschild's mathematics predicted is at its center has not been observed and never will be because, as mentioned earlier light cannot escape from a black hole.

Yet there are some who say that the mathematics used to predict the existence of a black hole also predicts, with equal certainty the existence of singularities.  In other words by verifying the existence of black holes though observation means that we have also verified the existence of singularities.

However that assumption is correct if and only if the formation of a singularity is consistent with the concepts of Einstein's General Theory of Relativity because as mentioned earlier that is conceptual basis for the mathematics predicating their existence.

However, it can be shown there is an inconsistency between the mathematics Schwarzschild used to predict the existence of a singularity and the concepts developed by Einstein in his Theory of General Relativity. 

To understand why we must look at how it describes both the collapse of a star to a black hole and then what happens to its mass after its formation.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity.  On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter.  They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect.  "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly.  However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star's surface.  The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference."

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped to an observer who remains at fixed circumference to that star.

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star.

Einstein showed that time is dilated by a gravitational field.  Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

This means, as it nears its critical circumference its shrinkage slows with respect to an observer who is external to its gravitation field because it’s increasing strength causes a slowing of time on its surface.  The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations of an external observer would be identical to those predicted by Robert Oppenheimer and Hartland Snyder using conceptual concepts of Einstein's theory regarding time dilation caused by the gravitational field of a collapsing star

However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side.  Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star's surface relative to its center.  The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference for both an observer who is at the center of the clasping mass and one who is at a fixed distance from its surface the contraction cannot continue from either of their perspectives.

However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reach the critical circumference.  Therefore, the surface of a star and an observer on that surface will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein's theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing.  Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference.  The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

Therefore, time would be infinitely dilated or stop in all reference that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

However, the contraction of a stars surface must be measured with respect to the external reference frames in which it is contracting.  But as mentioned earlier Einstein's theories indicate time on its surface would become infinitely dilated or stop in with respect to reference frames that were not on it when it reaches its critical circumference. 

This means, as was just shown according to Einstein's concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces.  Therefore it cannot move beyond the critical circumference because motion cannot occur in an environment where time has stopped.    `

This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

Therefore, based on the conceptual principles of Einstein's theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe and must maintain a quantifiable minimum volume which is equal to or greater than the critical circumference defined by Karl Schwarzschild.

This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations based on the General Theory of Relativity that many physicists used to predict the existence of a singularity because as has just been shown the theoretical predications made by them regarding its existence are contradictory to the concepts contained in the theoretical model they are base on.

We agree with Dirac that the connection between mathematics and nature goes far deeper than just being a useful tool in its description.

However as was shown above one must make sure that facts upon which the mathematics is based reliably follow the theoretical model they were development from if we want to use them to understand the "quality of Nature" defined by that model.

190
How could Einstein have
explained Dark Energy
June 15, 2014

The following excerpt from NASA's in its Astrophysics web site Dark Energy describes what we do and don't know about Dark Energy.

"More is unknown about it than is known. We know how much dark energy there is because we know how it affects the Universe's expansion. Other than that, it is a complete mystery. But it is an important mystery. It turns out that roughly 68% of the Universe is dark energy. Dark matter makes up about 27%. The rest - everything on Earth, everything ever observed with all of our instruments, all normal matter - adds up to less than 5% of the Universe. Come to think of it, maybe it shouldn't be called "normal" matter at all, since it is such a small fraction of the Universe.

One explanation for dark energy is that it is a property of space.  Albert Einstein was the first person to realize that empty space is not nothing. Space has amazing properties, many of which are just beginning to be understood. The first property that Einstein discovered is that it is possible for more space to come into existence. Then one version of Einstein's gravity theory, the version that contains a cosmological constant, makes a second prediction: "empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear. As a result, this form of energy would cause the Universe to expand faster and faster. Unfortunately, no one understands why the cosmological constant should even be there, much less why it would have exactly the right value to cause the observed acceleration of the Universe." 

Most scientists would agree the best case scenario would be to understand the causality of dark energy and how it interacts with its environment in terms of observations and our currently accepted theoretical models.

However, presently there are only two scientific disciplines that address those interactions.  The first or the laws of thermodynamics defines the forces associated with heat early in the universe's evolution and the second or Einstein's General Theory of Relativity defines how gravity influences that evolution.

Unfortunately neither of them, in their present form addresses the expansive force of Dark Energy and how or why it interacts with its environment to cause it to accelerate.

Yet one of the most obvious difficulties in integrating it into Einstein’s space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, in order to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions. 

In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive the physical properties of energy in a space-time universe in terms of its spatial properties is the bases for assuming, as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier it is difficult to integrate the causality of three-dimensional space expanding towards a higher *spatial" dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy if one reformulates it, as was shown above to be possible in terms higher fourth *spatial* dimension.

Yet this also allows one to understand how and why the force called Dark Energy is causing an accelerated spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use his equations to qualitatively and quantitatively define energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamics that energy flows from areas of high density to one of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means according to concepts developed in the article “Defining energy" that the three-dimensional "surface" occupied by the particles in our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.  

Yet this means similar to the water molecules occupying the elevated two dimensional surface of the water in the pool, the particles occupying a region of three-dimensional space that is elevated because of its 3.7 degree temperature will flow and accelerate outward in the four dimensional environment surrounding it.

This shows how reformulating Einstein's theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of Einstein's theories.

Many feel that because space is everywhere, the force called Dark Energy is everywhere so therefore its effects will increase as space expands.  In contrast, gravity's force is stronger when things are close together and weaker when they are far apart.  Therefore they feel the rate at which the universe expands will increase as time go by resulting in galaxies, stars, the solar system, planets, and even molecules and atoms could be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because, similar to the water in a collapsed pool the accelerative forces associated with it will decline as it expands. 

Yet, because the energy/mass of the universe remains constant through its history its gravitational potential will also.  Therefore in the future the gravitational contractive forces associated with it will exceed the expansive forces associated with Dark Energy because, as mentioned earlier according to this theoretical model its accelerative forces should decrease as the universe expands.  This would be true even though its components may be separated by extremely large distances because, as just mentioned if the above theoretical scenario is correct the force associated with dark energy will decease relative to gravity as time goes by.

However observations also suggest that early in the universe evolution the gravitational forces exceeded the expansive forces of Dark Energy.

The reason is that according the above theoretical model, just after the big bang when the concentration of energy and mass was high, the gravitational forces of the universe's energy/mass would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands its gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe. 

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.

This means that eventually gravitational forces will win because, as mentioned earlier the laws of thermodynamics tells us the total accelerative forces associated with Dark Energy will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

Therefore gravity will eventually win the battle with dark Energy because as was just mentioned the forces associated with it approach zero as the expansion progress while those of gravity remain constant.

There can be no other conclusion if one accepts the validity of Einstein's theories and the laws of thermodynamics because the theoretical arguments presented are a base solely on their validity.

It should be remember that Einstein's genius allows us to choose whether to view dark energy in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

189
Did Einstein predict
the Higgs mechanism in 1920?
June 1, 2014

Should we have given Einstein credit for being the first to predict the existence of the Higgs field?
 
The Higgs boson is an elementary particle whose discovery was announced at CERN on 4 July 2012. The discovery has been called "monumental" because it appears to confirm the existence of the Higgs field, which is pivotal to the Standard Model and other theories within particle physics.  It would explain why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless and why the weak forces have a much shorter range than the electromagnetic force. The discovery of a Higgs boson should allow physicists to finally validate the last untested area of the Standard Model's approach to fundamental particles and forces, guide other theories and discoveries in particle physics, and potentially lead to developments in "new" physics.  
Many believe the mechanism responsible for it was first proposed in 1962 by Philip Warren Anderson while the relativistic model was developed in 1964 by three independent groups: by Robert Brout and François Englert; by Peter Higgs; and by Gerald Guralnik, C. R. Hagen, and Tom Kibble.

However Albert Einstein in an address given on 5 May 1920 at the University of Leiden stated very clearly that according to the Theory of Relativity space must have the physical properties of what is now called the Higgs field, although he preferred to call it Aether.
 
He said in summation
 
"Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."
 
Granted Einstein did not specifically call it a scalar field, which is how modern scientists describe the Higgs field however he did say that it could not be tracked through time and that motion may not be applied which is another way of saying the same thing.  
 
One way of understanding how Einstein may have developed or defined the physical properties of Aether or the Higgs field, as it is now called would be to review his General Theory of Relativity and try to understand how he would have connected it to the physical properties he associated with gravity.

Einstein realized that one can understand how gravity "may act upon another at a distance through a vacuum" by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension world.  
 
However he was unable to tell us what mass is, he was only able tell us how it interacts with space-time. This is similar to Newton in that he was able to mathematically define how mass gravitational interacts with other masses but was unable to understand or define a physical mechanism that could account for that interaction.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why "one body may act upon another at a distance" by physically connecting it to the reality of what we can see and touch.
 
Einstein was often quoted as saying "If a new theory (such as that associated with the Higgs boson) was not based on a physical image simple enough for a child to understand, it was probably worthless."
 
In other words for us to fully understand the theoretical significance of the Higgs Field and why it is responsible for mass one should be able to describe how it interacts with its environment in terms of a physical image based on what we can see and touch in our three-dimensional world much as Einstein was able describe how space and time interacted with each other to cause gravity.
 
However Einstein's and modern scientist's inability to define or derive the casualty of mass in terms of a physical image can be traced to the fact that they chose to define the universe in terms of energy instead of mass.
 
Einstein told us that a curvature in space-time is responsible for gravitational energy and because of the equivalence been energy and mass defined by his equation E=mc^2 one must also assume that it is responsible for mass.

However the Higgs Field or what Einstein called Aether is associated with mass and not energy.  Therefore to understand what it is made up of one must convert or transpose Einstein's space-time universe which defines field properties of energy in terms of geometry of space-time to one that defines mass of in terms of its field properties.
 
He gave us the ability to do this when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions. 

However the fact that he defined the geometric relationship between energy and mass in terms of the constant velocity of light means that one can also quantitatively and qualitatively define a one to one correspondence between the field properties of energy in a space-time universe and those of mass in four *spatial* dimensions.

This was the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy including thermo and that associated with mass can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as of defining them in terms of a displacement in a space-time environment.
 
However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which the Higgs Field or the field properties of four *spatial* dimension creates mass and why it is quantized in the fundamental particles of the Standard Model in terms of a physical image formed by our three-dimensional environment.
 
For example one can form a physical image of why mass is quantized, as was done in the article #14 "Why is energy/mass quantized?" Oct. 4, 2007" by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions.  This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move in a three-dimension space to one consisting of four dimensional space-time.
 
(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).
 
Briefly that showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet in one consisting of four.
 
The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
 
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension at a frequency associated with the energy of that event.
 
However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.
 
Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency
 
Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties in terms of the field properties of four space dimension because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore their mass would be relative greater than the neighboring volumes.

However, one can also use the field properties of four *spatial* dimension to define the physical boundary of the mass component of a particle in terms "physical image simple enough for a child to understand".

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

In other words the confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article #14 “Why is energy/mass quantized?

This suggest that the Higgs field is made up of the field properties of four *spatial* dimensions and that the magnitude of a mass would be dependent on its geometrical configuration.
 
If true one should be able to use those field concepts to explain why the mass of corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below grows larger in each successive family.
 

Family 1

Family 2

Family 3

Particle

Mass

Particle

Mass

Particle

Mass

Electron

.00054

Muon

.11

Tau

1.9

Electron
Neutrino

< 10^-8

Muon
Neutrino

< .0003

Tau
Neutrino

< .033

Up Quark

.0047

Charm Quark

1.6

Top Quark

189

Down Quark

.0074

Strange Quark

.16

Bottom Quark

5.2

As mentioned earlier the article #14 “Why is energy/mass quantized?” showed that one can derive a particle's mass in terms of the energy contained within a resonant structure created by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy" showed that one can derive the energy or temperature of an environment in terms a displacement in that "surface" with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles the total mass of a particle would be defined by the sum of the energies associated with its resonant structure and its displacement in the "surface" of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article #14 “Why is energy/mass quantized?” but also on temperature or energy of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family." is because of an interaction between the resonant properties defined in the article #14 “Why is energy/mass quantized?” and the mass content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators because a lower energy state is available to them.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative "separation" in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "separation", with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the "separation" associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial "separation" associated with the second family.

Additionally the corresponding particle types across the three families have "identical properties" because as shown in the article #55 "The geometry of quarks" Mar. 15, 2009 they are related to the orientation of the "W" axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the "W" axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why "The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the field properties of four *spatial* dimensions.

Additional it shows how one can use the field properties of space to define and understand the physicality of the Higgs Field and how it causes mass in terms of a physical image based on the reality of what we can see and touch in our three-dimensional environment similar to how Einstein was able to define how gravity "may act upon another at a distance through a vacuum" by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold.

In other words as the article “Defining energy" showed the fact that one can derive all forms of energy including that associated with temperature and mass in terms of an asymmetrical displacement in a "surface" of space as we believe Einstein had done allows one to understand the why the Higgs field is the casualty of mass in terms of the observable reality most associate with our three dimensional environment.

In other words if one assumes as we believe Einstein did that energy/mass is created by an asymmetrical displacement in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can conceptually understand how it interacts with space to create the inertial properties associated with mass and the Higgs field in terms of the physical image formed by water in a dam.

This is because the potential energy of water is defined by its displacement with respect to the bottom of a dam. 

Therefore according to the above theoretical model, one could define the physicality of the Higgs field in terms of the potential energy or mass created by an asymmetrical displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Additionally it gives one the ability to derive the energy and therefore the mass of the Higgs bosom and where it should be located in an environment consisting of four *spatial* dimension in terms of the physical image of water in a dam because as mentioned earlier it is solely dependent on the height of the dam while that of the Higgs Boson would be dependent on magnitude of the spatial separation of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.

Another way of defining the physicality of Einstein's Aether or the Higgs field is that it is responsible for breaking the physical symmetry of space thereby allowing one to defining the mass of each individual fermion in the Standard Model in terms of an asymmetrical displacement in a "surface" of a three-dimensional space manifold with respect to a four *spatial* dimension.

This shows how it is possible to understand the reality of the Higgs Field in terms of a physical image by reformatting (as was done in the article 173 “Reformulating space-time” Oct 1, 2013) Einstein's General Theory of Relativity in terms of four *spatial* dimensions.

It should be remember that Einstein's genius allows us to choose whether to view the reality of the Higgs Field in either a space-time environment or one consisting of four *spatial* dimension because he defined the geometry of space-time in choose  terms of energy/mass and the constant velocity of light.

188
Should measurement
define "reality"
May 15, 2014

or should "reality" define measurement?

Robert Oerter, on page 83 of his book "The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics" said "Quantum mechanics has completely undermined the mechanistic view of the universe, by removing not one but two of its foundations. First, according to the Heisenberg uncertainty principle, it is impossible, even in principle, to determine the exact position and velocity or momentum of each particle in your body. The best that can be done, even for a single particle, is to determine the quantum state of the particle, which necessarily leaves some uncertainty about its position, velocity or momentum. Second, the laws of physics are not deterministic but probabilistic: given the (quantum) state of your body, only the probabilities of different behaviors could be predicted."

To a certain extent this is true however the same can be said for our inability to determine the exact position and momentum of many macroscopic objects in our environment.

For example in "reality" we can cannot determine or measure the exact position or momentum of the planets as they obit the sun because we do not have the ability, even with modern computers to calculate the gravitational effects all of the other objects in our universe, such as the planets or stars have on them.  In other words we can only determine their most probably macroscopic positions or momentum based on an incomplete set of initial conditions.  However we do not deny the mechanistic view of planetary science, in part because we can understand or determine the mechanism responsible for why they move the way they do and why we cannot determine their exact position or momentum though observations of the "reality" of our environment.  In others words because we define the measurements of their positions and momentum in terms of the "reality" or the ability to observe the conditions under which they interact we assume that they occupy a deterministic environment.

However the reason we view the quantum world as being non-mechanistic is in part because we cannot observe or understand a mechanism responsible for why the components of its environment interact the way they do.  Therefore we can only base its "reality" on our ability to measure the position or momentum of its components.  In others words we define it only in terms of measurements and not on observations of the conditions of responsible for those measurements.

Yet this is exactly how planetary scientists define the deterministic "reality" of planetary motion because as mentioned earlier, the influence other objects have on them makes it impossible to determine the exact position or momentum of a planet.

Some would say that this is not a valid comparison because we could at least, in theory refine our observations and computing power enough to be able to determine a planets initial conditions precisely enough to predict where it will be in the future.

But that still does not explain why modern science presently assumes that the motion of the planets is mechanistic on a microscopic scale when at the moment is it not.

As mentioned earlier the reason they feel justified in believing that it is, in part because they can define a mechanism in terms of a deterministic "reality" they can observed.

If it was not for this belief they would have to assume that environments the planets occupy fully agree with the non-mechanistic assumptions of quantum mechanics.

However one can define a mechanism in terms of the deterministic "reality" of our observable environment that would explain why the quantum mechanical world appears to be non-deterministic.

For example in the article #14 “Why is energy/mass quantized?” Oct. 4, 2007 it was shown it is possible to understand the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a deterministic three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.

However, it did not explain how the boundaries of a particle’s resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the "box" containing the resonant system the article #14 “Why is energy/mass quantized?” associated with a particle.

In quantum mechanics, the uncertainty principle asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

However, as mentioned earlier one can define a mechanistic "reality" for that environment in terms of the geometry of the four *spatial* dimensions because Quantum Mechanics mathematically defines the position and momentum of a particle in terms of one dimensional point.

Therefore according to the above concepts there would be an uncertainty in determining its exact position because that one dimensional point could be found any within the volume of the three-dimensional "box" mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of the movement of a one dimensional point.  Before one could determine a particle's momentum one would have to know its exact position in the box at the "end" points were one measured its velocity.  However, as mentioned above that one dimension point representing a particle could be found anywhere in the box containing the resonant structure that define a particle in the article #14 “Why is energy/mass quantized?” Therefore one could not determine its exact velocity and therefore its momentum because there will always be an uncertainty as to where in the box the one dimensional that represents a particle is relative to the dimensions of the "box" when a measurement is taken.

The reason why one cannot simultaneously measure both with complete accuracy is because the act of measure its momentum or position requires one to access different segments the "box" containing the one dimensional point particle.

For example if one wants to make the most accurate measurement possible of its momentum internal to the box one would have to measure the time it took for it to transverse a given segment of it.  However this means that one could not determine its position because it would be changing through the entire time that it took it to transverse that portion of the box.

However if one wanted to make the most accurate measurement possible of its position internal to the box it would have to be stationary with respect to the box's geometry meaning that one could not determine its monument because it would not be moving.  Since these two measurements required one to access different segments of particles geometry they are mutually exclusive. 

Therefore one cannot simultaneously measure a particle position x and momentum p with complete accuracy.

This defines why there is a limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

This shows that one can define a deterministic mechanism in terms of the "reality" of our observable environment responsible for the non-deterministic measurements associated with quantum mechanics.

However it also shows that one can define a mechanistic reason for Heisenberg uncertainty principle or why it is impossible, even in principle, to determine the exact position and velocity of each particle in your body.

As mentioned earlier we can cannot determine or measure the exact position or momentum of the planets as they obit the sun because we do not have the ability even with modern computers to calculate the gravitational effects all of the other objects such planet or stars in our universe have on them.  However we assume that they occupy mechanistic environment because we can define the measurements of their positions and momentum in terms of the "reality" or the ability to observe the conditions under which they interact.

We can and may never be able precisely measure the momentum and position of particle in a quantum environment however if we assume that the above mechanism is valid then one also has to assume that that environment is mechanistic for the same reasons we assume that the motion of the planets is mechanistic.

What determines if an environment is mechanistic is not the fact that we can precisely measure the position or momentum of its component because if it was we could not consider the motion of the planets mechanistic because presently we cannot.  What determines if an environment is mechanistic is if we can define a valid mechanism in terms of our observable "reality" that can explain and predict why we measure what we do even if we cannot observe all of its components.

If we let our inability to make precise measurements of the position or momentum of the planets or particles define "reality" then we must assume a mechanistic environment does not exist however if we can use our "reality" to define a mechanism responsible for why we cannot precisely make those measurements then must we assume they are "real" even though it may be impossible to precisely measure the positions and momentum of their components. 

187
A cosmological history lesson
May 1, 2014

History has shown that science cannot save a theoretical model that does not reflect the "reality" of current observations by randomly adding new parameters.

For example when the geocentric model of planetary motion was first proposed it was a good fit to the observational data available at the time.  However it became necessary to modify its theoretical structure to keep it in agreement with the new data provide by advancements in observational technologies.

There is absolutely nothing wrong with this if those modifications provide a deeper understanding of the processes and mechanisms it exposes.

However there is something very wrong with just adding something in an ad-hoc manner to make it fit the data.

For example components called epicycles were randomly added the geocentric model of planetary motion to allow it to conform to more accurate observation data as it became available in the 15 hundreds.  These add-ons were made on an individual bases and did nothing to help understand the mechanisms responsible for their motion.

In other words the scientific community in the 15 hundreds was unable or unwilling to consider the fact that their planetary models may be wrong because they required continued modification on an individual bases to conform to new data.  This is true even though many Greek, Indian, and Muslim savants had published heliocentric hypotheses centuries before which did not need these continued modifications and gave a more encompassing and consistent explanation of planetary motion.

This denial of a fundamental flaw in its structure delayed the advancement of the science of planetary motion in the European community for several centuries because as was just mentioned they were or should have been aware of the fact that there was a more encompassing theory available.

However this lesson seems to have been lost by many of today's scientists.

For example Alan Guth proposed the cosmological inflation model which assumes that early in the universe's evolution it underwent a period of extremely rapid (exponential) expansion. 

It was developed around 1980 to explain several inconsistencies with the standard Big Bang theory, in which the universe expands relatively gradually throughout its history

The Big Bang theory postulates the universe emerged from what is called a singularity and is presently expanding from the tremendously hot dense environment associated with it.  Additionally it assumes the momentum generated, in part by the heat of that environment is sustaining the expansion.

However as the National Aeronautics and Space Administration points on their web site there are several observational inconsistencies with it.

Notably

The Flatness Problem:

WMAP has determined the geometry of the universe to be nearly flat. However, under Big Bang cosmology, curvature grows with time. A universe as flat as we see it today would require an extreme fine-tuning of conditions in the past, which would be an unbelievable coincidence.

The Horizon Problem:

Distant regions of space in opposite directions of the sky are so far apart that, assuming standard Big Bang expansion, they could never have been in casual contact with each other. This is because the light travel time between them exceeds the age of the universe. Yet the uniformity of the cosmic microwave background temperature tells us that these regions must have been in contact with each other in the past.

The Inflation attempts to resolve these inconsistencies by assuming that the universe's it underwent an exponential expansion early in its evolution.

For example one can understand why the universe appear to be flat by assuming it underwent an exponential expansion early in its history by imagining you are living on the surface of a soccer ball. It might be obvious to you that this surface was curved.  However, if that ball expanded to the size of the Earth, it would appear flat to you, even though it is still a sphere on larger scales. Now imagine increasing the size of that ball to astronomical scales. To you, it would appear to be flat as far as you could see, even though it might have been curved to start with. Similarly an exponential expansion of our universe would stretch any initial curvature of the 3-dimensional universe to near flatness.

Inflation also appears to solve the Horizon Problem because it assumes the early universe experienced a burst of exponential expansion.  It follows that distant regions were actually much closer together prior to Inflation than they would have been with only standard Big Bang expansion. Thus, such regions could have been in casual contact prior to Inflation and could have attained a uniform temperature.

However the inflationary period appears to have been randomly added to the big bang theory simply to allow it to conform to more accurate observation data similar to the way epicycles were randomly added the geocentric model of planetary motion to allow it to conform as more accurate observation data in the 15 hundreds.

The randomness of this add-on is made apparent by the fact that as of yet there is absolutely no observational evidence to support its existence except allow the Big Bang theory to conform to current observations.

Another major problem with the inflationary model is that it violates one of the most sacred and tested laws of physics; the law of conservation of energy/mass

The reason this presents a problem because the law of conservation of energy/mass says that in a closed system it cannot be created or destroyed.  Since, by definition our universe is a closed system according to it energy/mass cannot be created or destroyed in it.

Therefore, one has to wonder where is the energy required to fuel this rapid inflationary expansion came form

Granted some cleaver scientists have come up with a mathematical model of what could be responsible for it but it has no basis in observations. 

For example some will try to convince you that a mathematical construct called an inflation field is responsible.  However, it seems a bit contrived because even though an inflation field may be responsible for the universe's expansion there is absolutely no observational evidence supporting its existence. What is even more damaging to its validity is that, as was mentioned earlier it goes against one of the most revered laws of physics; that of the law of conservation of energy/mass because it does not define how or where the energy fueling the inflation field originated from.  In other words it assumes that energy just appeared out of nothing which is a violation of that law.

Even more disturbing is that the proponents of the inflationary model must fine tune many of its parameters to make or force its theoretical predictions to agree with observations.   In other words they must arbitrarily modify on an individual bases specific perimeters to make it conform to observations similar to the way the scientific community in the 15 hundreds had to make modifications in an in individual basis to the geocentric model force it to conform the world around them.

As mentioned earlier this denial of a fundamental flaw in the theoretical structure of their evolutionary model may be delaying the advancement of the modern cosmology because, as is show below there is another one which does not violate any of the accepted laws of physics and does not require fine tuning.  This is because all of its parameters are quantifiable using the fundamental laws that govern our universe and the currently accepted physical parameters such as Planck's and Newton's gravitational constants.

We know from observations the equation E=mc^2 defines the equivalence between mass and energy in all environments and since mass is associated with the attractive properties of gravity it also tells us, because of this equivalence the kinetic energy associated with the universe's expansion also posse those attractive properties.  However the law of conservation of energy/mass tells us that in a closed system, such as our universe the creation of kinetic energy cannot exceed the gravitational energy associated with its total energy/mass.

However, not all of the energy of associated with the universe’s expansion is directed towards it because of the random motion of its energy/mass components.  For example, observations indicate that some stars and galaxies are moving towards not away us.  Therefore, not all of the energy present at the time of its origin is directed towards its expansion.

As mentioned earlier the law of conservation of energy/mass tells us that the kinetic energy of the universe’s energy/mass cannot exceed its gravitational contractive properties.  However because some of the kinetic energy of its components is not directed towards its expansion the total gravitational contractive properties of its energy/mass must exceed the kinetic energy of its expansive components.   Therefore, at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as just mentioned not all of its kinetic energy is directed towards its expansion.  Therefore at that point, in time the universe will have to enter a contractive phase.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate.  Therefore they believe that its expansion will continue forever.  However, as was shown in the article #158 “Dark Energy and the evolution of the universe” Mar. 1, 2013 if one assumes the law of conservation of mass/energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent eventually will have to exceed its expansive energy and therefore the universe must at some time in the future enter a contractive phase.  We must discard that law to assume otherwise. There are no other options)

We know from observations that heat is generated when we compress a gas and that this heat creates pressure that opposes further contractions.

Similarly the contraction of the universe will create heat which will oppose its further contractions.

Therefore the velocity of the contractions will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of its contraction.

At this point in time the total kinetic energy of the collapsing universe would be equal and oppositely directed with respect to the radiation pressure associated with the heat of its collapse.  From this point on the velocity of the contraction will slow due to the radiation pressure and be maintained by the momentum associated with the remaining mass component of the universe.

However, after a certain point in time the heat and radiation pressure generated by its contraction will become great enough to ionize the remaining mass and cause it to reexpand because the expansive forces associated with the radiation pressure caused by its collapse will exceed the contractive forces associated with its gravitational mass.

This will result in the universe entering an expansive phase and going through another age of recombination when the comic background radiation was emitted. The reason it will experience an age of recombination as it passes through each cycle is because the heat of its collapse would be great enough to completely ionize all forms of matter.

However, at some point in time the contraction phase will begin again because as mentioned earlier its kinetic energy cannot exceed the gravitational energy associated with the total mass/energy in the universe.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates the total mass and energy in a closed system remains constant.

This results in the universe experiencing in a never-ending cycle of expansions and contractions of equal magnitudes.

Many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed

Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it. This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass. This will cause the mass/energy of our three dimensional universe to oscillate around a point in the fourth *spatial* dimension.

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it.

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of our three dimensional universe is defined by its mass and the momentum of its components. Therefore, when one decreases the other must increase and therefore it must oscillate around a point in four dimensions.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space. Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

If this theoretical model is valid the heat generated by the collapse of the universe must raise the temperature to a point where protons and neutrons would become dissociated into their component parts and electrons would be strip off all matter thereby making the universe opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow matter to recapture and hold on to them.  This Age of Recombination, as cosmologists like to call it is when the Cosmic Background Radiation was emitted.

One could quantify this scenario by using the first law of thermodynamics to calculate the temperature of the universe when the radiation pressure generated by its gravitational collapse exceeds the momentum of that collapse and see if it is great enough to cause the complete disassociation of the proton and neutron into their quark components as it must to account for their observed properties and that of the Cosmic back ground radiation.

The above theoretical model does not require any adhoc add-on likes an inflation field to explain where the energy fueling our universe's current expansion came from because it is based solely on the currently accepted and observable laws of nature.

(Many would attempt to discredit it by pointing to the work by Richard C. Tolman in 1934 which showed that that due to the Second Law of Thermodynamics entropy can only increase therefore the period between cycles would become longer and longer and eventfully would stop.

However if, as we are suggesting above that the universe's energy/mass forms a resonate system in space similar to the one the article #14 "Why is energy/mass quantized" Oct. 10, 2007 showed was responsible for the stability of the energy/mass of the atom one would understand how with the universe's expansion and contractions w3ould result in the formation of a resonant system that would maintain the stability of those expansions and contractions.)

Yet what makes this theoretical model different from all others is that one can also define a solution to the horizon and flatness problems using the same logic and currently accepted laws of nature that were used above to derive the current expansion of our universe.

*****

The Horizon Problem

The resolution of the horizon problem can be found in the fact that the repeated cycles mentioned above would allow different regions of the universe to mix and equalize thereby explaining why their temperature and other physical properties are almost identical.

This would be analogous to mixing the content of two cans of paint by pouring one into the other.  The evenness of the mixture would increase in proportion to the number of times one pored one can into the other.

Similarly the evenness of the temperature distribution and physical properties of the universe would increase and level of after a specific calculable number of cycles.

However it also explains why there are small temperature and other physical irregularities in the large-scale structure of the universe.

One cannot completely mix two different colors of paint no matter how many times they pour one can into another because the random motion of the different colored paint molecules means that some regions will have more of one color that the other.

Similarly the quantum fluctuations associated with the baryonic component of the universe means that some regions will have more matter or be denser that others no matter how many cycles of expansions or contractions it has undergone.  These areas would be where the large-scale structures such as galaxies and galactic clusters should exist. This gives yet another way of quantifying the above theatrical model with observations because the number and distribution of large these large scale structures would be dependent on their thermodynamic properties.

*****

The Flatness Problem

Unfortunately understanding why our universe appears to be flat cannot be easily understood in terms of the space-time concepts of relativity because it involves the spatial not the time properties of our universe.

However Einstein gave us the ability to convert the time properties of a space-time universe to its spatial counterpart when he used the equation E=mc^2 and the constant velocity of light in that equation to define the balance between energy and mass because it provided a method of converting a unit of space-time he associated with energy to a unit of space he associated with mass.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a quantitative and qualitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must also assume that energy must have spatial properties.

This and the fact that one can use the equation E=mc^2 to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

One of the advantages to this approach is that it allows one to theoretically derive the energy of the universe’s momentum in terms (as was done in that article) of oppositely directed displacements in a “surface” of a three-dimensional space manifold with respect to the energy density of its matter component.  This means that the “flatness” of our universe would be an intrinsic property of its existence and would not require the fine-tuning of any of its components to explain it.

For example observations of the three-dimension environment occupied by a piece of paper shows us that if one crumples a piece that was original flat and views its entire surface, the overall magnitude of the displacement caused by that crumpling would be zero because the height of it above its surface would be offset by an oppositely directed one below its surface.  Therefore, if one views its overall surface only with respect to its height its curvature would appear to be flat.

Similarly, if the energy density associated with the momentum of the universe’s expansion is a result of oppositely directed displacement in a “surface” of a three-dimensional space manifold with respect to that associated with its matter component their overall density would appear to be flat because, similar to a crumpled piece of paper the “depth” of the displacement below its “surface” caused by matter would offset by the “height” of the displacement caused by its momentum.

Many proponents of the Big Bang Model assume it began from the expansion of mass and energy around a one-dimensional point.  However, if we are correct in assuming that density of the mass and energy components of our universe are a result of oppositely directed curvatures in a “surface” of a three-dimensional space manifold, the universe must have been flat with respect to their density at the time of the Big Bang.  This is because a one-dimensional point would have no “vertical” component with respect to a fourth *spatial* dimension and therefore the “surface” of three-dimensional space originating from it would be “flat”.

However, if the universe was flat with respect to the density of energy/mass in the beginning its overall geometry would remain flat throughout its entire expansive history because its expansion would result in a proportional reduction in the displacements above and below its three-dimensional “surface” as it expanded.

This would be analogous to why the overall flatness of a crumpled piece of paper does not change if one smoothed or stretches it because that would result in a proportional decrease in the height of the wrinkles above and below its original surface.

It is not possible to define the mechanism responsible for the flatness of our universe if one defines it in terms of four-dimensional space-time because time moves only in one direction forward and therefore cannot support the bi-directional movement required define the apparent flatness our universe in terms of its geometry.  This is why it necessary, as was done earlier to redefine the Einstein's space-time concept its four spatial dimension equivalent.

The above theoretical model has the advantages over an inflationary one because it allows one to quantify its early history when particle formation took place in terms of the first law of thermodynamics.  For example one could use that law to calculate when the radiation pressure generated by its gravitational collapse would exceed the momentum of that collapse thereby determining when and what the conditions were when the expansion began. This means that scientist's would not have to fine tune any of its parameters to make it conform to observations because those parameters would be determined by Planck's and the gravitational constant and the laws that govern their interaction with the energy/mass of our universe.

One purpose for studying history is to learn from our mistakes and hopefully eliminate or at least minimize the possibly of repeating them.

Unfortunately modern scientists seem to have ignored the lesson taught to us by their 15 century brothers in that they do not realize that the denial of a fundamental flaw in their understand of the evolution structure of our universe may be  causing a delayed the advancement of their science.

186
The reality behind
 quantum entanglement
Apr 15, 2014

Quantum entanglement is defined "as a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently instead, a quantum state may be given for the system as a whole.

For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. Because of the nature of quantum measurement, however, this behavior gives rise to effects that can appear paradoxical. For example any measurement of a property of a particle can be seen as acting on that particle (e.g. by collapsing a number of superimposed states); and in the case of entangled particles, such action must also act on the entangled system as a whole. It thus appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances."

Einstein referred to this as "spooky action at a distance" because it assumed that objects or particle can interact instantaneously, regardless of distance separating them which according to his perception of reality this was not possible.

To demonstrate this he co-authored a paper with Podolsky–Rosen which came to be called the EPR Paradox whose intent was to show that Quantum Mechanics could not be a complete theory of nature because it does not agree with his perception of reality.  The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a "hidden variable" that would allow Quantum Mechanics to become a complete theory of nature

The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known.  Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state.  Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion.  In other words, A and B have moved outside of each other's light cones and therefore are spacelike separated.

With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A?  Say, for example, one measures the momentum value for it.  Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B.  Thus, by making a momentum measurement of A, one can also measure the momentum of B.  Recall now that A and B are spacelike separated, and thus they cannot communicate in any way.  This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made.  If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place.  However, the two systems cannot communicate in any way!

If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B.  So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is!  Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.

In response to Einstein's argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles.  If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle's limited influence.

In other words he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are "spacelike" separated.

When Bell published his theorem in1964 the technology to verify or reject it did not exist.  However in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

This meant that science has to accept that either the reality of our physical world or the concept of separability does not exist.

But this may not be the case for two reasons.  The first is based on the core principals of Einstein's theories while the second involves the physical properties of the wave function that quantum mechanics used to define the probability of a particle's state.

However understanding why is only possible if one redefines Einstein's four dimensional space-time universe to one consisting of four *spatial* dimensions.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space identical to those of our three-dimensional space. Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravitational energy in terms of four *spatial* dimensions is one bases for assuming, as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy including gravitational and that of constant motion can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

One of the more common ways to visualize how gravity can be cause by a curvature in space-time is by comparing its effects to the effects a curved surface of a rubber diaphragm has on a marble.  The marble follows a circular pattern around the deformity in the surface of the diaphragm.  Similarly planets revolve around the sun because they follow a curved path in the deformed "surface" of space-time.

The same example can be used to visualize how a curvature in a "surface" of three dimensional space can be responsible for gravitational accelerations however in this case it would caused by a deformation in that "surface" with respect to a fourth *spatial* instead of a time dimension.

As was mentioned earlier one of the advantage to redefining Einstein space-time concepts in terms of four *spatial* dimensions instead of four dimensional space-time is that it not only allows one to understand gravitational energy but also the energy of constant relative motion in terms of the geometric properties of space.

Briefly the article “Defining energy?" showed one can define constant momentum or the energy of relative motion in terms of a constant displacement of a "flat surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.

One way of visualizing would be to use the earlier example of the rubber diaphragm.  However instead of its "surface" being curved it would be flat with respect to its soundings and the energy associated with its relative motion would be defined by its separation with respect to a four *spatial* dimension form the "surface" with which it's velocity is being measured from.

In other words one can define the energy of an object or particle in constant relative motion in terms of a displacement a "flat surface" of a three-dimensional space manifold with respect to a time or four *spatial* dimension because as was shown above they would be equivalent .

However Einstein's Theory of Relativity tells us the length of an object or particle contracts; approaching zero as it nears the speed of light.  Additionally he told us that at the speed of light it becomes zero when observed from all other reference frames because at that speed its length in the direction of motion becomes zero. 

But his theory also tells us from the perspective of the photon moving at the speed of light, the physical distance or space between observers and their observations must also be zero because from the photons perspective the observers are moving at the velocity of light with respect to them.

In other words according to the core principals of Einstein Theory of Relativity two entangle photons will interact instantaneously, regardless of the distance separating them from the perspective of external observers measuring their properties because from a photon perspective the distance between those measurements is zero.

There can be no other interpretation if one accepts the validity of Einstein theories.

However as mentioned earlier one can also understand the "reality" behind quantum entanglement by deriving the probability functions quantum mechanics associates with Schrödinger wave equation in terms of Einstein theories when they are redefined, as was done earlier in terms of four "spatial* dimensions.

This is because it is possible, as was done in the article #111 “The *reality* of quantum probabilities” Mar 31, 2011 to define the physicality of the probability function quantum mechanics associates the wave function of a particle as being the result of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Very briefly that article showed that one can derive the quantum mechanical properties energy/mass by extrapolating the laws of classical resonance to a matter wave in a continuous non-quantized field of energy/mass moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous form of energy/mass when he theorized all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

It showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet in one consisting of a continuous non-quantized field of energy/mass and four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the continuous non-quantized field of energy/mass to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in it.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

However assuming energy is result of a displacement in four *spatial* dimension also allows one to define the physicality of the probability distribution associated with the wave function of individual particles by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

As was shown earlier redefining Einstein space-time in terms of four *spatial* dimension tells us that the energy of a photon moving at the speed of light is distributed throughout the universe in a two-dimensional plane that is perpendicular to its velocity vector therefore as the article #111 “The *reality* of quantum probabilities” Mar 31, 2011 showed the probability's associated with a quantum particle's wave function would be distributed throughout the entire two-dimensional "surface' of the three-dimensional space manifold it is occupying with respect to a fourth *spatial* dimension.

The effect of this would be analogous to what happens when one vibrates a rod on a continuous rubber diaphragm.  The oscillations caused by the vibrations would be felt over its entire surface while their magnitudes would be greatest at the point of contact and decreases as one move away from it.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a "surface" of a three-dimensional space manifold one must assume the physical oscillations in the surface of three-dimensional space that associated with the wave function must exist everywhere in three-dimensional space.  This also means there would be a non-zero probability they could be found anywhere in our three-dimensional environment.

As mentioned earlier the article #111 “The *reality* of quantum probabilities” Mar 31, 2011 showed a quantum mechanical system is a result of a resonant structure formed on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us that resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a quantum system would most probably be found were the magnitude of the vibrations in a "surface" of a three-dimensional space manifold is greatest and would diminish as one move away from that point,

However this means each individual particle in a quantum system has its own wave and probably function and therefore the total probability of a quantum system being in a given configuration when observed would be equal to the sum of the individual probability functions of each particle in that system.

As mentioned earlier Allen Aspect verified that Bell inequities were violated by the quantum mechanical measurements made on pairs of polarized photons that were space like separated or in different local realities.

Yet, as just mentioned the wave or probability function of a quantum system is a summation of the probably function of all of the particles it contains.  Therefore, two particles which originated in the same quantum system and were moving in opposite directions would have identical wave or probability functions even if they were not physically connect.

The measurements Allen Aspect made on the polarized photon verified that Bells inequity was violated because a correlation was found between the probabilities of each particle being in a given configuration based on the concepts of quantum mechanics.  When this correlation was found many assumed that somehow they must be entangled or physical connected even though they were in different local realities.  In other words the Newtonian concept separability does not apply to quantum environment. 

However, this may not be true.

According to quantum mechanics act of measuring the state of a pair of entangled photons instantly affects the other no matter how far they are apart.  Yet if it is true as mentioned earlier that each entangled particle has an identical wave or probably function as it moves through space the measurement of the state of one particle would be reflected in the measurement of the other.  This is because the probability of them being in a specific state would be determined at the point of origin or where they were entangled and that common probably would be “carried” by each particle until a measurement was made. Therefore when making a measurement on one particle in a close system containing two entangled particles the rules of quantum mechanics tell us that the inequities found in Bell’s Theorem should be violated not because they are physically connected in space but because they are connected through their common probability function.

In other words the reason why Bell's inequity is violated in a quantum system is not because the particles are physically entangled or connected in space at the time of measurement but because their individual wave or probability functions were "entangled" or identical at the time of their separation and remained that way until a measurement was made on them.

But to say the correlation of the quantum characteristics of two particles are identical because they are entangle or are physically connected is like saying the correlation between the color characteristics of the hair of identical twins is because they have been physically connect throughout their entire life.

This shows that Quantum Mechanics is a "complete theory of nature" contrary to what Einstein believed because based on the core principals of relativity one can define a mechanism responsible for the correlation of the quantum characteristics of particles that exist in non-local environments by extrapolating the "reality" of a environment governed by the physical laws laid down by him or the rules governing quantum mechanics.

185
The geometry of a particle wave
Apr. 1, 2013
 

Is it possible to define a "reality" behind the quantum world in terms of the classical laws of physics and the space-time environment defined by Einstein?

In other words can one use our everyday experiences to understand the irrationality behind many of the assumptions made by quantum mechanics and integrate them into the space-time environment in which we all live

For example the paradoxical wave–particle behavior of energy/mass, one of the fundamental concepts defining Quantum mechanics defies the "reality" of the four dimensional world we live in because of its inability to describe/define how quantum-scale objects can simultaneously exist as waves and particles.  Many have tried to explain it as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

However, it is possible to explain the wave--particle duality of the quantum world in terms of the "reality" of classical concepts and four dimensional space-time by redefining Einstein's space-time environment to its equivalent four spatial dimension counterpart because it will allow one to directly apply classical concepts of Newtonian space to the wave properties quantum mechanics associates with particles.

(The reasons will become obvious latter.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.

This, as mentioned earlier will allow us to understand the reasons behind the paradoxical wave–particle duality of light when it is partially reflected by two surfaces, as outlined on pages 17 thru 23 of Richard P Feynman book "QED The Strange Theory of Light and Matter" in terms of the laws of classical physics.

On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass.  This indicates that their energy is not transmitted by a wave but by a particle.

However this observational paradox can be resolved if particles are, as mentioned earlier are viewed in terms four *spatial* dimension instead of four dimensions space-time because it shows their behavior can be described in terms of a resonant "structure" generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example in the article #14 “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of energy/mass and a photon by extrapolating the laws of classical of resonance in a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it showed that all energy must be propagated in these resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore if one extrapolates the laws of classical wave mechanics to a fourth *spatial* dimension these oscillations in a "surface" of a three-dimensional space manifold would generate a resonant system or "structure" in space. 

Classical mechanics tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency.

Similarly the incremental or discrete energies associated with individual photons in Richard Feynman's experiment could be explained by assuming that they are a result of the fundamental or a harmonic of the fundamental frequency resonant properties of four *spatial* dimensions.

This shows how one can derive the quantum mechanical properties of energy/mass and a photon by extrapolating the laws of classical wave mechanics to a matter wave on a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.

However, one can also describe the physicality of a particle in terms of the wave properties of its resonant structure.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article #14 “Why is energy/mass quantized?"

This provides the ability to understand how and why a photon can have the properties of both a wave and a particle because it clearly defines their interdependence in terms of the laws of Classical wave mechanics

However it also defines the physical reality of particle-wave duality in terms of the classical of the properties of a matter wave moving on the "surface" of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was show earlier they are equivalent

For example, the wave like interference of photons he observed would be due to the wave properties of the resonant "system" defined in the article #14 “Why is energy/mass quantized?".

If the distance between the two glass surfaces in Richard Feynman's experiment is equal to half of the wavelength of the resonant "system" associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.

If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.

However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article #14 “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy would be propagated in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying.

Yet this also defines the reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because Classical wave mechanics tells us that when two waves of the same frequency interact their frequency will or does not change.  Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.

This indicates that viewing the quantum mechanical world of wave–particle duality in terms of the geometric properties of a resonant "system" generated by a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to derive its "reality" by extrapolating the laws of classical mechanics in three-dimensional environment to a fourth *spatial* dimension.

It should be remember Einstein’s genius allows us to chose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the physical relationship of particles and waves.

184
The reality of quantum fields
Mar. 15, 2014

In physics a field is defined as a continuous physical quantity that has a value for each point in space and time while Relativistic Quantum Field Theory (QFT) defines particles as excited states of an underlying physical field.

However there is a conceptual discontinuity between QFT and its relativistic component because it is based on the abstract properties mathematics while the Einstein's Theory of Relativity is based on the continuous physicality of space and time.

For example the Schrödinger wave equation that is used to mathematically define a particle in QFT does so in terms of a non-dimensional harmonic oscillator at each point in space but does not define what is physically oscillating while Einstein defines the relativistic properties of space and time in terms of a physical interaction of time with three-dimensional space.  Additionally it is difficult to understand how non-dimensional point oscillation can be responsible for dimensional properties of a particle because by definition it cannot have those properties.

Yet one may be able resolve this issue if one views the relativistic properties of our universe in terms of four *spatial* dimensions instead of four dimensional space-time.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein's equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of the field properties of four *spatial* dimensions is one bases for assuming, as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space field with respect to a fourth *spatial* dimension. 

However it also allows one to define the physicality of the harmonic oscillator QFT associates with a particle in terms of physical interaction of the field properties of three-dimensional space with a fourth spatial dimensional similar to how Einstein define gravity in terms of a physical interaction of time with three-dimensional space.

For example the article, #14 “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can explain and understand the physicality of the harmonic oscillator QFT associates with particles terms of the classical field properties of a wave by extrapolating the laws of resonance in a three-dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explained why all energy must be quantized or exists in these discrete resonant oscillators when observed.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in a matter wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.

This allows one to define the physicality of the harmonic oscillators QFT associates with particles in terms field properties of either four dimensional space-time or four spatial dimensions because as was shown earlier they are equivalent.

However, one can also define its field properties of a particle in terms of the boundaries of its harmonic oscillator.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the harmonic resonator associated with a particle in the article #14 “Why is energy/mass quantized?"

However as mentioned earlier it also defines the physical boundaries of the harmonic oscillator QFT associates with a particle in terms of the properties of a wave moving on a continuous field consisting of four *spatial* dimensions or four dimensional space-time because remember as was show earlier they are equivalent

This also provides the ability to understand the inseparability of the concepts of a field and particles in QFT because it clearly defines how one is depend on the other.

However it also explains why a field can display either the properties of a particle or the wave properties of a harmonic oscillator when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.

Additionally it defines a classical reason why particles sometimes behave like oscillators and sometimes like particle and why it is impossible simultaneously observe these two different properties.

As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the wavelength of its harmonic oscillator.  In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure.  Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties behind. 

(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of the harmonic oscillator QFT associates with photon or other particle.)

The reason why one cannot simultaneously measure both its wave and particle of the harmonic oscillator it is because as mentioned the energy of a particle is defined by its wave properties. Since the energy that defines a particle is the smallest unit of its harmonic oscillator if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.

This shows that one can integrate the abstract mathematical properties of Schrödinger wave equation or the foundation of Quantum field theory with the continuous physical of space and time In Einstein's theory of relativity.

It should be remember Einstein’s genius allows us to chose whether to solve all problems in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe and gives us a new perspective on the integration of QFT with the relativistic properties of space and time.

183
A Classical interpretation
 of quantum mechanics
Mar. 1, 2014

Bohr summarized the complementary principal of quantum mechanics as follows:

"However far the quantum physical phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word "experiment" we refer to a situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point...implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear.... Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the object."

In other words he did not think that it was possible to use classical concepts to integrate the wave and particle characteristics of a quantum particle into a single picture therefore he felt that there exists a physical division between the macroscopic world of classical objects and the microscopic world of quantum particles. 

However this may not be the true and one can understand why if one views the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of a *spatial* dimension identical to those in our three-dimensional universe .  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein's equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

However it also allows one to understand the wave particle duality of energy/mass or its complementary property in terms of the concepts of classical physics.

For example the article, #14 “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can explain and understand the physicality of its particle properties in terms of the classical concept of waves by extrapolating the laws of resonance in a three-dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in a matter wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four spatial dimensions.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.

This allows one to define the particle properties of energy/mass in terms of the classical concepts of a wave.

However, one can define its wave properties in terms of the classical concepts of a particle in terms of the boundaries of its resonant structure.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the resonant system associated with a particle in the article #14 “Why is energy/mass quantized?"

However it also defines the particle properties of waves in terms of the classical concept of resonant properties of a box because its physical properties define its frequency and energy.

This also provides the ability to understand the inseparability of the wave particle duality of energy/mass because it clearly demonstrates how one is dependent on the other.

However it also explains why quantum systems either display the properties of a particle or a wave when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.

Additionally it defines a classical reason why particles sometimes behave like wave and sometimes like particle and why it is impossible simultaneously observe these two different properties.

As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the energy associated with the wavelength of it’s resonate structure.  In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure.  Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties.

(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of a photon or other particle whose energy would correspond to that difference.)

The reason why one cannot simultaneously measure both its wave and particle properties is because as mentioned the energy of a particle is defined by the wave properties of its resonant structure.  Since the resonant system that defines a particle is the smallest unit of its resonate structure if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.

This demonstrates how one can integrate the wave and particle characteristics of a quantum particle into a single picture and why the  physical division between the macroscopic world of classical objects and the microscopic world of quantum particles as was assumed by Bohr many not exist.   

182
Mass from first
 principles
Feb 15, 2014

Einstein told us that energy and mass are interchangeable in terms of the geometry of space-time however he did not define what mass is.  He only told us how mass interacts with it.

As Steven Weinberg said "Mass tells space-time how to curve while space-time tells mass how to move".

In other words Einstein did not tell us what mass is in terms of the principles he used to define their interactions.

While for the past 50 years, the Standard Model of Particle Physics has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.

But as Charles Seife mentions on page 142 of his book Alpha & Omega “Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless.”

In 1964 Peter Higgs showed that one can solve this problem and explain why particles have inertial or rest mass if one assumes space is permeated by what is called a Higgs field.

He was able to show that if a particle changes its velocity or accelerates, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass.  In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field

Recently a particle that closely resembles the Higgs boson has been observed at the Large Hadron Collider (LHC) particle. If confirmed it would verify the existence of the Higgs field which according the Standard Model of Particle physics is responsible for mass.

But even if its existence is confirmed it still does not answer the question "What is mass?" in terms of first principles because it does not define what the Higgs field is made up it only confirms it existence.

As mentioned earlier Einstein told us that energy and mass are interchangeable in terms of the geometry of space-time however he did not define what mass is. 

However one can use his theoretical model and how we observe mass and energy to interact in a classical three-dimensional environment to understand what it is in terms of the (first) principles of a space-time universe if one converts or transforms it into one consisting of only four *spatial* dimensions.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the constant velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of a *spatial* dimension identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

One of the primary advantage to doing this is that it, as was mentioned earlier would allow one to understand the physicality of the Higgs field and how and why it causes mass in terms of a fundamental property of the geometry of four *spatial* dimensions or the principles of the space-time environment exposed by Einstein because as was just shown their properties are interchangeable. 

For example observations of our three-dimensional environment tell us the total potential energy of an object or particle is related to the magnitude of its relative displacement.  In other words the potential energy of water in a bucket is determined by the height or displacement of its surface relative to the surface of the table it is resting on.  However, its potential energy is greater if one measures it relative to the floor on which the table is resting.

In the following discussion the potential energy of the water in the bucket relative to the table top will represent the mass of an object or particle while its energy with respect to the floor will correspond to the energy associated with its relative velocity.

In the article #11 “Why Space-time?” Sept. 27, 2007 it was shown one can derive the rest or inertial energy/mass of an object or particle in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was shown one can derive the causality of all accelerations including gravitational in terms of an interaction of mass with the slope of a curvature in a “surface” of a three-dimensional space caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was responsible for gravitational accelerations)

This means that one could define the potential, inertial or rest energy of mass by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a “surface” of a three-dimensional manifold with respect to  a fourth *spatial* dimension.  In other words one could define the physicality of the potential energy associated with inertial mass in terms of the displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension for the same reason as one can define the potential energy of the water in the bucket as being related to its displacement with respect to the table top.

However this suggests that the magnitude of a physical displacement in the geometry of three-dimensional space with respect to a fourth *spatial* dimension may be responsible for the mass of an object or particle.  In other words it would allow one to derive the physicality of the Higgs field by extrapolating the observable field properties of three-dimensional space to a fourth *spatial* dimension.

Yet as was shown in the article #23 “Defining energy” Nov 26, 2007 one can also derived the energy associated with the relative velocities in terms of a displacement of the three dimensional volume of an object or particle with respect to a fourth “spatial” dimension.  In other words it was able to show the energy of velocities are a result of a displacement of geometric properties of two masses in a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension.

(The energy of relative velocities would be associated with the displacement of the surface of the table with respect to the floor in the example mentioned earlier.)

Isaac Newton defined inertia as being responsible for why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed.

This means, one could define the potential energy of the velocity of an object or particle in terms of the displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with its rest mass plus that associated with its relative velocity because according to the concepts presented in those articles it would be defined by the sum of those components. (The momentum of an object at rest relative to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.) 

This also tells us the “relativistic” mass or inertia of an object or particle increases as its velocity approaches that of light because its total energy/mass would, according to the concepts presented here be related to the relative magnitude of the total displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension with respect to the velocity of light.

Yet, as mentioned earlier the article “Why Space-time?” showed that accelerations are caused by an object or particle interacting with a curved “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, if as mentioned earlier the momentum of a particle or object is caused by a displacement of a “surface” of a three-dimension space manifold it would tent to stay rest or ones in motion would tend to stay in motion unless it interacted with a “surface” that was curved with respect to a fourth *spatial* dimension.

In other words this enables one to define the physicality of the Higgs field in terms of the field properties of space-time or four *spatial* dimensions and that the magnitude of its associated "drag" would be defined in terms of ratio of its rest or inertial energy/mass and the slope of the curvature in space it interacts with.

This also defines mass and the Higgs field in terms of the principles first put forth in Einstein's General Theory of Relativity while showing that the properties of Higgs field are related to the irreducible the field properties of space because the result of removing or reducing space is nothingness.

It should be remember Einstein’s genius allows us to chose weather to solve all problems in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe and gives us a new perspective on questions regarding the origins of mass and a way of understanding how and why the Higgs field is responsible for mass.

181
Should we let our imaginations
 define reality
Feb. 1, 2014

or should we let "reality" define our imagination.

Unfortunately many physicists attempt to define reality based solely on what they measure and do not attempt to conceptually integrate those measurements into the realty we see around us.

One example can be found in Brian Clegg book Before the Big Bang: The Prehistory of Our Universe (p. 137) where he describes how Neils Bohr reacted when Heisenberg proposed his uncertainty principal.

"When Heisenberg first told his boss, Neils Bohr, about the uncertainty principle, he put it across in the form of an imaginary microscope. He described a particle as an electron passing through a make-believe ultra powerful microscope. We use light to examine the object, so a beam of photons (quantum particles just as the electron is) is constantly crashing into the electron. The result is that the electron’s path is changed. You can’t look at a quantum particle without changing things. Heisenberg is said to have been reduced to tears when Bohr ripped his idea to pieces. Heisenberg had assumed that until the microscope scanned the electron, the electron had an exact position and momentum. He thought it was the process of observing it that messed things up. But actually, Bohr pointed out, the uncertainty was more fundamental than that. There was no need to observe the electron for uncertainty to apply: it was inherent to the nature of a quantum particle."

In other words Neils Bohr said that because we will never be able to observe an electron without changing it or its environment one must simply accept the fact that we will never be able to understand why it behaves the way it does in terms of the "reality" we see around us.

However the science of physics is defined as "the asking fundamental questions regarding how and why matter and energy interact while demanding the answers be validated by observations.

Yet this definition appears to conflict with Neils Bohr assertion that the uncertainty principal is inherent to the nature of a quantum particle because that immunizes it from such questions.

Additionally he said since it is true that uncertainty principal is inherent to the nature of the unseen world of a quantum particle "Everything we call real is made of things that cannot be regarded as real".

Yet if one uses his philosophy that "reality" does not exist then the observations used to define that principal also cannot be real or exist because one cannot observe something that does not exist.  In other words the very arguments Neils Bohr uses to support his concept of the uncertainty principal leads to it invalidation.

However history has shown us that one of the advantages to defining the universe that we cannot and will never be able to see in terms of the "reality" of our observable environment is that it limits the ability of our imagination to create nonexistent or fantasy worlds to support them.

For example Einstein mathematically derived the force of gravity in terms of a curvature in a four dimensional space-time universe.  However even though he knew that he would never be able to physically observe how a time dimension interacts with the three spatial dimensions he attempted and succeeded in explaining how a curvature in a space-time environment can result in the force gravity by watching how a marble moved on a curved surface in our observable three dimensional universe.

In other words Einstein not only mathematically quantified the measurements of the force of gravity but he also provided a qualitative explanation of how it could act at distance by anchoring it to the observable properties of an object moving on a curved surface in three-dimensional environment.

This methodology is in sharp contrast to how Newton defined gravity in that he simply accepted the fact that he was able to accurately quantify it using the concept of action at a distance even though he was aware that it disagreed, as the following excerpt from a letter he wrote to Bentley with the "reality" he saw around him.

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.

However Einstein's unwillingness to accept action at a distance gave him the ability more accurately quantify gravity while providing an understanding of how it could act at a distance by anchoring it to the "reality" of our three-dimensional environment.  Additional it showed that Newton's concept of absolute space and time only existed in the fantasy world of his imagination because according to Einstein gravity is caused by their variability.

This shows the power of attempting to understand the unobservable in terms of the observable by anchoring it to the "reality" of what we see around us and why we should be skeptical about accepting the validity of the uncertain principal based on Neils Bohr assertion that it is inherent to the nature of a quantum particle

However what is even more damaging to his ideology of blindly accepting a mathematical interpretation of the uncertainty principle, is that it is possible (much as Einstein did) to extrapolate the observable properties of our three dimensional environment to a quantum one as was done in the article #152 “A classical interpretation of Heisenberg’s Uncertainty Principal" Dec. 1 2012 to explain and predict how and why it behaves the way it does.

However before we begin we must first reformulate Einstein space-time concept to their spatial equivalent.

(The reason will become obvious latter)

Einstein gave use the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define the geometry properties of space-time because it provided a method of converting a unit of space-time he associated with energy to a unit of space he associated with mass.   Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light provided a qualitative and quantitative means of redefining his space-time universe as was done in the article #24 ”The “Relativity” of four spatial dimensions"  Dec. 1, 2014 in terms of geometry of only four *spatial* dimensions.

On advantage to doing this is that it gives one a different perspective on the "reality" of the quantum environment and the uncertainty principal in terms of the observable "reality" of our three dimensional universe.

For example the article #14 “Why is energy/mass quantized?” Oct. 4, 2007 demonstrated it is possible to understand the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

Therefore the discrete or quantized energy of resonant systems in a continuous field of four spatial dimensions could explain the discrete quantized quantum mechanical properties of particles.

However, it did not explain how the boundaries of a particle’s resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the "box" containing the resonant system the article #14 “Why is energy/mass quantized?” associated with a particle and why quantum systems behave the way they do.

For example in quantum mechanics, the uncertainty principle asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

However, this means that one can define the physicality of the uncertainty principal in terms the geometry of the four *spatial* dimensions because Quantum Mechanics mathematically defines the position and momentum of a particle in terms of non dimensional point.  This means there would be an uncertainty in determining its position because that point could be found anywhere within the volume of the "box" mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of a non dimensional point.  Therefore before one could determine a particle's momentum one would have to know the exact position of the "end" points one uses to measure its velocity.  However, as mentioned above that non dimension point representing a particle could be found anywhere in the box containing the resonant structure that defined a particle in the article #14 “Why is energy/mass quantized?” Therefore one could not determine its exact velocity and momentum because there will always be an uncertainty as to where the non dimensional point representing a particle is in the box when the measurement was taken

The reason why one cannot simultaneously measure both with complete accuracy is because the act of measure its momentum or position requires one to access different segments the "box" containing particle.

For example if one wants to make the most accurate measurement possible of its momentum internal to the box one would have to measure the time it took for it to transverse a given segment of it.  However this means that one could not determine its position because it would be changing throughout the entire time that it took it to transverse that portion of the box.

However if one wanted to make the most accurate measurement possible of its position internal to the box it would have to be stationary with respect to the box's geometry meaning that one could not determine its monument because it would not be moving.  Since these two measurements required one to access different segments of a particles geometry they are mutually exclusive. 

Therefore one cannot simultaneously measure a particle position x and momentum p with complete accuracy.

This defines in terms of the reality we see around us why there is a limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

However it also tells us we should always attempt to conceptually integrate our theoretical models into the "reality" of what we "see" around us because it allows one to physically connect the abstract properties of a theoretical environment created by our imagination to the reality of the worlds they are describing thereby limiting its ability to create fantasy worlds such as the one Neils Bohr believed in to explain their theoretical models.

180
Deriving the fundamental
constants of nature
Jan. 15, 2014

One of the most fundamental questions in physics and cosmology is why the physical constants are what they are.

For example the fine structure constant is one of the about 22 empirical parameters in the Standard Model of particle physics, whose value is not determined within it.

In other words their values are not determined by theory but by experimentation. 

An even more puzzling question is why a certain number of them lie within a very narrow range, so that if any were only slightly different, the Universe would be unable to develop matter, astronomical structures, elemental diversity, or life as we presently understand it.

However there are several theoretical models that attempt to explain why we live in a universe that is so fine tuned for life.

For example the Multiverse class of theories assumes the value of the fundamental constants vary randomly though out many different universes and that we happen to live in one that have the values that will support life.

In other words they all assume the existence of many universes, each with randomly chosen physical constants, some of which are hospitable to intelligent life and because we are intelligent beings, we are by definition in a hospitable one.

However all of then suffer from the same problem in that are not verifiable or falsifiable because by definition universes are closed systems and cannot interact with each other.  Therefore because they cannot interact with ours there is no way to verify or falsify their existence.

This is why Critics of the Multiverse-related explanations argue that they are unscientific because there is no way to experimentally verify or falsify their existence.

Yet the reason why we live in a universe in which the values of fundamental constants are fine tuned to allow life to developed may not be due to a random property of their origins but may be because they are preordained to have those values by a dynamic resonant property of energy/mass defined by Einstein's General Theory of Relativity and his equation E=mc^2. 

In other words the fundamental constants are what they are because they correspond to the most stable configuration of energy/mass possible.

For example a guitar string has a frequency at which it will naturally resonant at due, in part to the tension it is experiencing, and will, if allowed to, drift towards and stabilize at that optimal value.

Similarly the values of the fundamental constants associated with the resonant structure of energy/mass defined by Einstein would have a tendency to drift towards and stabilize at their optimal value.

However if it is true that the fundament constants are due to a dynamic resonant property of energy/mass one should be able to determine their values, including that of fine structure and cosmological constant by measuring the components of the resonant system it creates. 

The dynamic relationship between mass and energy defined by the equation E=mc^2 tell us that they are oppositely directed in the sense that if one increases the other must decrease.  However this also tells that whenever they interact a resonant structure would be formed whose fundamental frequency would be determined in part by the "tension" created their oppositely directed components similar to how the frequency of a guitar string also depends on the tension it is under.

This suggest that the magnitude of the fine structure constant may be the result of a resonant structure formed by the "tension" created between the mass and the oppositely directed quantized electrical energy of its components defined by the equation E=mc^2.  Additionally because of the dynamic properties of energy/mass discussed above its value will adjust and stabilize around one that defines the optimal resonant structure for those components.

In other words the value of fine structure constant may not be a random feature of our universe but is determine by a dynamic relationship between energy/mass and its quantized components.

However if it is true that the values of all of the fundamental constants are due to resonant property of energy/mass defined by Einstein then, as with the fine structure constant one should also be able to determine the value of the cosmological constant in terms of those resonant properties.

The dynamic relationship between mass and energy describe above tells us that the universe's expansion would form a resonant structure whose fundamental frequency would be determined by the relative strengths of the "tension" associated with the kinetic energy of its expansion and the gravitational contractive forces associated with its mass.  Again this would be similar to how the fundamental frequency at which a guitar string resonates depends upon the tension of its strings.

This means the value of the cosmology constant associated with the universe's expansion may be related to the dynamic resonant properties of energy and mass and not to some random function as is assumed by most of Multiverse theories.

As mentioned earlier Einstein General Theory of Relativity tells us there is a dynamic balance between the universe's gravitational potential energy and the kinetic energy associated with its expansion.  However, not all of the energy associated with that expansion is directed towards it because of the random motion of its energy/mass components.  For example, observations indicate that some stars and galaxies are moving towards not away from us.  Therefore, not all of the kinetic energy present at the time of its origin is directed towards its expansion.

Additionally the equation E=mc^2 which defines the equivalence between mass and energy tells us the kinetic energy of the universe's expansion also posses gravitational potential.

However the law of conservation of energy/mass tells that energy/mass cannot be created or destroyed in a closed environment.  This also tells us since, by definition the universe is closed system the kinetic energy of the universe’s energy/mass cannot exceed its gravitational contractive properties of its mass because Einstein tells us that its kinetic energy is made up of that mass. 

Therefore because some of the kinetic energy of its components is not directed towards its expansion the total gravitational contractive properties of its energy/mass must exceed the kinetic energy of its expansive components. Which means at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as just mentioned not all of its kinetic energy is directed towards its expansion.  Therefore at that point, in time the universe will have to enter a contractive phase.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate.  Therefore they believe that its expansion will continue forever.  However, as was shown in the article "Dark Energy and the evolution of the universe" if one assumes the law of conservation of mass/energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent will eventually exceed its expansive energy associated with dark energy and therefore the universe must at some time in the future enter a contractive phase.)

We know from observations that heat is generated when we compress a gas and that this heat creates pressure that opposes further contractions.

Similarly the contraction of the universe will create heat which will oppose its further contractions.

Therefore the velocity of contraction will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of its contraction.

At this point in time the total kinetic energy of the collapsing universe would be equal and oppositely directed with respect to the radiation pressure associated with the heat of its collapse. From this point on the velocity of the contraction will slow due to the radiation pressure and be maintained by the momentum associated with the remaining mass component of the universe.

However, after a certain point in time the heat and radiation pressure generated by its contraction will become great enough to ionize the remaining mass and cause it to reexpand because the expansive forces associated with the radiation pressure will exceed the contractive forces associated with its mass.

This will result in the universe entering an expansive phase and going through another age of recombination when the comic background radiation was emitted. The reason it will experience an age of recombination as it passes through each cycle is because the heat of its collapse would be great enough to completely ionize all forms of matter.

However, at some point in time the contraction phase will begin again because as mentioned earlier its kinetic energy cannot exceed the gravitational energy associated with the total mass/energy in the universe.

Since the universe is a closed system, the amplitude of the expansions and contractions will drift and stabilize at a specific value corresponding to its resonant frequency similar to how a guitar string drift and stabilize at its resonant frequency

This result in the universe experiencing in a never-ending cycle of expansions and contractions whose frequency would be defined by its resonant properties.

Many cosmologists do not accept this cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed

Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it. This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass.

This would be analogous to the how momentum of a mass on a spring causes it to stretch beyond its equilibrium point resulting it osculating around it.

There can be no other interpretation if one assumes the validity of the first law of thermodynamics which states that the total energy is a closed system is defined its mass and the momentum of its components. Therefore, when one decreases the other must increase and therefore it must oscillate around a point in space and time.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space. Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

If this theoretical model is valid the heat generated by the collapse of the universe must raise the temperature to a point where it energy/mass would become ionized into their component parts thereby making the universe opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow them become deionized.  This Age of Recombination, as cosmologists like to call it is the causality of the Cosmic Background Radiation.

As mentioned earlier the frequency of the expansions and contractions of all resonant systems is defined by their resonant properties.

Similarly the resonant structure created by the contractive properties of universe's gravitational potential and the kinetic energy of its expansion will also have a natural frequency which would be determine by resonant properties.  Like all resonant structures any frequencies that do not correspond to that value will be attenuated.

Therefore the values of the cosmologic constant which would define the rate or frequency at which the universe is expanding or contracting would be determined by the resonant properties of energy/mass define by Einstein.

In other words the value of its cosmological constant may not be randomly chosen but would be defined by the physical relationship between mass and kinetic energy defined by Einstein.

This means one could experimentally quantify and this scenario by using Einstein equations to determine the value of the cosmology constant based on that relationship and see if it agrees with its observed value.

In other words it is not necessary to assume the existence of multiple universes to understand why fundamental physical constants lie within a very narrow range that allows life to develop because their values may not be random chosen but are preordained to have them by a physical property of energy and mass defines by Einstein.

As mentioned earlier many Critics of the Multiverse-related explanations argue that there is no evidence or any way of verifying or falsifying the existence of other universes.

However we can observe and verify the existence of the resonant properties of energy and mass and if want we have said above is true that values all of the fundamental constants in physics are related to those resonant properties them it would be falsified if it was found that the value of even one of them could not be derived using that concept.

179
The Geometry of
antimatter
Jan.  1, 2014

The existence of antimatter was predicted by Paul Dirac when he realized his relativistic quantum theory of an electron yielded up twice as many solutions as he thought he needed. Two of the solutions correspond to the spin-up and spin-down orientations of the electron. So what did the other two solutions correspond to?  He had some ideas of his own, but finally conceded in 1931 that they had to represent the spin-up and spin-down orientations of a previously unknown positive electron.  Dirac had discovered anti-matter.  The ‘positron’, the anti-particle of the electron, was subsequently found in experiments on cosmic rays, formed high in the earth’s atmosphere by collisions involving high-energy particles.

This is because the equation that it not only works for an electron with negative charge, it also works for a particle that behaves like an electron with positive charge.  At first, Dirac did not appreciate the significance of this finding, and even ignored it out of what he would call "pure cowardice".

However he soon realized this meant that every particle has a symmetrical or mirror-image antiparticle with nearly identical properties, except for an opposite electric charge.  And just as protons, neutrons and electrons combine to form atoms and matter, antiprotons, antineutrons and anti-electrons (called positrons) combine to form anti-atoms and antimatter.

Yet this presents a problem because if one assumes particles are three-dimensional objects occupying a four dimensional *spatial*-time environment the only thing they can be symmetrical or "image" against would be the time dimension. 

This is why in Quantum electrodynamics antiparticles are represented as their particle brothers moving backwards in time.

The problem is no one has ever observed time to move backwards.  How then can we justify defining antiparticles in terms of the existence of negative time when it has never been observed?

Additionally the only way to define the asymmetrical or oppositely directed mass component of antiparticles is by assuming they are made up of negative mass because the only term other than mass in relativistic formula that defines its energy or E=mc^2 is squared and therefore is always positive.  However this means that one cannot define the asymmetrical relativistic properties of matter and antimatter in terms of a negative time because in the equation defining it's relation to mass it is squared therefore its energy component must always be positive.  In other words the energy component of a mass moving in both time and negative time will always have the same sign or direction and therefore one cannot use it to define its asymmetrical properties.

Granted some like Richard Feynman have tried to use vectors to define negative energy/mass associated with anti-particles by assuming time moves backwards in them with respect to particles.  However, this methodology cannot define its "reality" in terms of Special Relativity because, as was just mentioned the time component of energy/mass in Relativistic formulas is squared which means that energy must always be positive. 

Additionally even thought the equations of Relativity permit time to move backwards no one has ever observed that to happen.

Some would argue that that is the only way in which one can interpret the mathematical solutions of Dirac's equations.

However, Einstein provided another way of mathematically deriving the asymmetrical relationship between matter and antimatter when he defined the geometric properties of space-time in terms energy/mass and the constant velocity of light because it gave us the ability to define that relationship in terms of the physical properties of a spatial dimension instead of one made of time.

This is because when he used the constant velocity of light and equation E=mc^2 to define its properties he provided a method of converting a unit of space-time he associated with energy to unit of space he associated with mass.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between the time related properties of a space-time universe with the spatial properties of one made up of four *spatial* dimensions.

In other words by defining the geometry of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining the curvature or displacement he associated with energy/mass in a space-time environment to a displacement in a fourth *spatial* dimension

Additionally he showed a curvature in a "surface" of a three dimensional space manifold with respect to time would be equivalent to that surface being curved with respect to a fourth *spatial* dimension

One of the primary advantages of using this process to reformulate Einstein's space-time concepts to its four *spatial* dimension equivalent is that it allows one to understand the asymmetry between matter and antimatter in terms of the observable properties of three-dimensional space.

As was shown above when Einstein define the geometric properties of energy and mass in terms of the constant velocity of light in a space time environment he showed the quantity of energy/mass in a environment can be derived in terms of a curvature of displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as a curvature or displacement in a space-time manifold.  Additionally as was shown in the article #24 “The reality of the fourth spatial dimension” Dec 1, 2007 the magnitude of a displacement in both a space-time environment and one consisting of four *spatial* dimensions defines the quantity of energy/mass it contains.

As mentioned earlier there a two problems with defining the asymmetrical properties of matter and antimatter in terms of time.  The first is no one has ever observed time to move backwards as is assumed in Quantum Electrodynamics and the is that the time component in relativistic formals is squared therefore always positive and therefore cannot be used to define the asymmetrical relativistic properties associated with matter and antimatter.

Yet this would not be a problem if one viewed their properties in terms of four *spatial* dimensions instead of four dimensional space-time because we have all observed that we can move backwards and forwards or in a positive of negative direction in three dimensional space therefore allowing one to derive the asymmetry between mass and antimatter in terms equal but oppositely directed displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

This also means, if this is a valid representation of the "reality" of matter and antimatter that one should be able to mathematically redefine Paul Dirac relativistic quantum theory of an electron in terms of the “reality” of a physical boundary between the third and fourth *spatial* dimension by using Einstein's equations to convert his space-time model to its equivalent one in four *spatial* dimensions.

Another significant advantage to redefining Einstein's space-time geometry to four *spatial* dimension is that would give one the ability derive a physical mechanism for why an antiparticle is created whenever a particle is based on observations of our three-dimensional environment

Classical hydrodynamics tells us if we push down on the surface of water in a closed container it will become displaced.  However, it also tells us that the volume of water displaced by that downward pressure will be offset by an equal but opposite volume displaced in the upward direction.

Similarly if mass is a result of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension any downward displacement in its “surface” will be offset by a equal but oppositely “upward” directed displacement.

However, as mentioned earlier the article #24 “The reality of the fourth spatial dimension” showed one can define all forms of energy/mass in terms of a spatial displacement in a “surface” of a three dimensional space manifold. 

Therefore, according to classical hydrodynamics a particle could not be created without the creation of antiparticles because as mentioned earlier it tells us that when a surface undergoes a displacement an equal but opposite or an asymmetrical one must be created on that surface.

In other words if one forces or creates a depression in the "surface" of a three dimensional space manifold with respect to a fourth spatial dimension associated with the mass of a particle one will also create equal and oppositely directed elevation associated with an antiparticle.

This would define why particle and antiparticle are always created in pairs.

It should be remember Einstein's genius allows us to chose weather to solve all problems, such those presented here or ones associated with Dark matter or Dark Energy (as was done in the articles #174 “The Geometry of Dark Matter“ Oct. 15, 2013 and ”Dark Energy and the evolution of the universe” Oct. 1, October 2012 in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe similar to how Newton laws of gravity broaden domain of Kepler's laws of planetary motion to their moons.

178
The quantum fallacy
Dec. 15, 2013

There can be no doubt that quantum mechanics predicts with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it.

However, Quantum mechanics assumes that our world is fundamentally probabilistic in nature while classical mechanics states that it is deterministic. 

Because of this there are many who feel these two disciplines cannot coexist because classical mechanics assumes that for a given set of initial conditions there can only be one outcome while the probabilistic interpretations of quantum mechanics assumes that there can be an infinite number.

Yet many have used the probabilistic predictions of quantum mechanics to make outlandish claims about the reality of the classical world.

For example because it predicts that there is a non zero probably one can observe a particle anywhere in the universe before an observation or measurement is made, many seemly rational scientists assumes that a particle simultaneously exists in at every point in space and only materializes as a specific point when it is observed.

In Brian Greene book "The Fabric of the Cosmos: Space, Time, and the Texture of Reality" (Kindle Locations 1825-1836) he explains the difference between the probabilistic world of quantum mechanics and the deterministic world of Newtonian mechanics.

"According to Newton, if we knew in complete detail the state of the environment (the positions and velocities of every one of its particulate ingredients), we would be able to predict (given sufficient calculation prowess) with certainty whether it will rain at 4:07 p.m. tomorrow; if we knew all the physical details of relevance to a craps game (the precise shape and composition of the dice, their speed and orientation as they left your hand, the composition of the table and its surface, and so on), we would be able to predict with certainty how the dice will land. Since, in practice, we can’t gather all this information (and, even if we could, we do not yet have sufficiently powerful computers to perform the calculations required to make such predictions), we set our sights lower and predict only the probability of a given outcome in the weather or at the casino, making reasonable guesses about the data we don’t have.

However, as mentioned earlier this does not necessarily mean that one cannot derive the probabilities of a quantum world in terms of the reality of a classical Newtonian one even thought experiments have shown that contrary to what Newton would have expected, identical experiments and starting conditions do not necessarily lead to identical measurements. Instead, our measurements of interaction in the quantum world yield a variety of outcomes.

One of the most fundamental laws of classical mechanics is that each cause has a specific effect and that identical causes will have identical effects.  However it also states that random causes will have random outcomes and that one can determine the probability of a certain event occurring based on the randomness of its cause.

However, this is precisely what we observe in a quantum world in that the outcome of experiments is determined by probability of that outcome occurring.

Yet many feel that one cannot apply the concepts of Classical Newton physics to the quantum world because as Brian Greene points out in his book The Fabric of the Cosmos: Space, Time, and the Texture of Reality (Kindle Locations 1833-1836).

"The probability introduced by quantum mechanics is of a different, more fundamental character (than classical Newton probabilities) Regardless of improvements in data collection or in computer power, the best we can ever do, according to quantum mechanics, is predict the probability of this or that outcome. The best we can ever do is predict the probability that an electron, or a proton, or a neutron, or any other of nature’s constituents, will be found here or there. Probability reigns supreme in the microcosmos."

However that does not mean the mechanism for determining those probabilities is not Newtonian one.

For example if someone strikes a pool ball on a pool table in a dark room and cannot measure or determine initial conditions there is an extremely high probability that he will find it on the table when he turns on the light.  However, he or she does not assume that the balls simultaneously exist on every point on its surface until the light is turned.  Additionally one apply Newton's laws to determine the most probable position of the pool balls after the light was turn on based on the probability of the different initial conditions associated with that event.  I think most would consider someone mentally deficient if he tried to convince us that the pool balls simultaneous existed every at every point on the surface of the pool table when the light off and only materialize when it was turn on just because he could not see how they got there.

Similarly why do some make the outlandish claim that a particle simultaneously exists in at every point in space and only materializes when it is observed based on the fact that they cannot "see" or measure the initial conditions and how they traveled to a specific point in space.

The reason is because quantum probability only deals with evolution or measurement of experimental outcomes and not with the probabilistic properties of their causality.  Therefore, it must assume that there is a non zero possibility that a particle can be anywhere in the universe before it is observed. 

However if that probability is a result of the lack of knowledge or randomness of the initial conditions then the probabilistic properties of the measurements of experimental outcome could be due to the probability of a set of specific initial conditions occurring and how Newton's laws indicate they would evolve.

This suggests the probabilistic outcomes of experiments in the quantum world in may be due our lack of knowledge or randomness initial conditions and not due the randomness of the outcomes of those events.

In other words even though quantum mechanics predicts a particle can be anywhere in the universe before an observation or measurement is made, it does not mean that it only materializes as a specific point when it is observed: it only means that we can never be sure of the single evolutionary path it took to get there because as Brian Greene pointed out in his book  "Fabric of the Cosmos: Space, Time, and the Texture of Reality" we are unable to precisely determine the initial conditions associated with its evolution.

This shows how shifting the probabilistic interpretations of quantum mechanics from measurement or observational aspects of experimental outcomes to their causality would eliminate the need to make the outlandish claims that a particle simultaneously exists every point in the universe while maintaining the integrity of the probabilistic approach of quantum mechanics.

177
The demise of
 the singularity
Dec. 1, 2013

Many physicists assume the General Theory of Relativity predicts that all the mass in a black hole is concentrated at its center in a singularity or a point which has zero volume and infinite density

However the idea it can be concentrated in a non-dimensional point of infinite density with zero volume is a bit hard to grasp even for Einstein whose theory is used to predict their existence.

What makes it even more bizarre is that scientists tell us the laws of physics which they use to predict its existence break down at a singularity.

Why then do many believe that they exist?

The reason is because many believe the mathematics of the General Theory of Relativity tells us that when star starts to collapse after burning up its nuclear fuel and forms a black hole the gravitational forces of its mass become large enough to cause matter to collapse to zero volume.

However even though there is observational evidence for the existence of black holes there never will be any for the singularity because according to the General Theory of Relativity nothing, including light can escape form one.

For example NASA's HubbleSite tells us that "Astronomers have found convincing evidence for a black hole in the center of our own Milky Way galaxy, the galaxy NGC 4258, the giant elliptical galaxy M87, and several others. Scientists verified its existence by studying the speed of the clouds of gas orbiting those regions. In 1994, Hubble Space Telescope data measured the mass of an unseen object at the center of M87. Based on the motion of the material whirling about the center, the object is estimated to be about 3 billion times the mass of our Sun and appears to be concentrated into a space smaller than our solar system."

However as mentioned earlier we will never be able to observe a singularity because they only exist inside black hole.  Therefore to determine its reality we must rely solely on the mathematical predictions of the General Theory of Relativity regarding their formation.

Yet there are some who say that the mathematics used to predict the existence of a black hole also predicts, with equal certainty the existence of singularities.  In other words by verifying the existence of black holes though observations means that we have also verified the existence of singularities.  

However this would only be true if the mathematics used to predict both a black hole and a singularity conform to the conceptual arguments associated with Einstein General Theory of Relativity because the mathematics used to confirm its existence is based solely on them and not on observations as is the case of black holes.

In other words the fact that we can observe a black hole tells us the mathematics used to predict its existence has a valid basis in ideas of General Relativity.

However the same cannot be said about the existence of a singularity because the conceptual arguments found in that theory tells us that we cannot extrapolate the mathematics associated with it to the formation of a black hole.

To understand why we must look at how it describes both the collapse of a star to a black hole and then what happens to its mass after its formation.

Einstein in his General Theory of Relativity predicted time is dilated or moves slower when exposed to gravitational field than when it is not.  Therefore, according to Einstein's theory a gravitational field, if strong enough it would stop time.

In 1915, Karl Schwarzschild discovered that according to it the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a singularity.  He also defined the critical circumference or boundary in space around a singularity where the strength of a gravitational field will result in time being infinitely dilated or slowing to a stop.

In other words as a star contacts and its circumference decreases, the time dilation on its surface will increase.  At a certain point the contraction of that star will produce a gravitational field strong enough to stop the movement of time.  Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

This critical circumference is called the event horizon because an event that occurs on the inside of it cannot have any effect on the environment outside of it.

Many physicists as mentioned earlier believe the existence of a singularity is an inevitable outcome of Einstein's General Theory of Relativity.

However, it can be shown using the concepts developed by Einstein; this may not true.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity.  On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter.  They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect.  "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly.  However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star's surface.  The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped to an observer who remains at fixed circumference to that star.

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star.

Einstein showed that time is dilated by a gravitational field.  Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

This means, as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface.  The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations of an external observer would make using conceptual concepts of Einstein's theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side.  Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star's surface relative to its center.  The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference for both an observer who is at the center of the clasping mass and one who is at a fixed distance from its surface the contraction cannot continue from either of their perspectives.

However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reach the critical circumference.  Therefore, the surface of a star and an observer on that surface will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein's theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing.  Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference.  The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

Therefore, time would be infinitely dilated or stop in all reference that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

However, the contraction of a stars surface must be measured with respect to the external reference frames in which it is contracting.  But as mentioned earlier Einstein's theories indicate time on its surface would become infinitely dilated or stop in with respect to reference frames that were not on it when it reaches its critical circumference. 

This means, as was just shown according to Einstein's concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces.  Therefore it cannot move beyond the critical circumference because motion cannot occur in an environment where time has stopped.

This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

Therefore, based on the conceptual principles of Einstein's theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe but must maintain a quantifiable minimum volume which is equal to or greater than the critical circumference defined by Karl Schwarzschild.

Some claim that the irregularities in the velocity of contractions in the mass forming the black hole would allow it continue to collapse beyond its event horizon.  However Einstein's theories tells us that time would move slower for the faster moving mass components of a forming black hole than the slower ones thereby allowing the them to catch up with their faster moving brothers.

In fact the conceptual arguments presented in Einstein's theories tell us the entire mass of a forming black hole must reach the event horizon at exactly the same time because of time dilatation predicted by his theories.

Therefore assuming the irregularities in the velocity of contractions in the mass forming the black hole would allow it continue to collapse beyond its event horizon is not justified by the conceptual foundations in the General Theory Relativity

This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations that many physicists used to predict the existence of singularities because as has just been shown the mathematical predications made by it regarding their existence is contradictory to its conceptual framework.

In other words just because we have observationally verified the existence black holes which were based on equations created from Einstein's theory does not mean that a singularity at its center is an inevitable outcome of his General Theory of Relativity. 

176
The “reality” of the
 Higgs field
Nov. 15, 2013

The Higgs Boson which was tentatively confirmed to exist on 14 March 2013 appears to confirm the existence of the Higgs field.  Its discovery is pivotal to the Standard Model and other theories within particle physics because it explains why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless, It should allow physicists to finally validate the last untested area of the Standard Model's approach to fundamental particles and forces, guide other theories and discoveries in particle physics, and potentially lead to developments in.

But what does the discovery of the Higgs Boson tell us about the reality of the Higgs field.

This is an import question because its existence is based on abstract mathematical constructs which may or may not describe its reality.  In other words even though they may have predicted its existence it has not yet been connected it to the observable reality of what we can see and touch.

The importance of connecting a theoretical idea to the observable properties of our world was demonstrated by Einstein 200 years after Newton realized that his gravitational theory meant "one body may act upon another at a distance".

"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

However Einstein realized that one can understand how gravity "may act upon another at a distance through a vacuum" by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension environment.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why "one body may act upon another at a distance" by physically connecting it to the reality of what we can see and touch.

However he was unable to tell us what mass is, he was only able tell us how mass interacts with space-time.

As Steven Weinberg said "Mass tells space-time how to curve while space-time tells mass how to move".

This is similar to Newton in that he was able to mathematically define how mass gravitational interacts with other masses but was unable to understand or define a physical mechanism that could account for that interaction.

Einstein was often quoted as saying "If a new theory (such as that associated with the Higgs boson) was not based on a physical image simple enough for a child to understand, it was probably worthless."

In other words to fully understand the theoretical significance of the Higgs Field and why it is responsible for mass one should be able to describe how it interacts with mass in terms of a physical image based on what we can see and touch in our three-dimensional world much as Einstein was able describe how space and time interacted with each other to cause gravity.

However Einstein's and modern scientist's inability to define or derive the casualty of mass in terms of a physical image can be traced to the fact that they chose to define the universe in terms of energy instead of mass.

Einstein told us that a curvature in space-time is responsible for gravitational energy and because of the equivalence been energy and mass defined by his equation E=mc^2 one must also assume that it is responsible for mass.

This suggest that one should be able to learn what the Higgs Field is made up of if one converts or transposes the Einstein's space-time universe which defines field properties of energy in terms of geometry of space-time to one that defines mass of in terms of its field properties.

He gave us the ability to do this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy by the equation E=mc^2 and the constant velocity of light.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy must also have spatial properties.

As mentioned earlier Einstein equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and the mass and energy it contains and when one coverts mass to energy in a closed three-dimensional environment it expands because it would reduce the magnitude of the curvature of three-dimensional space while if one coverts energy to mass, that environment contracts because that would increase its curvature. 

However the fact that he defined the geometric relationship between energy and mass in terms of the constant velocity of light means that one can also quantitatively and qualitatively define a one to one correspondence between the properties of energy in a space-time universe and the properties of mass four *spatial* dimensions.

Therefore one could also say that when one coverts mass to energy in a closed three-dimensional environment that environment expands towards a fourth *spatial* dimension while if one coverts energy to mass their environment would contract with respect to it.

This was the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy including thermo and that associated with mass can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time environment.

However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which the Higgs Field or the field properties of four *spatial* dimension creates mass and why it is quantized in the fundamental particles of the Standard Model in terms of a physical image formed by our three-dimensional environment.

For example one can form a physical image of why mass is quantized, as was done in the article #14 "Why is energy/mass quantized?" Oct. 4, 2007" by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions. This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move in a three-dimension space to one consisting of four dimensional space-time.

(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).

Briefly that article showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension at a frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

This suggest that the Higgs field is made up of the field properties of four *spatial* dimensions and that the magnitude of a mass would be dependent on its geometrical configuration.

If true one should be able to use those field concepts to explain why the mass of corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below grows larger in each successive family.

Family 1

Family 2

Family 3

Particle

Mass

Particle

Mass

Particle

Mass

Electron

.00054

Muon

.11

Tau

1.9

Electron
Neutrino

< 10^-8

Muon
Neutrino

< .0003

Tau
Neutrino

< .033

Up Quark

.0047

Charm Quark

1.6

Top Quark

189

Down Quark

.0074

Strange Quark

.16

Bottom Quark

5.2

As mentioned earlier the article #14 "Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article #23 “Defining energy" showed that one can derive the energy or temperature of an environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the "surface" of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article #14 "Why is energy/mass quantized?” but also on temperature or energy of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family." is because of an interaction between the resonant properties defined in the article #14 "Why is energy/mass quantized?” and the mass content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative "separation" in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "separation", with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the "separation" associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial "separation" associated with the second family.

Additionally the corresponding particle types across the three families have "identical properties" because as shown in the article #55 "The geometry of quarks" Mar. 15, 2009 they are related to the orientation of the "W" axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the "W" axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why "The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the field properties of four *spatial* dimensions.

This shows how one can use the field properties of four *spatial* dimension or the Higgs Field to understand the causality of the masses of the fundamental particles in the Standard model in terms of a physical image based on the reality of what we can see and touch in our three dimensional environment.

However assuming the Higgs Field is created by the geometry of four *spatial* dimensional allows one to understand the dynamics of the mass of the Higgs boson in same terms as the fundamental particles defined above.

As mentioned earlier the article #14 "Why is energy/mass quantized?” showed that one can derive the total mass of all particles in terms of the sum of energy contained within a resonant system generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the energy associated with displacement in the "surface" of three-dimensional space associated the environment it is occupying.

However if one assumes as was done above the Higgs field is created by a spatial displacement in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can conceptually understand how it interacts with space to create its potential energy in terms of the physical image formed by water in a dam. This is because the potential energy of water is defined by its spatial separation with respect to the bottom of a dam.  Therefore according to the above theoretical model, the potential energy or mass contained in the Higgs boson would be defined by its spatial separation in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words it gives one the ability to define the energy and therefore the mass of the Higgs bosom and where it should be located in an environment consisting of four *spatial* dimension in terms of the physical image of water in a dam.  This is because as mentioned earlier the potential energy of water in a dam is solely dependent on the height of the dam while that of the Higgs Boson would be dependent on magnitude of the spatial separation of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.

This shows how it is possible to understand the reality of the Higgs Field in terms of a physical image by reformatting (as was done in the article #173 “Reformulating space-time” Oct 1, 2013) Einstein General Theory of Relativity in terms of four *spatial* dimensions.

It should be remember that Einstein's genius allows us to chose weather to view the reality of the Higgs Field, Dark matter (Oct. 15, 2013) or Dark Energy (Mar. 1, 2013) in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

175
The role of reality in science
Nov 1, 2013

What is the connection between imagination and reality?  This question is particularly relevant to scientists because they are tasked with defining theoretical models to describe the reality our world.

The problem exists because by definition reality is independent of the mind and any abstract mechanism it can create concerning. Therefore only way we can be sure the theoretical models created by the imagination have any connection to reality or physicality of the world we see and touch is by connecting it to what we can see and touch. 

This would be true even though they make accurate predictions of all observable events in the environment it describes.

For example Quantum theory makes extremely accurate predictions of particle interactions based on mathematically generated probability functions.   However it also tells us that particles do not exist until a conscience observer looks at them.  In other words it is tells us that reality is completely dependent on the mind because it assumes the act of observation by the mind creates the physical reality of the particle world.

However this also it means there can be more than one reality because if it is completely dependent on the mind each individual mind can create one suited to its needs.

This presents a problem for science because as mentioned earlier it is tasked with defining a unique existence or set of facts describing the world in which we live.

However if existence is only defined by the mind as quantum mechanics suggests then identifying the unique existence of our world would be impossible because each mind can contain a different one.

In other word unless there is a way of physically connecting what our minds perceive existence to be to the observable world we live in, science cannot be sure that is has chosen the correct set of facts to define its existence no matter how accurate its prediction might be.

Granted the mind can systematical quantify the natural world as quantum mechanics does very well.  Yet it cannot tell us anything about the reality of how that quantification takes place.

For example there are an infinite number of ways one can mathematically describe the fact that there are two apples on a table. One can predict why based on the assumption that there were originally four apples and two were taken away or assume that originally there were six and four were taken away.  However if there only four apples to begin with the mathematical description using six apples even though it accurately quantifies the existence of the two apples it does not describe their world because in "reality' that world did not contain six apples.

Similarly just because quantum mechanics can very accurately predict the quantitative observation of the particle world does not mean that it defines its reality.

Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

He realized for science to make a claim that they have organized the natural world into a single set of patterns or laws that describes its reality they must be able to physically connect the independent models developed by our minds and imaginations to the world that exists outside of it.

For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

However Einstein realized he could explain this by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold to explain how gravity "may act upon another at a distance through a vacuum" in terms of a curvature in space and time.   This allowed him to understand the "reality" behind gravity based on a physical image formed by the reality of what we can see and touch in our three-dimension world.

In other words he was able to connect the world he created in his mind and imagination to the "reality" of our three dimensional environment in terms of a physical imaged formed by the observable properties of our three dimensional world.

Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Einstein.  They chose to look for reality only in terms of abstract mathematics instead of the physical imagery given to us by the reality of what we can see and touch.

One reason may be because it is easier to alter an abstract mathematical environment to conform to an observational inconsistency than it is to alter one based on physical imagery. 

For example Quantum theory makes predictions based on the random properties of a probability function.  However because its abstract properties are not connected to any physical images of our world all observations no matter how inconsistent they are with the physical world it is describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in our three-dimensional environment physically connects it to a four-dimensional space time-environment

For example a mass that was repelled by gravity instead of being attracted by it would contradict the physical model define by Einstein and would be extremely if not impossible to explain according his model because that would mean that we should observe objects rolling up hill in our three-dimensional environment.  In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses gravitational repelling each other impossible to incorporate into it.

If however if some observation happened to contradict the complimentary principal of quantum mechanics such as simultaneously observing both the particle and wave properties of mass it could easily explained in terms of the fact that its probability functions tell us that anything that can happen eventually will.  This makes it impossible to find an observation that would contradict it because it tells us the even the impossible is possible if we wait long enough.  However this can only happen in an abstract environment which is not bound by the physicality of our observational world because in that world we observe that some things just cannot happen.

But why should science put in the effort to understand the physical reality of our world when both the abstract mathematical foundation of quantum mechanics and the physics imagery of Einstein's theories make very accurate predictions of future events based on the past. 

Because the mission of a science is to define reality which can only be done in terms of what we perceive in the world around us which is not, by definition abstract.

174
The Geometry of Dark Matter
Oct 15, 2013

In 1933 Fritz Zwicky a Swiss astronomer, was trying to measure the mass of a galactic cluster using two different methods. First he tried to infer it from the rational speed of the galaxies around the center of the clusters.  Just like kids on a merry-go-round have to hold on to avoid being ejected, galaxies are held together in a spinning galactic cluster by the gravitational force provided by the matter it contains because if there were not enough matter to create this force, the galaxies would simply scatter.

He then compared his result with the mass evaluated from the light the galaxies shed. He realized that there was way more matter in the cluster than what was visible or baryonic matter. This matter of an unknown type generated a gravitational field without emitting light; hence its name, dark matter.

Further observations suggest the baryonic or visible forms of matter in the universe only comprise approximately 5 to 10% of the mass required to account for the total gravitational energy in the universe.

However, the fact that 90 to 95% of the mass of the universe is invisible or "Dark" even with the recent advancements in particle detection technology suggests that it may be made up some else.

Einstein's may have given us a clue as to what this could be when he defined gravitational forces and the quantity of mass in a give volume of space-time in terms of a displacement or curvature in space-time and not in terms of the particle or physical properties of mass.

This means the additional mass over and above that associated with the visible matter Fritz Zwicky measured in 1933 may be related to geometric property of space-time and not to the particle properties of baryonic or visible mass.

However it is easier to understand why if one reformulates his space-time theories in terms of four *spatial* dimensions.
 
(The reasons will become obvious later.)
 
Einstein gave us the ability to do this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 and used the constant velocity of light to define that balance because it provided a method of converting a of space-time he associated with energy to unit of space he associated with mass.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

As mentioned earlier Einstein define the magnitude of gravitational forces and quantity of mass in a given volume of space terms of the slope of a curvature or displacement in geometry of space-time.

However by reformulating his theories in terms of four *spatial* dimensions gives one the ability to analyze the gravitational forces associated with galaxy formation in terms of their spatial instead of their time or space-time properties.

For example most astronomers believe that there is a supper massive black hole at the center of most galaxies.  This belief is based on the fact that the General Theory of Relativity tells us that when a large mass such as that found many galactic center occupy a small enough volume it will cause space-time to curve back in on itself essentially separating it from the rest of the universe, making it impossible for anything even light to escape from it.

The General Theory of Relativity tell us the same thing would happen in a universe consisting of four *spatial* dimensions because, as mentioned earlier when Einstein used the constant velocity of light to define geometric properties of space-time he provided a method of converting the curvature in a space-time manifold he associated with gravity to one in four *spatial* dimensions.

Therefore according to Einstein a Black Hole would be present in the center of most galaxies in a universe consisting of four *spatial* dimensions for the same reason it would be present in a universe made up of four dimensional space-time because three-dimensional space would curve in on itself with respect to a fourth spatial dimension similar to how the two-dimension surface of a soap bubble curves in on itself essentially separating its contents from its external three-dimensional environment.

However what makes the gravitational field of a galaxy different from that of a black hole, star or planet is that it is distributed of a larger volume of space.  

In other words the gravitational field of a black hole, star or planet has a direct line of action towards its center while the gravitational field of a galaxy is distributed over an volume the size of its disk even though its line of action of the gravitational field of its individual stars is towards the center.

Einstein's equations, when reformulated in terms of their spatial properties tells us the spatial distribution of the gravitational fields of the individual stars in galaxies would increase their combined gravity potential and therefore the total mass of their galaxies over and above that which is associated with their baryonic or visible mass.

One can understand why by using the example of the curvature created by a marble on a rubber sheet.

In that example the curvature created in its surface gives a three-dimensional representation of a curvature in the surface a four dimensional space-time.  Additional it allows one to visualize the effects of gravity has on a mass moving through it by watching how the path of a marble is bent as it moves along its curved surface. 

In both cases these examples assume that all of the gravitational forces associated with the masses on the diaphragm are focus on a point in the center of the diaphragm.

However this does not accurately describe the gravitational fields associated with spiral galaxies because as mentioned earlier their rotational energy causes it to occupy a spatially extended region around its center.

Again one can understand the significance of the flattening of space caused by their rotational energy has on their total gravitational potential by using the example of a marble on a rubber diaphragm. 

But instead of using one marble one would have to use many to represent the individual stars.

As mentioned earlier the rotation energy of the individual stars in galaxies causes its gravitational field to be extended or flattened with respect to its center.

However Einstein told us that the magnitude of a curvature in space defines the magnitude of the gravitational forces and therefore the total mass of objects.

Therefore to be valid representation of the gravitational forces in a galaxy one would have to analysis what the flattening of the bottom of the displacement in the diaphragm does to the magnitude of the slope of the curvature in its surface.

If one flattens the distribution of the marbles around their original focal point while keeping their overall depth the same as it was before that flattening occurred the slope in sides of the displacement would be significantly steeper than it would be if no flattening had occurred.

Similarly because of the *flattening* of space by the rotation energy of the individual stars in galaxies the magnitude of the slope of the displacement in the "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension associated with gravitational forces would be greater than it would be if one only viewed the sum of that associated with the individual stars.

However, as mentioned earlier Einstein define gravitational force and the quantity of mass in a given volume of space in terms of the magnitude of a curvature in space.

Therefore, one would measure the total gravitational potential and mass of a galaxy or galactic cluster to greater than that associated with the individual stars or visible baryonic matter they contain.

Additionally because the gravitation potential due to spatial flattening of space-time would be cumulative and linear with respect to the distance from the galaxy's center the gravitational forces experienced by each star orbiting it would increase as its distance from the center does.  This also means that there should be linear relationship between a stars distance from the center of a galaxy and its orbital velocity.

In other words Einstein predicted the existence of Dark Matter when he defined gravitational potential in terms of a geometric property of space-time.

However this means that some of the gravitation potential associated with Dark Matter in galaxies galactic clusters and supper clusters and the recently observed dark matter web may not be due to baryonic matter but to the distortion or flattening of in space-time caused by their rotational energy.

One could observation verify the above hypothesis by determining the ratio of Dark matter to the orbital dynamics of galaxies.  If it is found that spiral galaxy have a larger ratio of dark matter to visible matter than globular clusters it would suggest that flattening of space does contribute the total gravitational potential in of a given volume of space.  This is because the rotational velocity of stars in spiral galaxies would have a slightly greater flattening effect on space than globular ones.

Another way of observational verifying this hypotheses would be to determine where the gravitational nodes would be located in the space between galactic clusters and determine if they match the patterns associated with the dark matter web.  If it does it would go a long way in confirming it.

However one must remember that the effects of even a small distortion in the fabric of space-time will be amplified by the fact that it would attract and therefore harbor a larger portion of dust than areas of space-time that are not distorted.  This would amplify the gravitational potential within the space-time distortion over and above that associated with the distortion alone.

It should be remember Einstein's genius allows us to chose weather to solve problems, such those associated with Dark matter or Dark Energy (as was done in the article #173 " Reformulating space-time" Oct 1, 2013) in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe similar to how Newton laws of gravity broaden domain of Kepler's laws of planetary motion to their moons.

173
Reformulating space-time
Oct. 1, 2013

History has shown the advantages to reformulating or expanding an existing theory or law to a wider environment.

For example Kepler's Laws are wonderful as a description of the motions of the planets.  However, they provide no explanation of why the planets move in that way.  Moreover, Kepler's Third Law only works for planets orbiting the Sun and does not apply to moon's orbiting around the planets.

However 1686, Isaac Newton presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" which provided a more general explanation Kepler's laws and allowed them to be applied not only to of the motions of the planets but also to those of their moons.

This is primarily because Kepler developed his laws directly from the quantitative observational records given to him by Tycho Brahe and did not attempt to generalize them.  Additionally he was unable or did not try to understand why those numbers appeared in nature but only to find a way of making the fit them into the consistent mathematical structure we now call Kepler's laws.

However Newton was able to reformulate them by defining a gravitational mechanism that not only provide a theoretical understanding of their validity but also expanded, as mentioned earlier their domain to a much broader environment.

There are many aspects of modern physics that might gain the same benefits from the reformulation of existing ideas.

One in particular would be Einstein theories because it may allow one to derive a theoretical understanding of the casualty of Dark Energy and what Dark matter is.

Dark Energy or the mysterious force that is causing the accelerated, spatial expansion of the universe does not appear to be integrable into any of the currently accepted theoretical models of our universe.

This is true even though Einstein foresaw its existence when he used his intuition to arbitrarily insert a term, called a cosmology constant into his General Theory of Relativity that would create an expanding force very similar to that of Dark Energy.  Similar to Kepler he based this addition only on the observational records of his time that suggested space was static and unchanging and not on any theoretical principal.  Additionally like Kepler he either could not or did not try to integrate it or explain why it exists in terms of a theoretical model.

However there are some who feel that we may be able to use his intuitive genius and the concept laid down in his space-time theories to understand the causality of spatial expansion associated with Dark Energy even though Einstein called the insertion of his cosmological constant "His big blunder" when it was discovered that the universe was not static.

As mentioned earlier Einstein either could not or did not try to conceptually integrate his cosmological constant or an expansive force now called Dark Energy into the theoretical structure of Relativity possibly because, as mentioned earlier they are both related to how three-dimensional space expanded or was prevented from contracting with respect to a higher spatial dimension not a time or space-time dimension.  
 
Therefore to understand Dark Energy in terms of Einstein space-time theory one would have to add a new *spatial* dimension to the three that it already contain to define its spatial properties thereby significantly increasing the complexity of its theoretical structure. 

This would be true if Einstein had not given us the ability reformulate his space time theories in terms of four *spatial* dimensions when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

As was just mentioned Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

As mentioned earlier it is difficult to integrate and define the causality of why three-dimensional space is expanding towards a higher *spatial" dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However one can easily integrate it into one consisting of four *spatial* dimensions because of the fact that it would allow three-dimensional space to expand toward a higher fourth *spatial* dimension.

In other words if one reformulates Einstein's equations and quantitatively defines energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space-time environment one can understand how the observed spatial expansion of three-dimensional space associated with Dark Energy can occur.

We know from the study of thermodynamics that energy flows from areas of high density to area of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article #23 “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it.

This shows how reformulating Einstein space-time concept in terms of four *spatial* dimension can provide a theoretical understanding of the accelerative force called Dark Energy which can be generalize to broader environment than a space-time universe.

For example observations tell us that five to seven billion years ago, the expansion of the universe stopped slowing due to gravity and started to accelerate due to Dark Energy.

However this is exactly what one would expect if the theoretical model outlined above was correct because in the early universe the distance between it mass components was small relative to the its energy components.   Therefore gravitational forces would predominate.  However because gravitation force decease with the square of the distance there would come a time when the expansive forces associated with Dark Energy  would be predominate because they would, according the above model decease linearly with respect to gravities.

This shows why reformulating Einstein's space-time universe into one of four *spatial* dimension allows it to be applied to a more broader more generalized environment and provide a theoretical understand of why we presently observed the expansive forces of Dark Energy overtaking the slowing force of gravity.

It should be remember Einstein's genius allows us to chose weather to solve problems, such those associated with Dark matter or Dark Energy in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe similar to how Newton laws of gravity broaden domain of Kepler's laws of planetary motion to their moons.

172
Gravity or dark energy:
which one will win?
Sept 15, 2013

Before the discovery of Dark Energy cosmologists had two models of how the universe's expansion would end.

In first scenario, there would be enough matter in the universe to slow the expansion to the point where, like the baseball, it would come to a halt and the gravitational forces associated with it would result in it retracting causing it to crash together in a "Big Crunch."

In the other scenario, there would be too little matter to stop the expansion and everything would drift on forever, always slowing and slowing but never stopping. This would end in a vast, dark, and cold state: a "Big Chill," as the stars faded and died out.

However the discovery of Dark Energy or a force causing the accelerated expansion of the universe opened up the possibility that the galaxies, solar system, stars, planets, and even molecules and atoms could be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.

Most scientists would agree that the best way of determining which one these scenarios defines its ultimate fate would be to list all of the observations regarding the forces controlling its expansion and try to understand them based on the most successful theories we have regarding the macroscopic properties of energy/mass.

For example it is assumed by many that because space is everywhere, the force called Dark Energy is everywhere therefore its effects should increases as it expands.  In contrast, gravity's force is stronger when things are close together and weaker when they are far apart.  Therefore many believe the expansion will continue at an ever increasing rate, eventually ripping space apart.

However if one views the observational evidence supporting the existence of Dark Energy in terms of the laws of thermodynamics and Einstein's theories, it strongly suggests that it will weaken not increase as space expands and that eventually gravity will become the dominate force in our universe.

Observations of the expansive force called Dark Energy tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein's theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is  the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier it is difficult to integrate the causality of how three-dimensional space can be expanding towards a higher *spatial" dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy integrate it if one reformulates it, as was done above in terms higher fourth *spatial* dimension.

Yet it also allows one to understand how and why the expansive force called Dark Energy is causing the spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use his equations to qualitatively and quantitatively define energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space-time environment.

We know from the study of thermodynamics that energy flows from areas of high density to one of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article #23 “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surrounding it and that the force associated with that expansion will decline as it expands.

This shows how reformulating Einstein's theories in terms of four spatial dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of the Einstein's theories.

As mentioned earlier many feel that because space is everywhere, the force called Dark Energy is everywhere, and its effects increase as space expands. In contrast, gravity's force is stronger when things are close together and weaker when they are far apart.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because similar to the water in a collapsed pool the accelerative forces associated with it will decline as it expands. 

Yet, because the mass of the universe remains constant through its history the gravitational potential associated with it will also.  Therefore the gravitational contractive forces associated with it will exceed the expansive forces associated with dark energy even though it components may be separated by extremely large distances because as just mentioned the force associated with dark energy will decease relative to gravity as time goes by.

However the equivalence between mass and energy defined by Einstein tells us that energy also posses gravitational potential.

Therefore, just after the big bang when the concentration of energy and mass was high, gravitational force would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands the its gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe. 

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.

This means that eventually gravitational forces will win because, as mentioned earlier thermodynamics tells us the total accelerative forces associated with Dark Energy will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

Therefore. gravity will eventually win the battle with dark Energy because as was just mentioned the forces associated with it approach zero as the expansion progress while those of gravity remain constant.

There can be no other conclusion if one accepts the validity of Einstein's theories and the laws of thermodynamics because the theoretical arguments presented are a base solely on their validity.

171
The Mysticism of a
non-dimensional particle
 Sept. 1 2013

Scientist especially physicists should always remember that describing reality is different from defining it because history has shown that it is possible to accurately define or quantify an environment in terms of the mystical properties of a non-existent entity.

In other words even though one can find equations to accurately quantify or define an environment does not mean that they have found an valid explanation as to how and why it is what it is.

For example both Quantum Mechanics and the Standard Model of Particle Physics define and quantify the environment of particles in terms of what could be considered the mystical properties of a non-dimensional mathematical point.

Mystical in the sense that the definition of mysticism as being or having vague speculation: a belief without sound basis could be applied to it.  This is because by definition no one has or ever will be able to observe the non-dimensional mathematical point they use to define a particle therefore we do not have an observational and therefore a sound basis for assuming its existence.

Most who have study the history of science are aware of the fact that many medieval and Renaissance astronomers assumed the planets were imbedded in rigid celestial spheres whose movement was guided celestial intelligences, souls or impressed forces.

Today many would classify that concept as being mystical because there is no observation evidence to support the assumption that the motion of the planets is control by some form of intelligence.

However many modern scientists would disagree with the assertion that a non-dimensional particle has similarities to the mystical ones we now associate with the Renaissance astronomer's celestial intelligences by pointing to the fact that it permits them to accurately quantify its environment within the limit of our modern observational capabilities.

Yet the same argument could and most probably was used by them to justify their belief in idea that a celestial intelligence were guiding the planet because it also permitted them to accurately define and quantify the orbital environment of the planets within the limits of their observational capabilities.

The Standard Model of particle physics uses the concept of point particle only because it makes its mathematical description of their properties possible.   However it assumes that a point is appropriate representation of any object whose size, shape, and structure are irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object.

While Quantum Mechanics derives the world of the very small in terms of the probability function based on mathematical representation of particle as a non dimension point for reason similar to why the standard model does.  In other words the only way to define the position of a particle in terms of a probably function is buy assuming that it does not have any spatial properties.  Therefore it also assumes that it size, shape, and structure are irrelevant in a given context.

Unfortunately for the proponents of Quantum Mechanics the concept of a point particle is complicated by the Heisenberg uncertainty principle, which tells us even in the domain of quantum mechanics an elementary particle, with no internal structure, occupies a nonzero volume because of the uncertainty involved in determine the exact point where it is located in space.

As mentioned earlier both of these theoretical models assume that non-dimensional point is an appropriate representation of a particle because its size, shape, and structure are irrelevant in a given context.

But what if it is relevant?

For example what if the Heisenberg's Uncertainty Principle which asserts there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known is related to the spatial extension of a particle and not to its point properties as quantum theory assumes.

As was shown in the article #14 "Why is energy/mass quantized?" Oct. 4, 2007 it is possible to understand the quantum mechanical properties of energy/mass in terms of an extended object by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four *spatial* dimensions.

The existence of four *spatial* dimensions would give three dimensional space (the substance) the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.

However, it did not explain how the spatial boundaries or volume of these resonant structures is defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the "box" containing the resonant system the article #14 "Why is energy/mass quantized?" associated with a particle.

The mathematics of Quantum mechanics support the assumption that a particle occupies a finite volume berceuse it defines the smallest possible unit of space and increment of energy in terms of Planck's length "h" while defining the size of an individual quantum of force in terms of the equation E = h c / L. 

As mentioned earlier both the standard model of particle physics and quantum mechanics assume that a point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context.

However, even though the size and shape of a particle may be irrelevant to someone looking at it from the macroscopic perspective of a human observer it may be very relevant to the process and mechanisms reasonable for what a human observes.

For example if one assumes, as quantum mechanics does that a particle is a non-dimensional point then according to the above concepts there would be an uncertainty in determining its position because that non-dimensional point could be found any with the volume of the three-dimensional "box" mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of the movement of a one dimensional point.  Before one could determine a particle's momentum one would have to know its exact position in the box at the "end" points were one measured its velocity.  However, as mentioned above that one dimension point representing a particle could be found anywhere in the box containing the resonant structure that define a particle in the article #14 "Why is energy/mass quantized?"  Therefore one could not determine its exact velocity and therefore its momentum because there will always be an uncertainty as to where in the box the one dimensional that represents a particle is relative to the dimensions of the "box" when a measurement is taken.

Classical mechanics uses also uses the existence of a point at the center of mass to calculate the position of an extended object and to predict how it would interact with other objects in a gravitational field.  Similar to quantum mechanics it assumes that the object position can be determined by measuring it from a point defining its center because from a distance they feel it gives them an appropriate representation of the size, shape, and structure of the object. 

Therefore they can define the position of an irregular shaped object such as an asteroid by determining the distance from that point to whatever reference point they chose.

However Classical mechanics accepts the fact that there are limitation to the concept of using the center of an object to predict its position and how it will interact with other objects because as the resolution of the measurements increase or distance between decreases between it and the measure device it accepts the fact that the object shape has an effect on those measurements.

Similarly fact that Quantum mechanics tells us the individual quanta of energy/mass have a spatial extension defined by the equation E = h c / L means that there would always be an uncertainty in determining its position related to its shape because as mentioned earlier the resonant structure defining its particle properties is made up of the dynamic components of a matter wave and therefore there would be a predictable randomness when interacting with a measurement device.

Therefore on a quantum scale the size, shape, and structure of a particle would be relevant in determining a particle position.

In other words one could derive the Uncertainty Principle in terms of a classical environment if one assumes that a quantum object has a spatial extension and that its "surface" is irregular in shape as it observed wave properties suggest.

This shows how one can not only mathematical describe the quantitative "reality" of a particles environment but also define how and why we observe them to interact the way we do based on the observable and therefore the verifiable properties of a three-dimensional environment instead speculating on the existence of an unobservable non-dimensional particle.

As mentioned earlier Scientist especially physicists should always remember that describing reality is different from defining it.

170
Can Mathematics
Define Reality
Aug. 15. 2013

Is there such a thing as mathematical reality?

All forms of mathematics are abstract by definition.  However scientists feel that it can be used to extract, by quantification the underlying essence of a physical environment and thereby eliminate any dependence on real world objects with which it might originally have been connected.

Many of our most successful theories began as a mathematical study of real world problems.  In other words scientists attempt to use mathematics to quantify real world environments and to establish the underlying rules that govern them.

However the fact that one can mathematically quantify an environment does not mean that they accurately defined the "reality" of the rules that govern it.

For example, Isaac Newton made qualitative observations of how objects in a "real world" environment interacted with the earth's gravitational field.  He then used the understanding develop form those observations and his knowledge mathematics to derive a theoretical model that could not only quantity them but also explain the rules as to why they interacted the way they did in terms of those observations. 

In other words he was able to provide a direct physical connection between the abstract properties of his mathematics and how the components of his environment interacted through his observations. 

However, with the advent of higher mathematics and advance computing technology physicists now have to ability to define "reality" of what we observe in purely abstract mathematical terms. 

For example, String Theory is based purely on mathematically analyzing the quantitative observation of the real world and then, using only that information defines its reality.  In others words they not only define the quantitative properties of the environment but also the rules for why its component interact in terms of abstract mathematics without physically observing how those interactions are taking place.

Therefore, String Theory does not and cannot provide a physical connection to the observable universe because its description is based purely on abstract properties of mathematics and not on the physical observations as Isaacs Newton's were, of how its components interact to form the environment they are describing.

These two different approaches to theoretical philosophies are called Empiricism and Realism.

On the surface they both to be appear to be viable methods for defining the rules that governing our observable environment even though their methodologies are different.

This is because Empiricists say that our theoretical models should only be concerned with the quantifiable properties of observations while the Realist tell us that our theories should not only make accurate quantitative predictions of an environment but also allow us to understand why nature behaves the way it does based on the observable properties of the environments they are describing.

For example empiricists feel that as mentioned earlier science should only be concerned with quantifying observations and that they should only be tested against the quantifiable properties of the natural world.  In other words they are not interested in or feel that it is important to integrate the observations of how objects interact in the "real world" to create our observable environment. This is the attitude most string theorist take because they attempt to define not only observations but why the nature world behave the way is does in terms of the abstract properties of mathematics.

Realists, on the other hand believe that science should not only be concerned with quantifying experiences but also explaining why the natural world behaves the way it does based on observations.  In other words they feel that mathematics should not only be used to quantity an environment but should also explain why object in the "real world"  interact the way we do in terms of the observable properties of that environment. This, they feel would give the underlying essence of a physical environment developed by mathematics a stronger tie to its reality.

For example, Einstein who some would call a realist first developed a conceptual understanding of space-time, based, in part on the observation that the speed of light was constant in all reference frames.  However unlike the Empiricists he then developed the theoretical structure of Special Relativity by forming a physical image of what it would be like to chase after a beam of light based on observable properties of the "real world" and then translating or transposing that understanding to define how and why matter and energy in motion would interact in a space-time environment.  Later he developed the equations that quantified and verified the accuracy of his conceptual model based on observations of speed of light in the natural world.

However, the proponents of Empiricism take the opposite approach to science.  They observe the quantitative results of observations and then, through trial and error define a series of abstract equations, which can accurately predict them.  They then use those equations to define a theoretical structure which then predicts the reality or rules governing the underlying essence of that environment.

For example, Quantum Theories, which espouses the empiricist approach defines the observations of the quantum mechanical environment of energy/mass based solely on mathematical probability functions or equations.  They then use those abstract equations to not only quantify those observations but to define the rules which govern of the environment they occupy.

However this circular method of predicting both observations and operating environments based on only on mathematics does not allow one to determine the physical reality of the environments they define because those mathematically created environments are by definition abstract and therefore are independent of the physical world they are defining.

But is there a way science can verify when a mathematical created environment defines the underlying essence of the "real world" when as just mentioned they are by definition abstract and therefore do not have a direct "physically connect" to it.

The realist answer to this is to connect the abstract environments created by mathematics as Newton and Einstein did to the physical environment they are defining though observations.

For example Quantum theory makes predictions based on abstract mathematical world of a probability functions.  However because its abstract properties are not connected to any physical images of the "real world" all observations no matter how inconsistent or bazaar they are can be incorporated into it.

This is in sharp contrast to the space-time environment defined by Einstein because he, as mentioned earlier developed the theoretical structure of a space-time environment based on a physical image of what it would be like to chase a beam of light in the real world. This not only gives the abstract properties of his mathematics a physical connection to the real world it also give science a way of checking its conceptual validity.

For example Einstein's theory would be invalidated if it was found that something could travel faster than the speed of light because that would contradict the physical model he define.

If however if some observation happened to contradict principals of quantum mechanics such as simultaneously observing of both particle and wave properties of mass it could easily explained of in terms of the fact that its probabilities functions tells us that anything that can happen will eventually happen.  However it is impossible to find any observation that would contradict the fact that anything can will and must happen at some time in the future. 

Yet this can only happen in an abstract environment which is not bound by the physicality our observational world because in that world we observe that some things just do not happen.

But why should science put in the effort to understand the physical reality behind our "real world" when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein's theories make very accurate predictions of future events based on the past. 

Because the mission of a science is to define reality in terms of what we perceive in the world around us which by definition is not abstract.

169
Thomson’s double slit
 experiment in
 four spatial dimensions

Richard Feynman the farther of Quantum Electrodynamics believed Thomson's double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability.

The wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.  Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

However it may be possible to understand it in classical terms if one assumes the universe is composed of four *spatial* dimensions instead of four dimensional space time.

(The reason will become obvious later)

The double slit experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes the light waves passing through both slits to interfere, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light is always found to be absorbed as discrete particles, called photons.

When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detailed.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygens–Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

It is a widespread misunderstanding that, when two slits are open but a detector is added to determine which slit a photon has passed through, the interference pattern no longer forms and it yields two simple patterns, one from each slit, without interference.  However, there ways to determine which slit a photon passed through in which the interference pattern will be changed but not be completely wiped out.  For instance, by placing an atom at the position of each slit and monitoring whether one of these atoms is influenced by a photon passing the interference pattern will be changed but not be completely wiped out.

However the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.  This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

Yet as mentioned earlier one can derive the fact that a photon exhibits both the characteristics of a particle and wave in terms of classical concepts by transposing or converting the space-time geometry of relativity to one of four *spatial* dimensions and the spatial properties quantum mechanics associates with its energy.

Einstein gave us the ability to do this when he used he used the velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein's equations to qualitatively and qualitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases of assuming as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

However it also allows one to understand the wave particle duality of photon and all other particles as is demonstrated in Thomson's double slit experiment in terms of the concepts of classical physics.

For example the article #14 "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the concept developed in the article #23 “Defining energy?” to explain and understand the physicality of the wave properties of all particles including a photon by extrapolating the laws of classical resonance in a three dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in a matter wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four spatial dimensions.

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for its quantum mechanical properties.

However, it did not explain how the boundaries of a particle’s resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric spatial boundaries of the resonant system associated with a particle in the article #14 "Why is energy/mass quantized?"

This provides the ability to understand, in classical terms the inseparability of the wave-particle duality of energy/mass because clearly demonstrates how the one is dependent on the other.

Briefly it shows the reason why the interference patterns remains in Thomson's double slit experiment when one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as mentioned earlier it is made up of a resonant system or "structure" therefore it occupies an extended volume which is directly related to the wavelength of its particle system.

This means a portion of a particles energy could simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern. 

It also explains why the interference pattern disappears, in most cases when a detector is added to determine which slit a photon has passed through.  The energy required to measure which one of the two slits its energy passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit   Therefore, the energy passing thought that slit will not be able to interact, in most cases with the energy passing through the other one to form an interference pattern on the screen.

However it also explains why, as was mentioned "there are ways to determine which slit a photon passed through that will cause a change in the interference pattern but will not completely wiped it out.

The fact that the interference pattern can still occur even if a measurement is made is because if the energy passing through one of the two slits is altered by a relatively small amount compared to what it originally was, classical wave mechanics tells us it will be able to interact to form a slightly different resonant system with a slightly different interference pattern on the other side than would be the case if no measurement was taken.

It should be pointed out that the fact that an interference pattern can be observed when a detector is added is a direct contraction of the Copenhagen interpretation of quantum mechanics.  It demands when a detector is added to the experiment to determine which slit a photon has passed through the interference pattern can no longer form.

However, this also means there should be a quantifiable minimum value of interaction between a measuring device and a photon that will permit the interference pattern although somewhat altered to be reestablished on the other side after measuring which slit the photon passes through.

It also defines in classical terms  the reason, why the measurements of energy/mass takes the form particles and not waves in Thomson's double slit experiment

As mentioned earlier, the article #14 "Why is energy/mass quantized?" showed energy must be propagated through space in quantized resonant systems if one applies the concept of classical mechanics to a matter wave on "surface" of a three-dimension space.  Therefore, because its energy must be propagated through space to be observed the energy impacting the screen will have the discrete non-wavelike characteristics of a particle.

Richard Feynman the farther of Quantum Electrodynamics or "OED" realized the significance of this experiment because it demonstrates the inseparability of the wave and particle properties of particles and felt a complete understanding of quantum mechanics could be gleaned from carefully thinking through its implications.

The above article demonstrates why.

It shows the quantum mechanical particle and wave properties of energy/mass displayed in the double slit experiment can be understood if one assumes they are made up of a resonant system in a moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

168
Faster than light in
four *spatial* dimensions
July 15, 2013

Einstein’s Theory of Relativity tells us that nothing can travel faster than the speed of light in our universe however it did not preclude space expanding faster than the speed of light

In other words because it allows for space to expand faster that the speed of light some things, like space itself can move faster.

Additionally there are observations that support the fact that space can and does move or expand faster than the speed of light which are not based on the theoretical predictions of Relativity

One is the fact that astronomers observe the rate at which galaxies move apart from each other is proportional to their distance from each other.  In other words the further the galaxies are away from each other, the faster they move apart.  Hubble's law, as this distance to velocity relationship has come to be called tells us that the space between two galaxies separated by around 4,200 mega parsecs (130,000,000,000,000,000,000,000 kilometers) must be moving relative to each other faster than the speed of light.

One way to understand why this does not contradict Einstein's Theory of Relative is think of the universe as a giant blob of dough with raisins spread throughout it (the raisins represent galaxies; the dough represents space). When the dough is placed in an oven, it begins to expand, or, more accurately, to stretch, keeping the same proportions as it had before but with all the distances between galaxies getting bigger as time goes on.

In other words galaxies in our universe are not moving faster than the speed of light in space but space between them is moving or expanding at a rate which is faster.

However the fact that space can expand at a rate faster that the speed of light means there must exist a universe that can support that motion.

Many of you are probably asking yourself is there a way of determining where this universe is and if it is possible for humankind to utilize its ability to support faster than light movement.

The answer can be found in observations related to how our universe is expanding

For example, we do not observe three-dimensional space to be expanding towards a time dimension but towards another spatial one because only the distance between galaxies is increasing not the time.

This suggests our three dimensional universe must be expanding in the direction of a four *spatial* dimension that is was not defined by Einstein because as was just mentioned observations of three-dimensional universe tell us that it is not expanding towards a time dimension but towards another *spatial* dimension.

Therefore to explain the observed spatial expansion of the universe one would have to assume the existence of a fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension contained Einstein’s theories.

This would be true if Einstein had not given us a means of quantitatively and qualitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

Einstein derived the geometric properties of his space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in the equation E=mc^2 to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and  quantitative means of redefining his space-time universe as was done in the article #102 "The “Relativity” of four spatial dimensions" Dec. 1, 2010 in terms of geometry of only four *spatial* dimensions

However if our universe is made up of four *spatial* dimensions instead of four dimensional space-time and if it is true three-dimensional space is expanding towards it, as observation suggest then the fact that we also observe that some sections of three-dimensional are expanding faster than the speed of light relative to others means that three-dimensional space can travel faster than the speed of light in the fourth *spatial* dimension.

In other words in the future we may have the technology to "elevate" a bubble of our dimensional environment, move it though the four *spatial* dimension at speed greater than that of light relative to the three-dimension environment where it was created and then have it materialize in another part of our universe.

167
Finding the graviton
July 1, 2013

One of the biggest problems in theoretical cosmology is understanding why we have been unable to observe the Graviton or the quantum of gravitational force.  Some have attributed this to the fact that its interaction with matter is not strong enough to be detected by modern instrumentation.

However the reason may be because gravity is not propagated by a particle such as a photon but by field properties of space.

The currently accepted view among most cosmologist and physicist is that all forces mediated by particles.  This viewpoint is support by the success the Standard Model of Particle Physics has had in explaining and predicting the observed properties of electromagnetic energy, weak, and strong nuclear forces in terms of particles.  It makes very accurate and verifiable predictions of the nature and causality of those forces in terms of particle interactions.

However it falls short of being a complete theory of fundamental interactions because it cannot or does not incorporate the full theory of gravitation as described by General Relativity.  This is because Einstein's General Theory of Relativity derives gravity in terms of a continuous curvature in the field properties of four-dimensional space-time and not in terms of the discontinuous properties of the quantum.

This fact makes it extremely difficult to conceptually integrate them because something that is discontinuous cannot be by definition continuous.

However it may be possible to integrate gravity with the particle properties of the forces defined in the Standard Model if instead of assuming they are propagated by particles one assumes that the particle properties of all forces are propagated by the fields

It is easier to explain the mechanism responsible for creating the quantum or discontinuous particle properties the Standard Model uses to define forces out of the continuous field properties of a space-time manifold by redefine Einstein's space-time universe into one consisting of only four *spatial* dimensions.

(The reason will become obvious latter in the article)

Einstein gave us the ability to do this when he used he used the velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

However it allows one to define a physical mechanism that would responsible creating a particle or quanta of space-time in terms of the field properties of four *spatial* dimensions.

For example the article #14 "Why is energy/mass quantized?" Oct. 4, 2007 showed it is possible to explain the discontinuous properties of space by extrapolating the laws classical resonance in a three-dimensional environment to a matter wave on a continuous "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

Therefore these discrete or quantized energy of resonant systems in a field consisting of four *spatial* dimensions would be responsible for the particle characteristics the standard model associates with the propagation of gravity electromagnetic energy, weak, and strong nuclear forces.

However, it does not explain how or why we observed them in terms of discontinuous properties of a particle instead of the continuous properties of a field as the above theoretical model and Einstein Theories predicts we should.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension defines the mechanism responsible for the quantization of the field properties of space associated with energy/mass in the article #14 "Why is energy/mass quantized?".

In other words defining space in terms of continuous field consisting of four *spatial* dimensions allows one to conceptually integrate the quantum properties of the Graviton, electromagnetism. the strong and weak forces into the continuous field properties four-dimensional space-time in terms of a resonant "structure" created by the observed wave properties of energy/mass.

This is because as mentioned earlier defining the geometric properties of a space-time universe in terms of energy/mass and the constant velocity of light Einstein provided a qualitative and quantitative means of qualitatively ti and quantitatively redefining it in terms of the geometry of four *spatial* dimensions. 

Quantum mechanics defines the smallest possible unit of space and increment of energy in terms of Planck's length "h" while defining the size of an individual quantum of force in terms of the equation E = h c / L. 

In other words the physical size of the fundamental quanta of all forces is not the same as is suggest by the Standard Model of Particle Physics and quantum mechanics but varies with their energy and the higher energy there is the smaller its volume.

However this means the length and therefore the volume of a Graviton would be considerably larger when compared to the volume associated with a quantum unit of the electromagnetic weak or strong forces because of its relatively low energy content with respect to theirs.

There is considerable observational and theoretical evidence to support this conclusion.

A theoretical foundation is provided by the fact that the energy of a quantum of force is mathematically defined by its frequency and wavelength.  This means a higher energy particle with a shorter wavelength would occupy a smaller volume than lower energy ones.

Observational evidence can be found in the fact that quanta of the strong and weak forces can only be observe in particle accelerators capable of generating the energy required to magnify their environment enough to allow for us to observe them.

In other words the reason why we can observe quanta of the strong and weak forces is because we can create experimental apparatus that can magnify the environment to the point where they become visible.

While a quantum of a less energetic electromagnetic force associated with visible light is observable because it size is comparable to the size to the sensing apparatus in the cones and rods in the eyes use to detect it.

However electromagnetic forced is about a million billion billion billion billion (10^42) times stronger than gravitational.

Using the same logic one reason why we have been unable to observe a Graviton may b e because we have been unable to construct an observing platform a million billion billion billion billion (10^42) larger than the one need to observe quanta of electromagnetic force of the same strength. 

However the relatively large size of a Graviton or an individual quanta of gravity predicted by quantum mechanics suggests another reason why we have been unable to observe it.

We know from observations that gravitational forces act on much smaller scales than the physical size of an individual Graviton predicted by quantum mechanics. However this means that we should observe that the orbital energy of objects should also be quantized.

Some may disagree by saying that the size of the quantum unit of gravitational force is too small relative to the mass of objects that the effect of its quantization would be unobservable.

However the equation that defines the size of a quantum ( E = h c / L ) tells us that it would relatively large with respect to the other forces of nature as well as the size of orbits of many of the observable planets.  Additionally the force of gravity is always attractive or only acts in one direction therefore the effects of its quantization would be cumulative

In other words if gravity is propagated by the graviton the cumulative effects over the life of the universe should be observable with the increased sensitivity and high resolution of modern instrumentation.

Therefore one must assume that Einstein was correct we he defined gravity in terms of its field and not the quantum properties of space-time because if it was propagated by the Graviton then quantum mechanics tells us due to its relative large size that we should have observed discrete regions of space where orbits of stars planets and moons are not found.

This strongly suggest the reason why we have been unable to observe a Graviton is because gravity is not propagated it but by the field properties of space.

166
A quantum of space-time
June 15, 2013

Both Einstein's General and Special Theories of Relativity define macroscopic properties of energy/mass in terms of the continuous properties of four-dimensional space-time while quantum mechanics defines its microscopic properties in terms of its discontinuous properties of three-dimensional space. 

This fact makes it extremely difficult to conceptually integrate them because something that is discontinuous cannot by definition be continuous.

However it is possible to define a mechanism responsible for creating a discontinuous or quantum unit of space-time if one redefines Einstein's space-time universe into one consisting of only four *spatial* dimensions.

Einstein gave us the ability to do this when he used he used the velocity of light to defined the geometric properties of space-time and energy/mass because it allows one to convert a unit of time in his space-time universe to a unit of space.  Additionally because the velocity of light is constant means it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

However as mentioned earlier doing so would also allow one to define a physical mechanism responsible for creating a quantum of space-time in terms of the existence of four *spatial* dimensions.

For example the article #14 "Why is energy/mass quantized?" Oct. 4, 2007 showed it is possible to explain the quantum properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on the continuous "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four spatial dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a continuous "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

Therefore the discrete or quantized energy of resonant systems in a continuous four dimensional environment would be responsible for the discrete quantized energy quantum mechanics associated with energy/mass.

However, it did not explain the mechanism responsible for quantizing the space containing energy/mass

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is responsible for the quantization of four-dimensional space because it would result in the formation of discrete or quantized volumes associated with the observed quantum properties of energy/mass.

In other words defining space in terms of four *spatial* dimensions allows one to conceptually the integrate the discontinuous quantum mechanical properties of energy/mass into the continuous field properties four-dimensional space in terms of a resonant system created by the wave properties of energy/mass.

However also allows one to integrate the quantum mechanical properties of energy/mass into the continuous field properties of Einstein's space-time universe because as mentioned earlier by defining the geometric properties of a space-time universe in terms of energy/mass and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions. 

Additionally it demonstrates it is not necessary to assume fundamental component of energy/mass is composed of a quantum of space-time or any other field as is assumed quantum field theory because it provides a valid and verifiable mechanism for creating it out of the field properties of space-time.

Physicists should remember that one cannot define a mechanism for the continuous properties of four-dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous.  However one can define a mechanism defining the quantum in terms of the continuous properties of space-time because something that is continuous by definition can be divided up into its component parts.

165
Plato’s lesson
on quantum mechanics
June 1, 2013

Many think the quantum mechanical world of probabilities define our reality.  However, the Greek philosopher, Plato around 375 BC would disagree.

In Plato's allegory "The cave" he describes how people who have been chained to a cave wall view the world outside of it.  "The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Plato's Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.

However he could have been talking about today's scientists who are locked into a worldview that projects shadows that cannot be made to agree with the reality of the world they are living in.

For example Quantum theory defines the existence of particles in terms of a mathematically generated probability function and that they do not exist until a conscience observer looks at it.  In other words it assumes the act of observation or measurement creates the physical reality of our particle world.  However because only conscience beings can be observers it implies that it cannot exist without them being there to observe it.

However if one assumes reality exist only after someone observes it one must also assume that we humans evolved out of something that did not exist.

This seems to contradict the most common definition of reality: that it is an environment with a set of physical properties that exists even when there are no observers present.  In other words most believe the world exist in even when no one is there to observe it.

Plato's in his allegory "The Cave" he tells us that one should base his or her interpretation of reality on direct physical observations of the "shadows" they cast on the cave walls because he feels it is the only way to connect their existence to the reality of the world outside of it.

This presents a problem for the proponents of quantum mechanics because it assumes that reality and existence is defined in terms of abstract mathematical probabilities which by definition do not have physical properties; therefore they are unable to cast shadows on the reality of the non-abstract environment we see all around us. 

In other words the reality defined by quantum mechanics cannot create or define the physicality of the shadows projected on the walls of our world or cave as Plato calls it because they themselves do not have any.

Some would argue the fact that quantum mechanics can accurately predict what we observe in the material world in terms of the abstract nature of probability functions means that what we perceive as the reality does not exist. 

However as Plato pointed out our only connection to reality is though the observation of the "shadows" it displays on our physical or material world.  Yet because of the abstract nature of probability functions of quantum mechanics they, by definition can never be part or interact with that world.  Therefore because we can physicality observe of the "shadows" of reality in our environment isn't it more likely the world defined by quantum mechanics does not exist instead of our material world that we can see and touch.

Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

He realized as Plato did that reality can only be discovered by forming a physical image of what its shadows are telling us.

For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

Einstein looked at the shadows of reality cast by gravity and realized they could be created by a universe made up of four-dimensional space-time.  He extrapolated the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold to show that it can explain and predict how gravity "may act upon another at a distance through a vacuum" in terms of a curvature in space and time.   This allowed him to understand the reality behind the shadows we can see in our three-dimension world in terms of a physical image based on the existence of four dimension space-time.

In other words he was able to explain the gravitational shadows on the Newtonian cave walls in terms of a physical image cast by four dimensional space-time on them.

As Plato would say he perceived the true form of reality based on a physical image of the shadows seen by its prisoners.

Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Plato and Einstein.  They chose to look for reality in terms of abstract mathematics instead of the physical imagery given to us by its shadows.

The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency that it is to alter one based on physical imagery. 

For example Quantum theory makes predictions based on the random properties of a probability function.  However because its abstract properties are not connected to any physical images of our world all observations no matter how inconsistent they are with the physical world it is describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in a four-dimensional environment directly connects it to the physicality of the shadows it casts on our three-dimensional environment.

For example a mass that was repelled by gravity instead of begin attracted would contradict the physical model define by Einstein and would be extremely if not impossible to explain according the that model because that would mean that we should observe objects rolling up hill in our three-dimensional environment.  In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses repelling gravitational each other impossible to incorporate into it.

If however if some observation happened to contradict complimentary principal of quantum mechanics such as simultaneously observing both the particle and wave properties mass it could easily explained in terms of the fact that its probability functions tell us that anything that can happen eventually will  This makes it impossible to find an observation that would contradict it because it tells us the even the impossible is possible if we wait long enough.  However this can only happen in an abstract environment which is not bound by the physicality of our observational world because in that world we observe that some things just cannot happen.

But why should science put in the effort to understand the physical reality behind the shadows of our world when both the abstract mathematical foundation of quantum mechanics and the physics imagery of Einstein's theories make very accurate predictions of future events based on the past. 

Because the mission of a science is to define reality in terms of what we perceive in the world around us which by definition is not abstract.

164
Light and the
 physicality of space
May 15, 2013

Einstein in the address "Aether and the theory of Relativity" delivered on May 5th 1920 at the University of Leyden Germany indicated that The General Theory of Relativity predicts, "space is endowed with physical qualities".

"Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether.  According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.  But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts, which may be tracked through time.  The idea of motion may not be applied to it."

But why have the best minds in the scientific community been unable devise an experiment to detect the physical properties of space that Einstein was so sure must exist to support the propagation of light.

The reason may be because they are not looking in the right direction.

For example 1887 Albert Michelson and Edward Morley devised an experiment to detect the relative motion of matter through the stationary Aether ("Aether wind") by creating a device that sent yellow light from a sodium flame through a half-silvered mirror that was used to split it into two beams traveling at right angles to one another. After leaving the splitter, the beams traveled out to the ends of long arms where they were reflected back into the middle by small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference. If the Earth is traveling through an Aether medium, a beam reflecting back and forth parallel to the flow of Aether would take longer than a beam reflecting perpendicular to the Aether because the time gained from traveling downwind is less than that lost traveling upwind.
However they did not observe a fringe shift and therefore conclude that space did not contain the "physical medium" called Aether. This negative result is generally considered to be the first strong evidence against the then prevalent Aether theory, and initiated a line of research that eventually led to special relativity, in which the stationary Aether concept has no role.  The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution".

However Einstein in his General Theory of Relativity did not endow space with the physical qualities of mass, he endowed it with the geometric properties of a space-time dimension.  Therefore, when Einstein referred to space as having physical properties he may not have been referring to the physical properties of a medium made up of mass such as the "Aether" but those imparted to it by the geometry of space-time.

The significance of changing one perspective form space having the physical properties associated with mass to one of the geometric properties of space or a space-time dimension can be best understood if, as has been done many times in the Imagineer's Chronicles one transposes Einstein's space-time universe to one of four *spatial* dimensions.  This is because one could use the physicality of the spatial dimensions instead of the non physical properties of a time or space-time dimension to derive the physical properties of Einstein's space. 

Einstein made this possible when he derived the geometric properties space-time, energy and the dynamic balance between it and mass in terms of the constant velocity of light and the equation E=mc^2. 

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three-dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event.  This spatial expansion and contraction would be analogous to how the two-dimensional surface of a balloon either expands of contract when air (energy) is added or taken away from it.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, one can use the fact that the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass to convert or transpose the curvature in space-time Einstein's equations associated with energy to one that would define it in terms of a curvature in a four *spatial* dimensions associated with the *spatial* properties of mass.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This was the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that one can derive all forms of energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.

Additionally it tells us the medium Einstein referred to in his address at the University of Leyden was most likely the geometry of three-dimensional space because his theories show that space it in itself has physical properties in that it can cause changes in its environment similar to how the geometric expansion and contraction of the two dimension surface of a balloon can cause physical changes in its environment.

If it is true that the physical medium Einstein was referring to was related to the geometric properties space and not a properties of mass as we are suggesting one should be able to explain why Albert Michelson and Edward Morley were unable to detect it in terms of the concepts contained in that article.

Part of the answer can be found in the article #163 "The causality of motion" May 1, 2013 which derived the causality of an inertial reference frame in terms of the relative separation the "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the causality of all accelerated motion including gravitational was a result of the interaction of an inertial reference frame with the slope of a curvature in the "surface" of three-dimensional space while deriving the causality of its inertial properties in terms of a constant linear displacement of two different "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of all acceleration reference frames.)

In other words it showed the energy of relative motion was not imparted to it by its motion through space but by a displacement of its three-dimensional geometry with respect to fourth *spatial* dimension.

However this means the casualty of the forces experience by the components of an inertial reference frame in constant motion are an integral part of the geometry of their moving environment and therefore would not be dependent of their relative motion.

The theoretical significance of defining the causality of constant motion in terms of the geometry of four *spatial dimensions is that it allows one to understand why the propagation of light or electromagnetic energy is independent of the motion of an inertial reference frame.

As mentioned the article #23 “Defining energy” Nov 27, 2007 derive all forms of energy in terms of a geometric displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This was the basis for defining the causality of electromagnetic energy in the article #12 "What is electromagnetism?" Sept, 27 2007 in terms of the differential force caused by the "peaks" and "toughs" of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed it is possible to derive the electromagnetic properties of electromagnetism by extrapolating the geometric properties of a three-dimensional environment to a matter wave moving on a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension.

A wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

However this also defines the causality of the electromagnetic properties of light and its propagation in terms of the physicality of the dimensional properties of space.

Yet this also means that the propagation of light would not be depend on the existence of the physical properties of mass as most including Albert Michelson and Edward Morley associated with the aether but only on the physicality of of the geometric properties of space.

This also means the velocity of light would not be influenced by the relative motion of an inertial reference frame because as mentioned earlier all of its components including light share the same geometry and therefore the same relative velocity.

This suggests that the "Aether" or the medium Einstein said must exist to support the propagation of light, and the existence for standards of space and time is a physical property of the geometry of space and not that of an independent element as is suggested by the modern interpretation of the Albert Michelson and Edward Morley.

However it also means that according to Einstein space-time concepts no experiment no matter how sensitive to motion will be able to detect any change in the velocity light due to the relative motion of an inertial reference frame.

163
The causality
of motion
May 1, 2013

According to Newton’s view, force does not the cause motion but only a change in it and because a freely moving object continues to move inertia and motion in itself needs no causal explanation.

However as Gao, Shan points out in on page 29 of his book "God Does Play Dice with the Universe" there is a problem with that concept of motion because:

"According to Newton, neither external force nor internal force is the cause of constant motion. So there is only one possibility left , i.e., that motion has no cause.  In other words the change in position or state of an object due to a constant velocity does not have cause.

However modern science is based on the assumption that all changes in the state of a system require a cause.  In other words one cannot integrate the Newtonian concept of motion or the change in position associated with it into our current scientific paradigms which are based almost entirely on causality".

Granted Einstein was able to define the causality of gravity and accelerated motion in terms of curvature in four dimensional space-time and the relativistic properties of motion in terms of that same four dimensional model however he was unable or did not chose to address the causality of that motion and the inertia Newton associated with it. 

However he did provide us with the conceptual foundations for the deriving the causality of inertia and constant motion when he define the dynamic relationship between space, time, energy, and mass in terms of the constant velocity of light and the equation E=mc^2.

Einstein defined accelerate motion in terms of a curvature in space-time and a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of space he associated with mass to a unit of acceleration he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

As mentioned earlier Einstein’s equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.

This is analogous to how the two-dimensional surface of a balloon either expands or contracts with respect to three-dimensional space when air (energy) is either added or removed from it.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the curvature in space-time Einstein’s associated with gravity and accelerated reference frames to a curvature or displacement in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions

This fact that one can quantitatively derive the spatial properties of all forms of energy including that associated with constant motion in a space-time universe in terms of four *spatial* dimensions is one of the bases of assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

One of the theoretical advantages to transposing Einstein space-time concepts to four *spatial* dimensions is that it allows one define a common mechanism for the causality of gravity, acceleration, inertia and constant motion.

For example the article #11 "Why Space-time?" "Sept. 27, 2007 showed the energy associated with rest mass is directly proportional to the magnitude of a curvature or "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was shown that one can derive the causality of all accelerations including gravitational in terms of an interaction of rest mass with the slope of a curvature in the "surface" of three-dimensional space caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of all accelerations.)

However as was shown in the article #23 "Defining energy" there will be a 1 to 1 correspondence between an objects rest mass and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object, as is confirmed by observations would be directly proportional to its rest mass if one assumes as was done in that article that causality of both is related to a displacement caused by a curvature in "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension.  This allows one to define the causality of inertia in terms of an interaction of the rest mass of an object with a curvature in a three-dimensional space manifold with respect to a four *spatial* dimensions.

This also to defines the causality of constant motion because according to the theoretical concepts presented in that article the energy associated with its momentum would be defined by a constant linear displacement of the depression associated with its rest mass in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore motion will continue unchanged unless it interacts with the curved "surface" of three-dimensional space that article associated with accelerations. This allows one to define the casualty constant motion in terms of a linear or constant displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However it also enables one to define causality of the relative properties of constant motion because according to the concepts develop in that article the momentum of an object in motion would be determined by the relative separation its three-dimensional "surface" has with respect to the three-dimensional "surface" of the object or measuring device used to determine its velocity.  In other words all motion is relative because its causality is directly related to the relative separation of its three-dimensional "surface" with respect to the three-dimension "surface" of another object or measuring device.

This defines a causal link between constant motion inertia, rest mass gravity and all accelerations in terms of an interaction of the "surfaces" of a three-dimensional space manifold and a fourth *spatial* dimension.

This cannot be done in terms of four dimensional space-time because it does not allow for the linear displacement of a "surface" of three-dimensional space with respect to a time dimension.

This shows how one can integrate the causality of a change in position associated with constant motion into our current scientific paradigms which are based almost entirely on causality and conceptually link it with Einstein's concept of gravity and accelerate motion in terms of four *spatial* dimensions.

Additionally it allows one to fully integrate the Newtonian concept of motion or the change in position associated with it into our current scientific paradigms which are based almost entirely on causality.

162
The reality of
 Quantum Fields
Apr. 1, 2013

Is it possible to define the physical "reality" of a Quantum field?

We think so.

Many including Albert Einstein and Erin Schrödinger, had difficulty accepting the "reality" of quantum mechanics because many of its concepts appear to contradict those of our observable universe.

For example in a quantum system Schrödinger's wave equation defines the field properties of its environment and predicts the future distribution of a particle's position only in terms of the abstract properties of probabilities.

However many including Einstein and Schrödinger define reality in terms of what they see or touch.

For example, Einstein used the observable "reality" of the interactions of electromagnetic energy with a photoelectric material to derive the quantum mechanical properties of energy/mass while using the observable properties of light in our three-dimensional environment to define his space-time universe.

In other words his conclusion that electromagnetic energy is quantized was based on the physical "reality" of the environment sounding the photoelectric material and how electromagnetic energy interacted with it, not on the abstract probabilities associated with quantum fields.

However the abstract properties of probabilities share a common characteristic with Einstein space-time universe in that time or a space-time dimension have never be seen or touched and therefore they like the probability functions of quantum field theory are, by definition abstract quantities.

Fortunately they also have a common element, as mentioned earlier in the physically observable non-abstract properties of the *spatial* dimensions because the probabilities associated with Schrödinger's wave equation are expressed in terms of the spatial properties of position.

Therefore because they share a common connection to the observable "reality" of our three-dimensional spatial environment one should be able to define the physical "reality" of both Einstein space-time dimension and the field properties of quantum mechanics in terms of their non-abstract spatial components.

Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define how energy/mass effects a space-time environment.  Additionally because the velocity of light is constant it also allows one to defined a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three-dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event.

This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

However observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the space-time curvature Einstein’s associated with energy to one that would define it terms of a spatial curvature in a four *spatial* dimensions.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use the Einstein’s equations to qualitatively and qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one bases for assuming, as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

One of the theoretical advantages of a modeling the existence of energy/mass on four *spatial* dimensions instead of four dimension space-time is it allows one to derive the "reality" of a quantum fields in terms of the observable non-abstract properties of our three-dimensional environment.

The physical "reality" of the field properties energy/mass in four *spatial* dimension was developed in the article #12 “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on field consisting of four *spatial* dimensions.

Briefly it showed that one can derive its field properties by extrapolating the observable non-abstract properties of a three-dimensional environment to a fourth *spatial* dimension.

For example a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore observations  of our three dimensional "reality", if extrapolated  to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become "attracted" to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a non-abstract mechanism for understanding why similar charges repel each other because observations of wave on the surface of water tell us that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, observations of our three dimensional environment tell us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows how one can explain and predict the continuous field properties of electromagnetism by extrapolating the observable non-abstract properties of our three dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, as was shown in the article #13 “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimension can also be derived by extrapolating the observable non-abstract resonant properties of a three-dimensional environment to one consisting of four *spatial* dimension.

There are four conditions required for resonance to occur in a three-dimensional environment an object or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations in four *spatial* dimensions, would meet the requirements mentioned above for the formation of a resonant system or "structure" in space. 

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet field energies associated quantum and electromagnetic field theories

This shows how one can define the "reality" of the continuous field associated with Schrödinger's wave equation and a physical mechanism responsible for the creation of particles in that field in terms of the observable non-abstract "reality" of our three-dimensional environment.

161
The geometry of
Quantum Mechanics
Apr 1, 2013

By the early 19 hundreds many felt the sum total of all human knowledge about the physical universe could be found in two theories.  The first, Einstein's Theories of Relativity gave us an understanding of the very large while the other, quantum theory gave us a theory of the very small, the bizarre world of the atom.

However there was considerable disagreement as to how one should interpret the quantum mechanical world.

Some like Bohr thought that one should not attempt to define it in terms of causality but only in terms of the probabilities associated with Schrödinger's wave equation

However Einstein disagreed.  He thought the quantum mechanical properties of energy/mass could be a subset of a larger theory based on the causality he had associated with the geometric properties of space-time.

As Michio Kaku pointed out in his book Einstein's Cosmos: "How Albert Einstein's Vision Transformed Our Understanding of Space and Time, "Einstein used an analogy drawn from his own work to explain why he felt that way."

Einstein pointed out that Relativity did not prove the Newtonian theory was completely wrong; it only showed that it was incomplete, that it could be subsumed into a larger theory.  Thus, Newtonian mechanics is quite valid in its own particular domain: the realm of small velocities and large objects. Similarly, Einstein believed that the quantum theory’s bizarre assumptions about the lack of causality could be explained in a higher theory."

However he was unable to do so.

One reason may be because they do not have a common parameter that can be used for their integration.

For example Einstein's theories defined the domain of energy/mass in terms of a continuous property of time or a space-time dimension whereas quantum mechanics defines its domain in terms of the discontinuous spatial properties associated with particles.

Additionally Schrödinger’s wave equation that is used to define a quantum system, only defines the probability a particle will be located in a given volume of space without giving reference to causality while Einstein defined the casualty he associated with the geometric properties of space-time in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 without giving reference to its probabilistic non-casual properties.

This suggests that the inability to merge these two theories is due to the incompatibility of the probabilistic, discontinuous based explanations and predictions of quantum mechanics and the continuous, casual or deterministic ones of Relativity.

However Einstein gave us an opportunity to resolve this conundrum when he derived the geometric properties space-time, a particles energy and the dynamic balance between it and mass in terms of the constant velocity of light and the equation E=mc^2. 

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three-dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event.

This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

However observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the space-time curvature Einstein’s associated with energy to one that would define it terms of a spatial curvature in a four *spatial* dimensions.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use the Einstein's equations to qualitatively and qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one bases of assuming as was done in the article #23 “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

One of the theoretical advantages of a model based on four *spatial* dimensions is that it provides a common parameter for comparing or integrating the discontinuous properties energy/mass associated with quantum mechanics with the continuous ones associated with Einstein's theories in terms of its spatial properties.

For example the fact that one can define energy/mass in terms of a spatial displacement on a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension means that one should be able to, as was done in the  article #14 “Why is energy/mass quantized?” Oct. 4, 2007 derive its quantum mechanical properties in terms of those spatial properties.

Briefly that article showed that one can derive the quantum mechanical properties of energy/mass in terms of the four conditions required for resonance to occur in a spatial, three dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four *spatial* dimensions.

The existence of four *spatial* dimensions would give the "surface" of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations on a "surface" of three-dimensional space, would meet the requirements mentioned above for the formation of a resonant system or "structure" in space.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet discontinuous values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

Therefore these resonant systems in four *spatial* dimensions define the discreet discontinuous energy associated with quantum mechanical wave function in terms of a causal mechanism based on the existence of four *spatial* dimensions.

One cannot accomplish this in an environment consisting of four dimensional space-time because time or a space-time dimension is only observed to move in one direction forward therefore it cannot support the bidirectional spatial movement required for classical resonance to occur.

As mentioned earlier Einstein was convinced that quantum mechanics was an incomplete theory.

He used the analogy that Relativity did not prove that Newtonian theory was completely wrong; it only showed that it was incomplete, that it could be subsumed into a larger theory.  Similarly Einstein believed that quantum mechanics could be subsumed in a larger theory.

However to understand how quantum theory could be integrated or subsumed into a larger theory of four *spatial* dimensions one must not only show why the energy/mass associated with the quantum mechanical wave function would be discontinues in four *spatial* dimension as was done in the article #14 Why is energy/mass quantized?one must also explain the physical significance of Planck's length one of its fundamental components and how it is related to the uncertainties associated with quantum mechanics in terms of four *spatial* dimensions. 

In quantum physics Planck's length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate.  In other words Planck's length the smallest measurement of length with any meaning in relativistic theories.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the resonant system associated with a the wave function in the article #14 "Why is energy/mass quantized?"  However, it also allows one define the physical significance of Planck's length in terms of the size or length of one side of the quantum mechanical "box" in four *spatial* dimensions containing the wave function of a quanta.

Another fundamental component of quantum theory, Planck’s constant which can be derived from Planck's length is related to Heisenberg’s Uncertainty Principle which asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.  For example attempting to measure an elementary particle’s position (▲x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particle’s momentum (▲p) to an equally high degree of accuracy.  Heisenberg’s Principle is typically written mathematically as ▲x▲p ≥h / 2    where h represents Planck constant

As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article #14 "Why is energy/mass quantized?" predicts that a particle will most likely be found in the quantum mechanical "box" whose dimensions would be defined by integral number of Planck's lengths.  However quantum mechanics treats particles as one dimensional points and because it could be anywhere in that "box" there would be an inherent uncertainty involved in determining its exact position.

For example the formula give above ( ▲x▲p ≥h / 2  ) tells us that uncertainty of measuring the exact position of the point in that "box" defined by its resonant wavefunction would be equal to ▲x▲p ≥h / 2 .   However because we are only interested in determining its exact position we can eliminate all references to its momentum.

However one cannot measure the particle position to an accuracy greater than 6.626068 × 10-34 meters or the equivalent of Planck’s constant expressed in meters because as mentioned earlier there is an uncertainty involved in determining the exact position of a particle is because it is impossible to determine were in the "box" the quantum mechanical point representing it is located.

This shows how one can define the physical mechanism responsible for the uncertainty principal and why at Planck's scale the classical ideas about gravity and space-time cease to be valid, in terms of the existence four *spatial* dimensions because it defines the maximum degree of accuracy one can measure the position or momentum of a particle.

However it also defines a physical mechanism responsible for the lack of causality the quantum world because if one cannot make an exact measurement of the initial conditions of a system one cannot use it to predict its future evolution.  Therefore one cannot define a casual or deterministic relationship between its past and future.

Yet the above discussion also shows that Einstein's theories were not completely wrong because it is still valid in own particular domain: the realm of macroscopic space and time while demonstrating how his relativistic concepts of a space-time environment and quantum theory’s bizarre assumptions about the lack of causality could be a subset of a higher theory based on the existence of four *spatial* dimensions.

160
Will time end?
Mar 20, 2013

Does time have an end?  If so when and where will it happen?

This question is a difficult to answer definitively because if time does end no one would have the time to tell us it had.

How then can we determine if it will?

One was is by analyzing what we know about the present time and project it into the future.

For example cosmologists believe that time will come to an end because our universe is expanding and will experience heat death or a state were no thermodynamic process occur.  This conclusion is base in part on the observation that the expansion of the universe is accelerating and therefore they feel it will continue until it reaches thermodynamic equilibrium.

However they make this prediction even though they do not have a theoretical model defining what is causing its expansion to accelerate or how long it will continue.

Yet one can look at those same observations regarding an expanding universe and come to a completely different conclusion using Einstein concepts of space-time and observations of our three dimensional environment.

For example Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

He told us the energy associated with mass causes a curvature or a contraction in the "surface" of space time and when mass is converted to energy it causes space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

However one of the difficulties in integrating an accelerating universe into Einstein's space-time concepts is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore to explain the observed spatial expansion of the universe one would have to assume the existence of a fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein's theories contain.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

As mentioned earlier Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in the equation E=mc^2 to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein's one must  also assume that energy must have spatial properties because Einstein equation E=mc^2 tell us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts. 

Yet as mentioned earlier it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward.

However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that we can move in two direction in a spatial environment up down forwards of backwards.

The fact that one can use the equation E=mc^2 to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words one can use Einstein's equations to define energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamics that energy flows from areas of high density to area of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example if the walls of an above ground pool filled with water collapse, the elevated two dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it and that the force associated with that expansion will decline as its surface spread out.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article #23 “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be "elevated" or "displaced" with respect to a fourth *spatial* dimension,

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it and that the force associated with that it will decline as it expands. 

This shows how one can use Einstein experimental verified relationship between mass and energy defined by the equation of E=mc^2 to explain the casualty of the force called dark energy and why it is causing the accelerated expansion of the universe in terms of the geometry of four *spatial* dimension.

However it should be remembered this solution was derived directly from Einstein's General Theory of Relativity and the observable and therefore verifiable properties of three-dimensional space.

Yet the equation E=mc^2 also tells us the ratio of the attractive gravitational mass component of a three-dimensional environment with respect to the expansive component of dark energy must increase as space expands because it tells that each unit of space that undergoes cooling or reduction in energy must be accompany by an increase in its mass component.  Granted this mass would be spread out over a very large volume however it would still exert a gravitational influence on its environment that would counter act the expansive properties of Dark Energy. 

(Some may try to dismiss this by saying that as the universe expands its energy is spread out over a larger volume so after a while it just vanishes so to speak or as some like to say that the universe experiences a heat death.  However Einstein theories do not permit energy to just disappear or "die".  It unequivocally tells us that if the energy content in a closed environment decreases the mass content of that environment must increase irrespective of the volume of that environment.  Therefore because by definition the universe is a closed system one must assume that any reduction in its overall energy content of the universe including its heat energy must be must be compensated for by an increase in its total attractive gravitational mass content.)

Yet this also tells us the evolution of time would be defined by a dynamic interaction between the spatial components of mass and energy because it tells the forces associated with them diametrically oppose each other.

Current observations of our universe tell us, if the above theoretical model is correct that it is undergoing an accelerated expansion with respect to a fourth *spatial* dimension because as mentioned earlier the expansive energy due to the elevated "surface" of three-dimensional space exceeds the contractive gravitational forces associated with its energy/mass component.  However as time goes by the power of its expansive component will decrease for the same reason as the expansive power of the water in a pool whose walls have collapsed decrease as it expands.  This means the contractive gravitational forces Einstein associated with energy/mass created by the decrease in its energy content will become predominate.  This will result in the entering a contraction phase.

(For a more detailed explanation of causality this process please review the article #27 "The Return of the Big Bang" Jan 15, 2008)

This contraction will continue until the heat generated by its collapse elevates the "surface" of three dimensional space with respect to a fourth *spatial*enough to counter act the contractive forces caused the gravitational component of its energy/mass thereby causing it to enter a period of expansion.

However after a given period the power of its expansive forces will decrease because as mentioned the elevation in the "surface" of three dimensional space with respect to a fourth *spatial* dimensions decreases as it expands in a four dimension environment and the contractive force Einstein's equation E=mc^2 associates with mass will again take over.

As mentioned earlier it should be remember this theoretical model was derived directly from Einstein experimentally verified equation of E=mc^2 and the observable and therefore verifiable properties of three-dimensional space. .

This suggests that there may not be and end of time because our universe would not experience heat death or thermodynamic equilibrium and therefore it would continue uninterrupted through dynamic cyclic interchange of mass and energy brought on by contraction and expansion of our universe.

159
The geometry of
 Einstein’s Aether
Mar. 15, 2013

Einstein in the address "Aether and the theory of Relativity" delivered on May 5th 1920 at the University of Leyden Germany he indicated that The General Theory of Relativity predicts, "space is endowed with physical qualities".

"Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether.  According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no

possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.  But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts, which may be tracked through time.  The idea of motion may not be applied to it."

But why have the best minds in the scientific community been unable devise an experiment to detect the physical properties of space that Einstein was so sure must exist.

The reason may be because they are not looking in the right direction. 

For example 1887 Albert Michelson and Edward Morley devised an experiment to detect the relative motion of matter through the stationary Aether ("Aether wind") by creating a device that  sent yellow light from a sodium flame through a half-silvered mirror that was used to split it into two beams traveling at right angles to one another. After leaving the splitter, the beams

traveled out to the ends of long arms where they were reflected back into the middle by small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference. If the Earth is traveling through an Aether medium, a beam reflecting back and forth parallel to the flow of Aether would take longer than a beam reflecting perpendicular to the Aether because the time gained from traveling downwind is less than that lost traveling upwind., However they did not observe a fringe shift and therefore conclude that space did not contain the "medium" called Aether. The negative results are generally considered to be the first strong evidence against the then prevalent Aether theory, and initiated a line of research that eventually led to special relativity, in which the stationary Aether concept has no role.  The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution".

However Einstein in his General Theory of Relativity did not endow space with the physical qualities of mass, he endowed it with the geometric properties of a space-time dimension.  Therefore when Einstein referred to space as having physical properties he was talking about the physical properties imparted to it by the geometry of space-time,

This suggests that the physical qualities Einstein was referring to in the statement "Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether" was the geometric properties of space-time universe and not the physical properties of mass most including Albert Michelson and Edward Morley associated with the Aether.

The significance of changing one perspective form the Aether having the physical properties associated with mass to one of the geometric properties of space can be best understood if, as has been done many times in the Imagineer's Chronicles one transposes Einstein's space-time universe to one of four *spatial* dimensions. This is because one could use the physical properties of the spatial dimensions instead of the non physical properties of a time or space-time dimension to define the physical properties of Einstein's Aether. 

Einstein made this possible when he derived the geometric properties space-time, energy and the dynamic balance between it and mass in terms of the constant velocity of light and the equation E=mc^2. 

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the curvature in space-time Einstein's field equations associated with energy to one that would define the curvature in a four *spatial* dimensions he indirectly associated with the *spatial* properties of mass.

Additionally because the velocity of light is constant it allows for the defining of a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This was the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that one can derive all forms of energy including those associated with velocities, mass and the medium Einstein was referring to in his address mentioned earlier in terms of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of four dimensional space-time.

Einstein in his address he gave at the University of Leyden was careful to define the "quality characteristics" of the physical medium his General Theory of Relativity tells us space must be endowed with.  Specifically he said that it could not consist of parts, which could be tracked though time.  This would be true for both the geometric properties of space-time and four *spatial* dimension because by definition their geometry is continuous and therefore they do not have "parts which may be tracked through time".

As mentioned earlier Einstein's General Theory of Relativity defined the physical of qualities of mass in terms of the geometry of space-time.  However because he defined an equivalence between all forms of energy and mass we must also assume the energy associated with velocity is also related to the geometric properties of space.

However as was shown above one can use Einstein's equations to define a one to one qualitative and quantitative correspondence between his space-time universe and one consisting of four *spatial* dimensions.

Therefore according to the theoretical concepts presented in the article #23 “Defining energy” which defined energy in terms of four *spatial* dimensions instead of four dimensional space-time, the energy associated with the "quality characteristic of ponderable media" Einstein referred to in his address and its motion through his space-time universe could also be defined by a geometric displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

Yet as was mentioned earlier defining energy in terms the of physical properties of a spatial dimension instead of a time or space-time dimension allows one to understand the physical properties of Einstein's Aether because one can apply the rules of spatial geometry to it.

For example the *spatial* displacement associated with center of the inertial reference frame Albert Michelson and Edward Morley used to conduct their experiment would be centered on the point similar to the way geometry of a circle is centered on a point at its center.

However, this means the "idea of motion may not be applied to it" similar to how the idea of motion cannot be applied to the center of a circle with respect to its circumference because if was it could it would no longer be its center.

Additionally if one defines energy associated with medium Albert Michelson and Edward Morley were trying to detect in terms of the geometric properties of four *spatial* dimensions as was done in the article #23 "Defining energy" it would be an integral part of that geometry and the idea of motion could not be applied to it for the same reason as one could not apply the idea of motion to the center of a circle with respect to its circumference.

This is not possible in a space-time environment because the linear progression or flow of time does not allow one to define energy of a point associated with the relative center of an inertial reference frame with respect to the spatial geometry of that reference frame.

This suggests that the Aether or the medium Einstein said must exist to support the propagation of light, and the existence for standards of space and time is a physical property of the geometry of space and not that of an independent element as is suggested by the modern interpretation of the Albert Michelson and Edward Morley.

158
Dark Energy in
 four spatial dimensions
Mar. 1, 2013

We have shown throughout "The Imagineer's Chronicles" and its companion book "The Reality of the Fourth Spatial Dimension" there would be many theoretical advantages to assuming the universe is made up of four *spatial* dimensions instead of four-dimensional space-time.

For example it would allow one understand why the force called Dark Energy is causing the expansion of our universe to accelerate by extrapolating observations made in a three-dimensional environment to one consisting of four *spatial* dimensions.

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

For example he told us the energy associated with mass causes a curvature or a contraction in the "surface" of space-time and when mass is converted to energy it causes space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract with respect to three-dimensional space when air (energy) is added or taken away from it.

However one of the difficulties in integrating the expansive force called Dark Energy into Einstein's space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three-spatial dimensions and one time dimension that Einstein's theories contain to account for the observation that three-dimensional space is undergoing a spatial expansion.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence between mass and energy defined by Einstein's one must assume that energy must also have spatial properties.

As mentioned earlier Einstein's equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.

Yet, as mentioned earlier it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences with time tells us that it only moves in one direction forward.

However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that a spatial environment such as three-dimensional space can move in two directions, like the surface of a balloon in a higher spatial dimension allowing it to either expand or contract. 

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words one can use Einstein's equations to quantitatively define energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space time environment.

We know from the study of thermodynamics that energy flows from areas of high density to area of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article #23 “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension,

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it.

This show how one can understand and explain what the force called dark energy is and why it is causing the accelerated expansion of the universe in terms of the geometry of four *spatial* by extrapolating observations made in a three-dimensional environment to a fourth *spatial* dimension.

It should be remembered this answer to the question as to what is causing the expansion of our universe to accelerate was derived from Einstein's Theories of Relativity and the currently accepted laws of physics and absolutely nothing else

157
Particles or fields
 you cannot have it both ways
Feb. 15, 2013

Is our universe made up of particles or fields? 

On the one hand quantum physics tells that the universe is made up of discrete units of energy/mass while relativistic physics tells us it is composed of a continuous field of space-time

Unfortunately these two ideas do not work well together because a continuous field by definition cannot be made up of discrete parts as is suggested by quantum mechanics.

Some have tried to merge them by defining what is has come to be called a relativistic quantum field theory.  It assumes that particles can be understood as the quanta of some quantum field which in essence elevates fields to the most fundamental objects in nature and that each type of field generates its own particular type of particle.

However, you cannot have it both ways because by definition a field is continuous and saying they can be understood in terms of some quantum field does not mean that you have connected them to the continuous properties of a relativistic space-time field or any field for that matter.  All it does is elevate its size to that of the entire universe because by definition a field is continuous throughout its entire domain.  Therefore if the fundamental component of the universe is a quantum field as quantum field theory suggests then it could only contain one quantum entity because if it contained more the continuity of the field would be broken.  In words saying one can understand the continuous properties of a field in terms of a quantum field is like saying that one can understand why a circle is round is because it is a circle. 

Another reason why it is so difficult to conceptually to integrate Quantum field theory with the field properties of Einstein's theories is because it defines space in terms of a field consisting of time or a space-time dimension while Quantum field theory defines itself in terms of its spatial properties of energy/mass.  

For example Schrödinger's wave equation only defines the probability of a particle will be located in a given volume of space without giving a reference to time while Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

Yet one can overcome the difficultly in integrating a quantum of energy/mass into the continuous field of space-time by redefining the field properties of space-time Einstein associated with energy/mass to its spatial properties Quantum field theory associates with it. 

Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define how a quantum of energy/mass effects a space-time environment.  Additionally because the velocity of light is constant it  also allows us to defined a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy also must have spatial properties.

Einstein's equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.  Yet it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward and therefore does not have the ability to both expand and contract.  However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that spatial environments can more in two directions up or down, forwards or backwards and therefore three-dimensional space would have the ability to both expand and contract with respect to it.

One of the theoretical advantages to assuming that the universe is made up of four *spatial* dimensions instead of four dimensional space-time is that it allows one to derive the quantum mechanical properties of energy/mass in terms of the field properties of four *spatial* dimensions instead of defining the field properties of space in terms of its quantum mechanical properties as is done in quantum field theory.

The field properties of four *spatial* dimension was developed in the article #12 “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on a continuous field consisting of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed that one can derive its properties by extrapolating the laws of Classical Wave Mechanics to a field consisting of fourth *spatial* dimensions.

A wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become "attracted" to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows how one can explain and predict the electrical and magnetic field properties of an electromagnetic wave by extrapolate the laws of classical wave mechanics in a three dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, as was shown in the article #13 “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimensions can be explained and predicted by extrapolating the resonant properties of field in a three-dimensional environment to one consisting of four *spatial* dimension.

There are four conditions required for resonance to occur in a classical environment an object or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations in four *spatial* dimensions, would meet the requirements mentioned above for the formation of a resonant system or "structure" in space. 

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet field energies associated with relativistic quantum field theories.

This shows that it is possible to logically and consistently explain and predict the quantum mechanical field properties energy/mass in a microscopic environment by assuming by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

However it also shows it is more logical and consistent with observations to assume that our universe is fundamentally composed of fields not quanta of energy/mass as is assumed by quantum field theory.

These arguments would not be valid in a universe consisting of four dimensional space-time because as mentioned earlier time is only observed to move in one direction forward and therefore would not support the transverse or bi-directional oscillatory movement required to establish a resonant system.

156
Deriving mass without
 the Higgs Boson
Feb. 1, 2013

Einstein told us that energy and mass are interchangeable however he did not define what mass is.  He only told us how mass interacts with space-time.

As Steven Weinberg said "Mass tells space-time how to curve while space-time tells mass how to move".

However Einstein's inability to define or derive the casualty of mass is can be traced to the fact that he chose to define the universe in terms of energy instead of mass.

Einstein told us that a curvature in space-time is responsible for the physical properties of gravitational energy and because of the equivalence been energy and mass defined by his  equation E=mc^2 one must also assume that it is responsible for the physical properties of mass and inertia of the objects and particles associated with that energy.

Therefore one should be able to learn what mass is if one converts or transposes the Einstein's space-time universe which defines mass in terms of energy to one that defines the space-time properties of energy in terms of mass because as mentioned earlier they are equivalent.

He gave us the ability to do this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 and the constant velocity of light.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy must also have spatial properties.

As mentioned earlier Einstein equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and the mass and energy it contains in that when one coverts mass to energy in a closed three-dimensional *spatial* environment it expands because it would reduce the magnitude of the curvature of three-dimensional space while if one coverts energy to mass, that environment contracts because that would increase its curvature.  This is the conceptual basis for redefining the energy he associated with mass in a space-time environment in terms of its spatial properties in four *spatial* dimensions.

This was also the bases for assuming as was done in the article #23 “Defining energy” Nov 27, 2007 that all forms of energy including thermo and inertia or momentum of mass can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time environment.

However the fact that he was able to defined the geometric relationship between energy and mass in terms of the constant velocity of light means that one can quantitatively and qualitatively define a one to one between the properties of energy in a space-time universe to the physical properties of mass four *spatial* dimensions.

In other words one can use Einstein’s equations to quantitatively and qualitatively define energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions not only gives one the ability to understand the causality of mass but also give one the ability derive its quantum mechanical properties as was done in the article #14 "Why is energy/mass quantized?" Oct. 4, 2007" in terms of its wave component and the resonant properties of four *spatial* dimensions.

(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).

Briefly that article showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension at a frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

This would allow one to, not only understand the causality of the absolute properties of mass such as inertia but it would allow us to derive all of its relativistic ones.

For example one can use these concepts to explain why the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below have identical properties except for their mass, which grows larger in each successive family.

Family 1

Family 2

Family 3

Particle

Mass

Particle

Mass

Particle

Mass

Electron

.00054

Muon

.11

Tau

1.9

Electron
Neutrino

< 10^-8

Muon
Neutrino

< .0003

Tau
Neutrino

< .033

Up Quark

.0047

Charm Quark

1.6

Top Quark

189

Down Quark

.0074

Strange Quark

.16

Bottom Quark

5.2

As mentioned earlier the article #14 "Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article #23 “Defining energy" showed that one can derive the energy of its environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the "surface" of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article #14 "Why is energy/mass quantized?” but also on temperature of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family." is because of an interaction between the resonant properties defined in the article #14 "Why is energy/mass quantized?” and the energy content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative "separation" in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension..

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "separation", with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the "separation" associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial "separation" associated with the second family.

Additionally the corresponding particle types across the three families have "identical properties" because as shown in the article #55 "The geometry of quarks" Mar. 15, 2009 they are related to the orientation of the "W" axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the "W" axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why "The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the existence of four *spatial* dimensions.

However it also allows one to derive the absolute properties of mass associated with Newton's first and second laws of motion because as was shown in the article #39 “The Equivalence Principal: an alternative” July 15, 2008 all accelerations or forces (including gravitational) can be derive in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to the curvature in space-time Einstein assumed was responsible for gravitational forces.)

Newton's first law of motion which defines the inertial properties of the mass of an object or particle states that "Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it"  However this is what one would expect if one assumes, as mentioned earlier the momentum of an object is caused by a displacement of a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension because according those concepts it would tent to stay rest or once in motion would tend to stay in motion because its displacement would remain constant unless it interacted with an external force or as was shown in the article #39 "The Equivalence Principal: an alternative" a three dimensional "surface" that was curved with respect to a fourth *spatial* dimension.

However it also allows on to understand the causality of Newton's second law which defines the relationship between an object's mass "m", its acceleration "a", and why the change in velocity of an object or particle is define by the equation is F = ma because as mentioned earlier, the rest mass of an object is directly proportional to a displacement a "surface" of three-dimensional space manifold with respect to fourth *spatial* dimension.  Therefore, as was shown in the article #23 "Defining energy" there will be a 1 to 1 correspondence between it and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object or its resistance to change in velocity would be directly related to its mass. 


155
What came before
 the Big Bang
Jan. 15, 2013

We have shown throughout “The Imagineer’s Chronicles” and its companion book "The Reality of the Fourth *Spatial* Dimension" there would be many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would give cosmologists the ability to theoretically understand what came before the "Big Bang" in terms of the classical properties of energy/mass.

The Big Bang theory postulates the universe emerged from a singularity and is presently expanding from the tremendously

 hot dense environment associated with it.  Additionally it assumes the momentum generated by the heat of that environment is sustaining its expansion.

However, it has difficulty explaining where the energy originated to cause its expansion.

The reason this presents a problem is because the law of conservation of energy/mass says that in a closed system it cannot be created or destroyed. Since, by definition our universe is a closed system energy/mass cannot be created or destroyed in it.

However the proponents of the big bang model would like us to believe that it was created out of nothing which would be a violation of that law.

Granted some physicist's have devised a cleaver and what some believe to be a contrived or "adhoc" mathematical solution to this problem by postulating the existence of an inflation field even though there is absolutely no experimental or observational evidence to support its existence.

However there is another explanation for origin of the energy powering the expansion of our universe which does not violate any of the accepted physical laws, makes a great deal more sense than assuming its expansive energy originated out nothing and would give us the ability to understand what came before the beginnings of our present universe.

We know the equation E=mc^2 defines the equivalence between mass and energy and since mass is associated with the attractive properties of gravity it also tells us, because of this equivalence the kinetic energy associated with the universe's expansion also has those attractive properties.  Additionally the law of conservation of energy/mass tells us that in a closed system the creation of kinetic energy cannot exceed the gravitational energy associated with the total energy/mass in the universe.

However, not all of the energy of associated with the universe’s expansion is directed towards it because of the random motion of its energy/mass components.  For example, observations indicate that some stars and galaxies are moving towards not away us.  Therefore, not all of the energy present at the time of its origin is directed towards its expansion.

As mentioned earlier the law of conservation of energy/mass tells us that the kinetic energy of the universe’s energy/mass cannot exceed its gravitational contractive properties.  Therefore, at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as mentioned earlier not all of that energy is directed towards its expansion. Therefore at that point, in time the universe will have to enter a contractive phase.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate.  Therefore they believe that its expansion will continue forever.  However, as was shown in the article #148 "Dark Energy and the evolution of the universe" Oct. 1, 2012 if one assumes the law of conservation of mass / energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent will eventually have to exceed its expansive energy and therefore the universe must at some time in the future enter a contractive phase.)

The velocity of contraction will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of its contraction.

At this point in time the total kinetic energy of the collapsing universe would be equal and oppositely directed with respect to the radiation pressure associated with the heat of its collapse. From this point on the velocity of the contraction will slow due to the radiation pressure and be maintained by the momentum associated with the remaining mass component of the universe.

However, after a certain point in time the heat and radiation pressure generated by its contraction will become great enough to ionize the remaining mass and cause it to reexpand because the expansive forces associated with it will exceed the contractive forces associated with its energy/mass.

This will result in the universe entering an expansive phase and going through another age of recombination when the comic background radiation was emitted. The reason it will experience an age of recombination as it passes through each cycle is because the heat of its collapse would be great enough to completely ionize all forms of matter, including protons and neutrons to their quark components.

However, at some point in time the contraction phase will begin again because as mentioned earlier its kinetic energy cannot exceed the gravitational energy associated with the total mass/energy in the universe.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates the total mass and energy in a closed system remains constant.

This results in the universe experiencing in a never-ending cycle of expansions and contractions of equal magnitudes.

Many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed

Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it. This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and therefore it would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass. This will cause the mass/energy of our three-dimensional universe to oscillate around a point in the fourth *spatial* dimension.

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it.

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of our three dimensional universe is defined its mass and the momentum of its components. Therefore, when one decreases the other must increase and therefore it must oscillate around a point in four spatial dimensions.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space. Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

If this theoretical model is valid the heat generated by the collapse of the universe must raise the temperature to a point where protons and neutrons would become dissociated into their component parts and electrons would be strip off all matter thereby making the universe opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow matter to recapture and hold on to them.  This Age of Recombination, as cosmologists like to call it is when the Cosmic Background Radiation was emitted.

One could quantify this theories model by using the first law of thermodynamics to calculate the temperature of the universe when the radiation pressure generated by its gravitational collapse exceeds the momentum of that collapse and see if it if it great enough to cause the complete disassociation of the proton and neutron into their quark components as it must to account for their observed properties and that of the Cosmic back ground radiation.

Additionally because of its cyclic nature it would give one the ability to understand the mechanism responsible for our expansion of our present universe in terms of the properties of the universe that preceded it.

154
Why something
 rather than nothing
Jan. 1, 2013

The Big Bang theory suggests that matter and antimatter should have been produced in equal quantities.  Since collisions between matter and antimatter result in their mutual annihilation there should not be any ordinary matter, and its antimatter equivalent left in the universe.  However, it is obvious this did not happen because no galaxies or intergalactic clouds of antimatter have yet been detected that have the ability to offset the observed quantity of matter in the universe.

This is the reason the question "why is there something rather than nothing?" one of the most perplexing in modern physics.

It is perplexing because the asymmetrical relationship between matter and antimatter is difficult to explain in terms of the geometric properties of a space-time universe.

Einstein defined mass in terms of a unidirectional curvature in the "surface" of a space-time manifold generated by a slowing or dilation of the time dimension and because rate or passage of time cannot increase beyond the value defined by the velocity of light this curvature must always be in the same "concave" direction with respect to the "surface" of three-dimensional space.

Therefore in the space-time universe of Einstein one cannot define the asymmetries between matter and antimatter in terms of their geometric properties because according to it all matter including antimatter is created by a symmetrical concave curvature in a space-time manifold.

Granted some have devised cleaver or "adhoc" mathematical solutions to this problem by postulating the existence of negative time or time that moves backwards however there is no experimental or observational evidence to support its existence.

Yet one can understand the asymmetry between matter and antimatter if one converts or transposes Einstein's field equations that define mass in a space-time universe to those that would define it in terms four *spatial* dimensions.  This is because observation of our environment tell us we can move in two directions in the spatial dimensions upwards or downward backward or forwards whereas they tell us we can only move in one direction in a space-time dimension, forwards. 

Therefore transposing Einstein's space-time concepts to four *spatial*  dimensions would enable one to derive the properties of matter and antimatter in terms of a asymmetrical bi-direction curvature in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension whereas one cannot in a space-time dimension.

This is possible because Einstein derived the geometric properties space-time, energy and the dynamic balance between it and mass in terms of the constant velocity of light and the equation E=mc^2. 

For example he told us the energy associated with mass causes a curvature or contraction in the "surface" of space-time and when mass is converted to energy it causes the three dimensional properties of space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy also has a spatial component.  However, because the equation E=mc^2 uniquely defines the geometric properties of a space-time universe in terms of both energy and mass one can use it to convert or transpose the curvature in space-time Einstein's field equations associated with energy to one that would define the curvature in a four *spatial* dimensions he indirectly associated with the *spatial* properties of mass.

Additionally because the velocity of light is constant it also defines a one to one qualitative and quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

One of the theoretical advantages to this change in perspective is that observations tell us that one can move, as mentioned earlier in two directions in a spatial environment upwards or downward and backwards or forwards whereas can only more in one directions forwards in time. This would enable one to conceptually derive the asymmetrical relationship between matter and antimatter in terms of a bidirectional displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words one can derive the asymmetrical properties of matter and antimatter in terms of a asymmetrical bi- directional displacement in a universe consisting of four *spatial* dimension whereas one cannot in one made up of space-time.

In the article #23 "Defining energy"  Nov. 27, 2007 it was shown the quantity of energy/mass in a system can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the magnitude of that displacement defines its quantity.

This displacement is analogous to the space-time curvature that Einstein postulated is responsible for the energy/mass content in a volume.

However, even though they are based on different geometries they make, as has and will be shown in "Imagineer's Chronicles" and its companion book "The Reality of the Fourth Spatial Dimension" identical predictions regarding the relativistic properties of space and time and the equivalence between gravitational and accelerated reference frames as Einstein's' theories. 

As mentioned earlier this would allow one to conceptual derive the asymmetry properties of matter and antimatter in terms of a classical environment without having to assume the existence of negative time because one could derive it in terms of oppositely directed displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words one could define the energy/mass associated with the particle component of  matter in terms of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while define the energy/mass of its anti particle in terms of a "elevation" in that "surface".

Therefore using the concepts develop in the article #23 "Defining energy" one could derive the total energy in a matter / antimatter system in terms of the oppositely directed displacement in a "surface" of a three- dimensional space manifold with respect to a fourth *spatial* dimension associated with their particle properties.  In other words, the total energy of a particle / anti-particle system would be equal to the sum of absolute magnitudes of their displacements.

This means that one can understand why particle antiparticle annihilation occurs in terms of the "upward" directed displacement in a "surface" of a three-dimensional space manifold associated with an antiparticle "filling in" the equal but oppositely directed "downward" displacement associated with a particle while defining the energy released when they do so in terms of the sum of the absolute value of their oppositely directed displacements.

However, this also provides an explanation of why there is more matter than antimatter in there universe

As was mentioned earlier, one can derive the energy/mass of a particle in terms of a "downward" directed displacement in that "surface" with respect to a fourth *spatial* dimension while the energy/mass of an antiparticle in terms of an "upward" directed one in that same surface.

But this indicates on average it would require less energy to form an antiparticle than a particle for the same reason that it takes less energy to fill a bucket with water by pushing it down below its surface than it does by lifting the water into a bucket that is above its surface because the one above the surface is at a higher gravitational potential.

Similarly the energy/mass content of matter would be greater than its antimatter counter part because it would be at a higher energy potential with respect to the "surface" of three dimensional space.

Therefore, there would be some energy left over if an equal number of particles and antiparticles were annihilated.  This left over energy is responsible of energy/mass of particles presently in the universe.

The reason this left over energy/mass takes the form of a particle and not an anti particle is because the relative properties of energy/mass means it can be defined in terms of a reference frame that would result in it being called particle instead of an antiparticle.

This defines the reason in terms of the geometry of four *spatial* dimensions for the asymmetry between particles and antiparticles and why there should be more particles than antiparticles left over after the big bang even though they were produced in equal numbers.

As mentioned earlier this cannot be done in a universe consisting of four dimensional space-time because time is only observed to move in one direction forward and therefore could not support the bi-directional movement of three-dimensional space required to define the asymmetry between matter and antimatter.

 

153

Instrumentalism and realism
Dec 15, 2012

In the philosophy of science instrumentalism and realism define what constitutes an acceptable theory.

Instrumentalists claim that scientific theories are merely useful tools for predicting phenomena instead of true or approximately true descriptions of the physical world while realists hold the view that they should be. 

As Richard DeWitt points out in his book "Worldviews: An Introduction to the History and Philosophy of Science"

"The disagreement between instrumentalists and realists as to what constitutes a valid theory goes back to the beginnings of science. Both agree that an adequate theory must accurately predict and explain the relevant data. However realists require, in addition, that an adequate theory pictures, or models, the way things really are.

For example to an instrumentalist between AD 150 and 1500, the question “Are epicycles real?” would not have been an important question to ask because Ptolemy’s theory which involve epicycles accurately predicts and explains the observation data relevant to that time, and that is all that is important.

On the other hand, for a realist this question would be important because they are not only are concerned with how accurate a theories predictions are but on establishing the "reality" of the conceptual basis for those predictions.  In other words do epicycles really exist or are they illusion created by the human intellect to explain why Ptolemy's predictions are accurate.

This issue whether we should require theories to reflect the way things really are, which distinguishes instrumentalists and realists is just as controversial today as it was Ptolemy's time.

For example even though the quantum mechanics with its "peculiar-looking" wave functions makes excellent predictions of quantum facts should we ask ourselves if it reflects the way things really are or accept it only on the bases that it allows us to make very accurate predictions of quantum phenomena.

This is particularly important because the wave function of quantum mechanics may be one of the weirdest inventions of the human mind to explain the "reality" of the facts or observations our environment.

Weird because no one has been able to interpret what it tells us in terms of the "reality" we observe around us.

For example the Copenhagen interpretation defines the existence or "reality" of a particle in terms of the mathematical properties of a wave function that is spread out over the entire universe and tells us it only appears in a specific place when a conscience observer looks at it. Therefore it assumes the act of measurement or observation creates its physical reality. However because only conscience human beings can be observers it implies that nothing can exist without them being there to observe them.

However because human are made up of atoms if one assumes that atoms exist only after being observed by a human one must also assume that humans evolved out of something that did not exist.

Clearly the Copenhagen explanation deviates from the "reality" of the observable world and the presently accepted laws of physics because up until it came along they told us that something cannot be created out of nothing.

However instrumentalists claim this is not a problem because quantum theory makes extremely accurate predictions of all observed facts regarding a quantum environment however the realist say wait a minute are you telling us that we should accept your explanation of the facts that have no resemblance to the "reality" we see around us.

Who is right?

Both the instrumentalists and realists have created valid arguments to support their positions as to what constitutes a valid theory so how should we decide.

One way to determine which is best suited to the advance our ability to accurately define what we observe in our environment would be to look at the evolutionary history of theoretical science and determine which of these philosophies provide the greatest motivation for scientific progress.

Historically most paradigm shift in our understanding of our universe has been a result of attempting to understand what we observe in terms of the "reality" of what we see around us.

For example, new discoveries, such as those involving Galileo and the telescope, eventually led to the rejection of the Ptolemy’s geocentric model and the adoption of the more observationally corrected heliocentric one based on a new understanding of the "reality" they provided.. 

However even before Galileo's observation there were suggestions that something was not right with Ptolemy model because no one had ever observed objects spontaneous moving backwards in what is called retrograde motion other than the planets.

This should have and did cause some to question the validity of Ptolemy explanation of planetary motion long before Galileo made his observations. 

Why then did it take almost 1500 years before its validity was rejected by the majority of the scientific community?

It may have been because of the instrumentalist's attitude of that period allowed the majority of thinkers at that time to focus primarily on its ability to make accurate predictions of where the planets would be located in the future and not on the mechanism defining how they got there.

In other words because instrumentalism was the predominate philosophy at the time, scientists were able to ignore or marginalize those who questioned the validity of the Ptolemy's model.

Therefore one could justifiably say that instrumentalists of that period created an atmosphere that caused or gave science the ability not to explore or ignore possible explanations that were more closely related to reality behind those observations.

This is one of the fundamental flaws in the instrumentalist’s philosophy. 

By saying that a theory does not have to represent a true or approximately true descriptions of the physical world gives them an excuse not to look for a way explaining the "reality" or attempt to understand what we observe in terms of the mechanistic properties world we see around us.

Today the instrumentalist's attitude towards understanding of reality is alive and well as today's acceptance of quantum mechanics which is based solely on its mathematically predictive ability demonstrates. 

However should we trust their abstract mathematics to define our understanding of reality or should we let the "reality" of observations guide our understanding of the mathematics that define it.

History has shown the pitfalls of the instrumentalist’s philosophy or basing theories validity only on its mathematical ability to make accurate predictions of what we observe.

152
A classical interpretation of
 Heisenberg’s Uncertainty Principal
Dec. 1, 2012

We have shown throughout "The Imagineer’s Chronicles" and its companion book "The Reality of the Fourth *Spatial* Dimension" there would be many theoretical advantages to defining space in terms four *spatial* dimensions instead of four-dimensional space-time.

One of them is that it would allow one to understand the classical origins of Heisenberg's Uncertainty Principle by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension. 

In the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown it is possible to understand the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.

However, it did not explain how the boundaries of a particle’s resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the "box" containing the resonant system the article "Why is energy/mass quantized?" associated with a particle.

However, this is not possible in space-time environment because time is only observed to move in one direction forward and therefore could not support the bi-direction movements required to define the boundary conditions for a resonating system.

In quantum mechanics, the uncertainty principle asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

However, as mentioned earlier one can define its physicality in terms the geometry of the four *spatial* dimensions because Quantum Mechanics mathematically defines the position and momentum of a particle in terms of one dimensional point.

Therefore according to the above concepts there would be an uncertainty in determining its position because that one dimensional point could be found any with the volume of the three-dimensional "box" mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of the movement of a one dimensional point.  Before one could determine a particle's momentum one would have to know its exact position in the box at the "end" points were one measured its velocity.  However, as mentioned above that one dimension point representing a particle could be found anywhere in the box containing the resonant structure that define a particle in the article "Why is energy/mass quantized?"  Therefore one could not determine its exact velocity and therefore its momentum because there will always be an uncertainty as to where in the box the one dimensional that represents a particle is relative to the dimensions of the "box" when a measurement is taken.

The reason why one cannot simultaneously measure both with complete accuracy is because the act of measure its momentum or position requires one to access different segments the "box" containing the one dimensional point particle.

For example if one wants to make the most accurate measurement possible of its momentum internal to the box one would have to measure the time it took for it to transverse a given segment of it.  However this means that one could not determine its position because it would be changing through the entire time that it took it to transverse that portion of the box.

However if one wanted to make the most accurate measurement possible of its position internal to the box it would have to be stationary with respect to the box's geometry meaning that one could not determine its monument because it would not be moving.  Since these two measurements required one to access different segments of a particle’s geometry they are mutually exclusive. 

Therefore one cannot simultaneously measure a particle position x and momentum p with complete accuracy.

This defines in terms of classical mechanics why there is a limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

151
Who should teach “reality”?
Nov. 15, 2012

This question is especially relevant for the scientists who struggle on a daily basis to help us understand the reality of the world of things as they are revealed to our senses and interpreted by our intellect.

However history has shown us that defining the "reality" of the world of things is not as easy as some might believe.

For example most European scientists in the Middle Ages believed that Ptolemaic or geocentric system of astronomy defined the reality of planetary motion in terms of the existence of epicycles.

It was not until scientific investigations were stimulated by Copernicus and advancements in observational technology made in the 15 hundreds did they realize epicycles did not exist and that the planets did not revolve around the earth but the sun.

This is true even though many Greek, Indian, and Muslim savants had published heliocentric hypotheses centuries before Copernicus.

Yet how is possible that two groups can have such a divergent concept of reality and why did it take so long for the heliocentric, the more representative interpretation of that "reality" to be accepted by the European scientists.

The reason cannot be attributed to different technologies because they were both based on naked eye observations.  In other words they both had access to the same world of sensory information.

This suggests the reason may have been related to how these two groups interpreted data.

In the Middle Ages the Catholic Church was the dominate force in the European society and was able to influence how the world was viewed.  In fact many blame them for the lack of progress in the sciences during what has come to be called the Dark Ages.  

They will often point to how in 1633 they forced Galileo to recant the concept of a heliocentric universe he was promoting.

However the fact it took more than a 500 years for Europeans to accept the more representative concept of a heliocentric solar system points to a more fundamental flaw not only in that culture but in the functionality of the human mind that is related to the Churches desire to suppress it.  In other words during that period the flexibility of its creative process were inhibited by the rigidity of the authoritarian rulers of that period

This was not as much of a problem for Greek, Indian, and Muslim savants because they had a more diverse and less rigid historical tradition.

Many think that we have left the age where those in authority can dictate how a population views reality.

Yet there are many similarities between then and now

This become apparent when looks at how modern science is attempting to integrate the new discoveries relating to dark matter and energy into the current theoretical models.

As mentioned earlier one reason the Dark Ages lasted so long was because the educational authorities (The Church) of that period felt that it agree more closely with their ideology or what they believe reality to be.  Therefore they only considered the Ptolemaic or geocentric model even after new observations, such as the one made by Galileo suggested that a heliocentric one was a more plausible.   Another contributing factor was that they also controlled the education system and had the ability to dictate what ideas were and were not studied and therefore the intellectual direction students could take.

In other words the intellectual authorities of that period prevented or at least made it extremely difficult for European's to look in direction other than what they wanted them to. 

Unfortunately not much has changed since then because the authoritative nature of the modern science and educational systems still dictates what ideas can and cannot be explored by their members.

For example most modern educational systems dictate to their students what subjects they will study and which books are used by limiting the selection of them.  However, similar to the authorities in the Dark Ages it gives them the ability to control or influence the intellectual direction students can take because in many cases the books and subjects they are required to study champion the ideas and concepts that support those of the intellectual authorities.  In other words modern system of education are similar to the ones in the Dark Ages in that in many cases it prevents or at least makes it extremely difficult for today's students to look in direction other than one that intellectual authorities of our time what them to.

Some say this is not a valid comparison because modern educators in most cases do not overtly threaten their students who challenge them with them with physical harm as was sometimes done in the dark ages. However modern students know that they must graduate to get good jobs and to do that they must prove to their teachers that they have mastered the ideas contained in the books they are required to read.  Unfortunately due to the repetitive nature of most of our educational systems it also has the undesirable effect of conditioning their minds to think only in those terms.

Additionally similar to the earlier 19 hundreds today's higher education makes it very difficult for those individuals who have voice their dissatisfaction with the current theoretical models to get accepted to a graduate program which discourages them form thinking "outside of the box".

Some might disagree and point to Einstein who in those years successfully promoted a new paradigm that changed our understanding of our universes.  However he accomplished that not with the help of the authorities but in spite of them. They should remember he developed those ideas not as a graduate student or in the confines of a facility devoted to higher education but as a low level clerk in a patent office.

This means that at a very early age most are indoctrinated by the intellectual authorities to their way of thinking because they know if they do not or voice opposition to it they will have negative impact on their ability to get a good job or continue their education.

This does not present a problem if their thinking is correct however it does if it is not because that indoctrination makes it extremely difficult to look in a new direction.

History has shown the most reliable way of interpreting reality is based on observations.  New observations related to Dark Matter and Energy among others is forcing many in the scientific community to question how modern theories have interpreted the "reality" which defines our universe. 

Changing an authoritative regime is very difficult in politics as well as in science.  However history has shown that changes are inevitable when the facts demand it no matter how much they try to prevent it.

150
The physical significance
 of Planck's constant
Nov 1, 2012

We have shown throughout "The Imagineer's Chronicles" and its companion book "The Reality of the Fourth *Spatial* Dimension" there would be many theoretical advantages to defining space in terms four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow for understanding of the physical significance of Planck's constant in terms of the laws of classical physics.

In the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown it is possible to explain and predict the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in an environment of four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency

This means that one can theoretically derive the quantum mechanical properties of Schrödinger's wave function in terms of the physicality of resonant properties of four *spatial* dimensions if one assumes as is done here that its mathematical properties are representative of wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However it also gives one the ability to understand the physical meaning of Planck's constant or 6.626068 × 10-34 (kg*m2/s) by extrapolating the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries or the "box" containing the wave or wave function the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a particle. 

Planck's constant is one of fundamental components of Quantum Physics and along with Heisenberg’s Uncertainty Principle it defines the uncertainty in the ability to measure more than one quantum variable at a time.  For example attempting to measure an elementary particle’s position (▲x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particle’s momentum (▲p) to an equally high degree of accuracy.  Heisenberg’s Principle is typically written mathematically as ▲x▲p  ³ h / 2 where h represents Planck constant

As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article "Why is energy/mass quantized?" predicts that a particle will most likely be found in the quantum mechanical "box" whose dimensions would be defined by that resonant wave.  However quantum mechanics treats particles as a one dimensional point and because it could be anywhere in it there would be an inherent uncertainty involved in determining the exact position of a particle in that "box".

For examine the formula give above ( ▲x▲p ³ h / 2 ) tells us that uncertainty of measuring the exact position of the point in that "box" defined by its wavefunction would be equal to ▲x▲p  ³ h / 2.   However because we are only interested in determining its exact position we can eliminate all references to its momentum.

However if we eliminate the momentum component from the uncertainty in a particle position become 6.626068 × 10-34 meters or Planck's constant.

As mentioned earlier the uncertainty involved in determining the exact position of a particle is because it is impossible to determine were in the "box" defined earlier the quantum mechanical point representing that particle is located.  However as mentioned earlier Planck's constant tells us that one cannot determine the position of a particle to an accuracy greater that 6.626068 × 10-34.  This suggest that Planck constant 6.626068 × 10-34 defines the physical parameters or dimensions of that "box" because it defines the parameters of where in a given volume of space a quantum particle can be found.

This shows how one can define and understand the physicality of Planck's constant by extrapolating the laws of classical physics in three-dimensional environment to a fourth *spatial* dimension if one assumes as is done here that the quantum mechanical properties of the wave function are cause by a resonant structure in four *spatial* dimensions.

149
Time dilatation in
 four spatial dimensions
Oct. 15, 2012

We have shown throughout the Imagineer’s Chronicles and its companion book "The Reality of the Fourth *Spatial* Dimension" there would many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

One of them is that it would give explanation of why time is dilated in bodies that are in relative motion or a gravitational field that is more consistent with its observed properties than is provided by the space-time concepts of Albert Einstein's Special and General Theories of Relativity. 

For example observations made by both physicists and non physicists alike suggests that time is only a non-physical measure of when in relation to other events a physical, chemical, and biological change take place similar to how a unit of length is a non-physical measure of the where in relation to other objects one is located in a three dimensional environment. This is because similar to time, length is not perceived as having the physical properties of matter or space but only as measurement of where one object is located relative to another. 

In other words observations regarding time suggest that it only has the non-physical properties associated with a measurement and not the physical properties of Einstein's time or space-time dimension.

Additionally our perception of irreversibly of time or that it always moves in one direction, forward also appears to contradict the concept that it has physical properties because it is possible to reverse the position of an object in a spatial dimension whereas one cannot in a time or space-time dimensions.  For example, one can move an object to a different position with respect to where it was and then reverse the process and move it back to its original position three-dimensional space whereas one cannot in a move an object forward in a space-time dimension time and then move it back to its original position with respect to time.  Therefore observations suggest that a time or a space-time dimension does not share the physical properties associated with the spatial dimensions.

Therefore, defining a space-time dimension in terms of its physical properties as Einstein did does not appear to be consistent with the observation that time is irreversible.

However, this same observation, as was shown in the earlier article  "Defining time" Sept 20, 2007 suggest that time may only be a non-physical a measure of the sequential ordering of the casualty of events because one cannot reverse the causality of an event without creating a new event thereby making it consistent with the perception of its irreversibility.

That article also showed why assuming time only has the non-physical properties of a measurement would provide an unambiguous definition of it that is more consistent with both physical and mathematical observations of time than defining it in terms of the physical properties of a dimension as Einstein had done.

It also points out one of the most obvious observational flaws with Einstein's assumption of the physicality of time or a space-time dimension is that no one has ever observed any of its physical properties and therefore it is difficult to explain or understand how it can interact with the physicality of three-dimensional space to cause gravity. 

Yet Einstein gave us a way of translating the non observable physical properties of time to the physically observable properties of a spatial dimension when he defined its geometry in terms of the constancy of the velocity of light.

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in the equation E=mc^2 to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of energy/mass and the constant velocity of light he provided a quantitative means of redefining his space-time universe in terms of geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein's one must assume that energy also must have spatial properties.

As mentioned earlier Einstein equation E=mc^2 tell us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.  Yet it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward.  However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that we can move in two direction in a spatial environment up down forwards of backwards.

The fact that one can use the equation E=mc^2 to qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article  “Defining potential and kinetic energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words one can use Einstein's equations to quantitatively and conceptually define energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

However, as was shown in the article “Gravity in four spatial dimensions” Dec. 01, 2007 one can use the same technique to derive a one to one qualitative and quantitative correspondence between the space-time curvature Einstein postulated was responsible for gravity and the curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension that article postulated was responsible for it.  Additionally because they are both based on constancy of the velocity of light the relative magnitude of the "curvature" caused by given quantity of energy/mass in a space-time universe and one consisting of fourth *spatial* dimensions will be identical.  In other word the magnitude of a gravitational field in both a space-time environment and one of four *spatial* dimensions would be dependent on the quantity of energy/mass that environment contained.

However as was mentioned earlier a worldview based on the existence of four *spatial* dimension instead of four dimensional space-time has an advantage in that it also allows one to explain time dilation and predict relativistic properties of space, time, mass, and energy in terms of the observable spatial properties of a three-dimensional environment instead of as Einstein did of using the unobservable ones of a time or a space-time dimension.

For example we observe that the kinetic energy associated with a satellite opposes the gravitational energy of the object it is orbiting.

It is difficult to understand in terms of four dimensional space-time because as mentioned earlier all forms of energy in a space-time environment are defined in terms of a curvature in its geometry. However because time is observed to only move in one direction this curvature for both kinetic and gravitational energy must always be in the same direction thereby making it difficult to explain why they oppose each other.

However this is not a problem if one defines energy as was done in the article  "Defining potential and kinetic energy?" in terms of the geometry of four *spatial* dimensions because we observe that we can move in two direction upwards and downwards or backwards and forwards in a *spatial* dimension.

Therefore one can explain and understand why kinetic and gravitational energy oppose each other by deriving them in terms of oppositely directed curvatures in "surface' of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However this means according the concepts outlined above the total energy/mass of an object would be equal to the sum of the absolute value of the displacements in a "surface" of a three-dimensional space manifold caused by the rest mass of an object and that caused by its relative velocities.  This is because the total curvature associated the kinetic and gravitational energy in a given volume of space would be equal to sum of the difference between their magnitudes and because there are opposite or negatively directed with respect to the each other one would have to add their absolute magnitudes to get the total energy/mass in a given volume space.

Therefore, the total energy/mass of an object would be dependent on its relative motion because one must add the energy/mass associated with its motion to its rest energy/mass.

However defining the gravity and kinetic energy in terms of oppositely directed curvatures in four *spatial* dimensions not only defines the reason for the mass increases associated with relative velocities that is more consistent with observations but it also provides an more consistent explanation for the casualty of time dilation and the length foreshortening observed in gravitational and moving reference frames based on physical observations made in a three-dimensional environment.

The following analogy can be used to understand and define the relativistic properties length and time based on observations made in a three-dimensional environment.

Assume that two "2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop.

Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.

If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.

Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.

Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of a three-dimensional curvature in the surface of the paper.  Therefore each will measure the distance between them on their piece of paper as being longer as the diameter of the pencil increases then they would if they viewed it on the other piece.

Similarly, because three-dimensional beings could only "view" a three-dimensional translation of a "curvature" or displacement in four *spatial* dimension caused by the relative motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is in relative motion to it.

This is the mechanism responsible for the relativistic properties of length in terms of the geometry of four *spatial* dimensions.

The two-dimensional creatures in the earlier example will also notice that time is effected by a curvature in the surface of their paper.

Each of them will view the others “time” as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two dimensional translation of that curvature. Therefore, it will take longer for events "move" through a curvature in three-dimensional space on the surface of the others piece of paper relative to the time it would take for it to move thought the two-dimensional translation of that curvature.

Earlier it was mentioned that time can be defined only being the measure or the "distance between" the sequential ordering of the causality of an event.

Therefore, according to that definition time will become dilated in reference frames that are in relative motion because the curvature generated in three-dimensional space by its motion will cause three-dimensional beings in that reference frame to view the distance between events to be longer in than it would be for an observer who is outside of it.  Therefore, they will view time in a reference frame that is in motion relative to them as moving slower than if they were in that reference frame.

As mentioned earlier article  "Defining potential and kinetic energy?" showed both “gravity” and kinetic energy can be define in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as a curvature in a space-time manifold.

However, this means that one can also define the foreshortening of the length of an object in a gravitational field in terms of the cord to the arc similar to how it was earlier derive in terms of the curvature caused by the kinetic energy of an object.  This is because the cord of an arc is always shorter than the arc itself and since three-dimensional beings can only observe the three-dimensional cord of an arc in four-dimensional space they would view the length of the objects to be shorter when viewed in relative motion or in a gravitational field.

However it would also provide a mechanism for why time dilated with gravitational field that is consistent with our observations of three-dimensional space.

Time would be dilated with respect to a reference frame that is external to a gravitational field because as mentioned earlier the length of the arc generated in three-dimensional space by a gravitational field or the kinetic energy of relative motion to be longer than the cord of that arc.  Therefore, the distance between events would be greater for an observer in those reference frames than for one who is outside of it.  However, this means an observer outside of those reference frames would measure the time between those events as being dilated with respect to an observer who is inside because the time required for objects to move between events in that reference frame will be longer.

This shows one can theoretically define a mechanism responsible for both the time dilation and foreshortening of the length associated with objects in relative motion or in a gravitational field based on physical observations of a three-dimensional environment that is fully consistent with the qualitative and quantitative predictions of relativity by assuming space is composed of four *spatial* dimensions.

However as was mentioned earlier a worldview based on the existence of four *spatial* dimension instead of four dimensional space-time has an advantage in that it also allows one to derive them by extrapolating the observable spatial properties of a three-dimensional environment to a fourth *spatial* dimension instead of as Einstein did by extrapolating the unobservable property of time to a space-time dimension.

148
Dark energy and the
 evolution of the universe
Oct 1, 2012

We have shown throughout "The Imagineer's Chronicles" and its companion book "The Reality of the Fourth Spatial Dimension" there would be many theoretical advantages to assuming the universe is made up of four *spatial* dimensions instead of four-dimensional space-time.

For example it would allow one to theoretically integrate Dark Energy or the force that is causing the accelerated expansion of the universe into Einstein theories and explain how it would affect the future evolution of the universe. 

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

For example he told us the energy associated with mass causes a curvature or a contraction in the "surface" of space time and when mass is converted to energy it causes space-time to expand because of a decrease in its curvature he associated with that event. This expansion and contraction would be analogous to how the two dimensional "surface" of a balloon either expands of contract when air (energy) is added or taken away from it.

However one of the difficulties in integrating the expansive force called Dark Energy into Einstein's space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore to explain the observed spatial expansion of the universe one would have to assume the existence of a fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein's theories contain.

This would be true if Einstein had not given us a means of quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

As mentioned earlier Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in the equation E=mc^2 to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a quantitative means of redefining his space-time universe in terms of geometry of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein's one must assume that energy also must have spatial properties.

As mentioned earlier Einstein equation E=mc^2 tell us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.  Yet it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward.  However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that we can move in two direction in a spatial environment up down forwards of backwards.

The fact that one can use the equation E=mc^2 to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article  “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words one can use Einstein's equations to quantitatively define energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamic that energy flows from areas of high density to area of low density very similar to how water flows form an elevated or "high density" point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it and that the force associated with that expansion will decline as its surface spread out.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article  “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension,

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it and that the force associated with that it will decline as it surface increases. 

This would explain what the force called dark energy is and why it is causing the accelerated expansion of the universe in terms of the geometry of four *spatial* dimension.

However it should be remembered this solution was derived directly from Einstein's General Theory of Relativity.

As mentioned earlier one can use the equation E=mc^2 to show the ratio of the attractive gravitational mass component of a three-dimensional environment with respect to its expansive energy component must increase as space expands because it tells that each unit of space that undergoes cooling or reduction in energy must be accompany by an increase in its mass component.  Granted this mass would be spread out over a very large volume however it would still exert a gravitational influence on its environment that would counter act the expansive properties of Dark Energy. 

Yet this tells us the evolution of our universe would be defined by a dynamic interaction between the spatial components of mass and energy because it tells the forces associated with them diametrically opposed each other.

Presently the universe is in an overall state of expansion with respect to a fourth *spatial* dimension because as mentioned earlier the expansive energy due to the elevated "surface" of three-dimensional space exceeds the contractive gravitational forces associated with its energy/mass component.  However as time goes by the power of its expansive component will decrease for the same reason as the expansive power of the water in the pool whose walls have collapsed decrease as it expands.  This means the contractive gravitational forces Einstein associated with energy/mass will become predominate.  This will result in the entering a contraction phase.

This contraction will continue until the heat generated by its collapse elevates the "surface" of three dimensional space with respect to a fourth *spatial*enough to counter act the contractive forces caused the gravitational component of its energy/mass thereby causing it to enter a period of expansion.

However after a given period the power of its expansive forces will decrease because as mentioned the elevation in the "surface" of three dimensional space with respect to a fourth *spatial* dimensions decreases as it expands in a four dimension environment and the contractive force Einstein's equation E=mc^2 associates with mass will again take over.

It should be remember this derivation of the evolution of the universe is based entirely on Einstein experimentally verified equation of E=mc^2 and absolutely nothing else

147
A Classical Quantum environment
Sept. 15, 2012

Many scientists assume that we must define the "realty" or non-reality of our classical world based on the concepts defined by quantum mechanics. 

For example the Copenhagen interpretation tells us that a particle is spread out as a wave over the entire universe and only appears in a specific place when a conscience observer looks at it.  Therefore it assumes the act of measurement or observation creates its physical reality and that of the universe.  However because only conscience human beings can be observers it implies that nothing can exist without them being there to observe them.

Not only is it a bit self centered for humans to assume that they (humans) are the sole arbiters of the physicality of the universe but it is also shows how out of touch with reality those who believe in it are for the simple fact that the is overwhelming scientific evidence that humans physically evolved over a finite period of time.  However, if one assumes that atoms exist only after being observed by a human one must also assume that humans evolved out of something that did not exist.

However one of the reasons many scientist believe this is because they feel it the only way to resolve the physical conflicts they find between the experiment observations of the microscopic realm of the atom and the "reality" we see in our macroscopic universe.

For example quantum mechanics assumes that all energy/mass is encapsulated in what is called a wave function which collapses into the reality most of us associate with our particle world only when it is observed. 

However as Greene, Brian points out in his book "The Fabric of the Cosmos: Space, Time, and the Texture of Reality" (Kindle Locations 3750-3752).

"No one has been able to explain how an experimenter making a measurement (observation) causes a wavefunction to collapse? In fact, does wavefunction collapse really happen, and if it does, what really goes on at the microscopic level? Do any and all measurements cause collapse?

The name give to the inability to define what happens to the wave properties of energy/mass when a measurement or observation is made is called the measurement problem and has given rise to different interpretations of quantum mechanics.  Many of these interoperations assume that Schrödinger wave function defines an atom in terms of the linear superposition of its particle and wave states even though actual measurements always find the physical system in a definite state.   Additionally experiments tell us that any future evolution must be based on the state the system was discovered to be in when the measurement was made and not on its history, meaning that the measurement "did something" to the process under examination.   Many believe whatever that "something" may be does cannot be explained in terms of classical theories.

However, it can be shown that one can explain and understand the "something" that happens when a measurement of the wave function is made by extrapolating the theoretical concepts of classical mechanics in a three-dimensional environment to a fourth *spatial* dimension.

In the article  "A classical Schrödinger’s wave equation" Mar. 15, 2010 it was shown one can derive the physical reality of the quantum mechanical properties of energy/mass associated with Schrödinger's wavefunction by extrapolating observations of classical three-dimensional space to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one made up of four.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established on a "surface" of a three-dimensional space manifold.

Yet classical theories of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with the fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties associated with the wavefunction in that it only takes on the discontinuous or discreet energies associated with the formula E=hv where "E" equals the energy of a particle, "h" or Planck’s constant would correspond to the energy associated with the fundamental frequency of four *spatial* dimensions and "v" equals the frequency of its wave component.

This shows how one can not only define the physicality of the quantum mechanical properties of Schrödinger wavefunction but also of Planck's constant by extrapolating the classical laws governing resonant system in a three-dimensional environment to a resonant system formed by a matter wave moving in four *spatial* dimensions. 

Yet if so one should be able to explain why in terms of classical theory a measurement "does something" to it and why the future evolution of a quantum mechanical system must be based on the state the system was discovered to be in when the measurement was made and not on what came before it.

Classical mechanics tells us that one should be able predict the future evolution of a system based on its history.  In other words if one knew every detail of a systems history one could measure its future evolution with complete certainty.  However it also tells us that one must interact with a system and therefore change its history to make a measurement.  Therefore, the laws of classical mechanics tell us that one must base the future evolution of a system on new history created by a measurement.  However it also assumes that one can always make the affects of measurement small enough so that it does not significantly change the its evolution.

Yet this is precisely what we observed in a quantum environment in that the act of measurement creates a new history for a system.  The only difference between a classical and a quantum environment is that in the latter the act of measurement always makes significant change which cannot be ignored in determining the future of the environment. 

However this does not mean that one cannot use the conceptual "reality" defined by classical mechanics to understand the physicality of the quantum world because as mentioned earlier classical mechanics also tells us the act of measurement must affect the future evolution of a system.

Granted one cannot use it to quantify the observations of the quantum world because its assumption that one can always make the effects of measurement small enough so that it does not significantly change the future evolution of a system is invalid in the quantum world   However this does not means that we can use it to qualitatively define the realty or the mechanisms responsible for those observations.

The other as of yet unanswered question that Brian Breen brought up in his book, mentioned earlier involving what happens to the quantum mechanical wave function when a measurement is made can also be found in classical mechanics.

As mentioned the earlier article "A classical Schrödinger’s wave equation" showed that one can derive the quantum mechanical properties of energy/mass in terms of a resonant structure by extrapolating the laws of classical mechanics in a three-dimensional environment to a fourth *spatial* dimension.

However, it did not explain how the boundaries of that resonant structure are defined.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the physical boundaries or "box" containing the wave function the article "A classical Schrödinger’s wave equation" Mar. 15, 2010 showed was responsible for the quantum mechanical properties of energy/mass.  In other words this upwards and downwards movement of three- dimensional space with respect to a fourth *spatial* dimensions means that evolution of the wave function would be primary confined to a three-dimensional "box" whose dimensions would be defined by its energy.

In Classical mechanics there are two ways to determine the energy of a wave.  The first is to is to measure it directly by allowing it to impact a measure device or one can do it indirectly by measuring its frequency and using the equation provide by classical mechanism to determine its energy. 

For example one can determine the energy of a wave in a wave tank by observing it from the side to determine it wavelength.  Yet one can also determine it by measuring how much energy is imparted to a measuring device when the wave impacts it at the end of the tank. 

However the wave energy which is transferred to a measuring device does not disappear when it is measured at the end of the tank.  Instead the vertical or up and down displacement associated its (the waves) peaks and valleys is transferred or rotated about its axis to generate horizontal or back and forth displacements in the measuring device that would appear to originate from relatively small or "point source" compare to the wave that generated it.  Classical mechanics also tells us the energy loss associated with that measurement would result in a decrease or "collapse" of a portion of the wave energy in the tank because it tells us that all measurements involve an interchange of energy.

However these methods will give to completely different perspectives of what is happening in the tank.  In the first case the measuring device would view energy source in terms of its extended wave properties while the measuring device at the end of the tank would view it more in terms of a condensed or point like energy source compared to the one associated with its wave properties.

Yet this is exactly what we see in a quantum environment.

As mention earlier the wave function that defines the quantum mechanical of properties of energy/mass is confined to a three-dimensional "tank" or "box" defined by its energy content. 

However if it is true that one can extrapolate the laws of classical mechanics in a three-dimensional environment to a fourth *spatial* dimension to explain why we observe what we do in the quantum world one should be able to use them to explain what happens to the wave function when it is measured.

For example it tells us that there would be two ways to measure the energy of the wave function.  One could measure it by looking down the "side" of the quantum mechanical box mention earlier that contains it or one could observe how much energy is imparted to a measuring device when it impacts it at the "end" of that "box".

However it also tells us these methods will give to completely different perspectives of what is happening in the tank.  In the first case the measuring device would view the energy of the wave function in terms of its extended wave properties while the measuring device at the end of the tank would view it more in terms of a point or particle like energy source.

Yet it also tells us what happens to the wave function when it is measured. It tells us the vertical or up and down displacement associated with it peaks and valleys is transferred and rotated about its axis to generate horizontal or back and forth displacements in the measured device.  These horizontal displacements would appear to originate form a point like or particle source.  It also tells us the energy loss associated with that measurement would result in a decrease or "collapse" of portion of the wave function in the "box" and its evolution would begin again from a new stating point within the measuring instrument.

This demonstrates how one can use the laws of classical mechanics to define the quantum environment and "explain how an experimenter making a measurement (observation) causes a wave function to collapse" by showing that the act of measurement cause its evolution be redirected and why, when one is made its energy appears originate form a point or particle like source.

It should be remember that we are not trying to quantify our quantum experiences but only to explain how and why we experience it the way we do in terms of the "realty" most of us associate with our particle or classical world.

146
The Illusion that is time
Sept 1, 2012

Does time have a physical existence?  If it does why are we not able point to it and say there it is?  If it does not why do physicists define our universe in terms of its physical properties?

This question is relevant because Einstein theories, the foundation of modern cosmology are based on the physical existence of time or a space-time dimension.

Unfortunately there is absolutely no direct observational or experiment evidence supporting its physicality. 

For example no one has ever devised an experiment that can measure its mass or provide observational evidence of its physical existence.

In fact one of the most persistent observations regarding time is that it is not directly perceived in terms of a physical entity such as matter or space but only as a measure of an irreversible physical, chemical, or biological change in a physical system.

However this suggest a unit of time may only be a non-physical measurement of the sequential ordering of a physical, chemical, or biological change in space similar how a unit of length is a non-physical measure of a change in the ordering of the position of an object in space. This is because similar to time, length is not perceived as matter or space but only as a non-physical measure of where an object is located with respect to a given point in space.

Yet this appears to contradict the assumption that time or a space-time dimension is or has the properties of a physical entity because as mentioned earlier most of us do not perceived it as having the physical properties of matter or space.

However, what is even more damaging to the concept that it has physical properties is that it is not required to define relativistic properties of our universe as many physics seem to think.

As mention earlier the primary reason scientists assume that time has physical properties is because the foundation of modern cosmology is based on the physical existence of time or Einstein's space-time dimension.

Yet when Einstein derive the equation E=mc^2 and the relationship between mass and energy in a space-time environment based on the constant velocity of light he the provided a method of converting a unit of space associated with mass to a unit of space-time he associated with energy.  Additional because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions. 

However using Einstein's equations as is suggested above to redefine the universe in terms of four *spatial* dimensions instead of four dimension space-time would not only give it the same quantitative predictive powers because as mentioned earlier there is a one to one correspondence between them but it would also allow us to qualitatively define its components in a manner that is more consistent with our observations of space and time.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein one must assume that energy must also have spatial properties.  Additionally, as mentioned earlier the equation E=mc^2 this gives one the ability to uniquely define the spatial properties of both energy and mass in terms four *spatial* dimensions instead of four dimensional space-time. 

For example the article "Embedded Dimensions" Oct 22, 2007 showed how one can derive all forces including gravitational in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.

Briefly one can understand how that displacement can be is responsible for gravity by comparing it to caused by a rod pushing down on a surface of a rubber diaphragm that has on marble on it.

The marble on the diaphragm will represent the energy/mass of an object and the rod will represent the “W” axis of a fourth *spatial* dimension.

(The "W" axis of a fourth *spatial* dimension was defined in the article "Embedded Dimensions" Oct 27, 2007)

If the end of the rod is orientated perpendicular to the "surface" of the diaphragm and is allowed to touch it without putting any pressure on it, the surface of the diaphragm will remain flat. The marble on the flat diaphragm would not move.

However, if pressure is applied to the rod, the "surface" of the diaphragm will become displaced and will no longer be perpendicular to the rod.

Gravitational forces will then have a tangential component along the "surface" of the rubber diaphragm. The tangential component of the gravitational force directed along the "surface" of the diaphragm will cause the marble to move towards the ape0x of the depression.

However, the article mentioned earlier "Embedded Dimensions" also derived all forms of energy including that contained in mass  in terms of a curvature or displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because mass is a form of energy it should, according to the concepts contained in that article cause space to curve and objects interacting with it will experience a differential force directed towards the apex of that curvature. This force is called gravity.

This is analogous to the force causing the marble in the earlier example to move towards the apex of the curvature in the rubber diaphragm.

However one can also derive the relativistic properties of space time and mass in term of observable properties of the spatial dimensions.

As mentioned earlier the "Embedded dimensions" Oct 22, 2007 derived all forms of energy including gravitational and kinetic in terms of a displacement or curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension and why one can derive kinetic energy in terms of an oppositely directed displacement in its "surface" than the one associated with gravity.

The conclusion that the causality of kinetic energy is a result of an oppositely directed displacement in a "surface" of three-dimensional space with respect to the one associated with gravity is based on the observation that they are oppositely directed.  For example, the kinetic energy of an orbiting satellite is oppositely directed with respect to the gravitational energy associated with the planet it is orbiting.  Therefore, if one defines gravity in terms of a "depression" in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension one should define kinetic energy in terms of a oppositely directed "elevation" in that "surface".

However this means according the definitions given in the article "Embedded dimensions" the total energy/mass of an object would be equal to the sum of the displacements of a "surface" of a three-dimensional space manifold caused by the rest mass of an object and that caused by its relative velocity.

Therefore, the energy/mass of an object would be dependent on its relative motion because one must add the energy of its motion to its rest energy/mass.

This defines the mechanism responsible for why the energy/mass of an object increases when viewed by an observer who is in relative motion to it in terms of the geometry of four *spatial* dimensions.

The following analogy can be used to understand and define the relativistic properties length and time

Assume that two "2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop.

Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.

If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.

Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.

Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of a three-dimensional curvature in the surface of the paper and each will measure the distance between them on their piece of paper as being longer then they would if they viewed it on the other piece.

Similarly, because three-dimensional beings could only "view" a three-dimensional translation of a "curvature" or displacement in four *spatial* dimension caused by the motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is not in relative motion to it.

The "movement" of “time” on both surfaces will also be affected.

Each of the two dimensional creatures mentioned earlier will view the others “time” as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two dimensional translation of those events.  Therefore, it will take longer for events "move" through the curvature in three-dimensional space relative to the time it would take for them to move along two dimension translation of that surface.

Earlier it was mentioned that the magnitude of the displacement or "curvature" an object generates in a fourth *spatial* dimension is dependent on its velocity.

However as mentioned earlier, we have defined time as only being the measure or the "distance between" the sequential ordering of the causality of an event.

Therefore time will become dilated in reference frames that are in motion because of the curvature generated in three-dimensional space by its relative motion, three-dimensional beings in that reference frame will view the distance between events to be longer in it than it would if they were in motion relative to it.  Therefore, they will view time in a reference frame that is in motion relative to them as moving slower than if they were in that reference frame because events in those reference frames will have a greater separation.

The velocity of light is constant despite the relative motion of an observer because the foreshortening or shortening of the length or distance the light travels is proportional to the motion of the observer.  Therefore, the velocity of light will be constant in all reference frames despite the relative velocities of the observers to those reference frames because velocity is defined in terms of distance divided by time.

It should be remember this scenario applies to all forms of energy including gravitational because, as the article “Embedded dimensions” Oct. 22, 2007 showed, three-dimensional beings perceive energy in terms of the magnitude of a "curvature" in "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The Lorentz transformations derived from this theoretical model will take on the same form as the Lorentz transformations derived from Relativity.

This is because this theoretical model postulates that a displacement or curvature in "surface" of a three-dimensional space manifold, with respect to a fourth *spatial* dimension caused by the gravitational or kinetic energy of an object is proportional to the velocity of light.

Therefore, because both Relativity and the above mechanism predict a physical shortening of length and a slowing of time are related to the geometry of space, the form of the Lorentz transformations associated with the foreshortening length and slowing of time will be identical for both of these models.

However, this theoretical model differs from that of Relativity's in that it defines the magnitude of a foreshortening of length and a slowing or dilation of time in terms of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of curvature in four dimensional space-time manifold.

As mentioned earlier the article  "Defining energy" derived the mechanism responsible for gravity in terms of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it was shown earlier that a curvature in a "surface" of a three-dimension space manifold with respect to a four *spatial* dimension was responsible for length foreshortening and time dilation.

Therefore, because both gravitational and the kinetic energy of relative motion are derived from a common "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension they will have a similar effect on physical properties of length and time.

This means both Relativity and this paper predict an observer in a gravitational field will measure the length of an object to be shorter and passage of time to be slower with respect to an observer who is located outside of a gravitational field.

However, as mentioned earlier this paper defines this shortening of length and slowing of time in a gravitational field in terms of four *spatial* dimension instead of four-dimensional space-time manifold.

The "relative" characteristics of a "curvature" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with kinetic and gravitational energy would also make it impossible for an observer to determine if an acceleration is caused by gravitational or kinetic energy such as that from an exhaust of a rockets engine.

This is because the mechanism defined above indicates the magnitude of a force associated with both gravitational and kinetic energy is related to the absolute magnitude of a "curvature" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because a three-dimensional observer can only observe the three-dimensional effects of a curvature in four *spatial* dimensions he or she could not determine whether he or she is in a gravitational field or an accelerated reference frame.

This means the concepts contained in this article would make identical qualitative and quantitative and predictions with respect to the relativistic properties of space and time and the inability to determine the casualty of acceleration in terms of the physical properties of four *spatial* dimensions instead of four dimensional space-time because they are based on the analytical and qualitative properties of Einstein's experimentally verified equation E=mc^2.

As mentioned earlier the primary reason why most scientist assume the physicality of time or a space-time dimension is because the foundation of modern cosmology is based on the physical existence of time or Einstein's space-time dimension.

Yet as this article shows one can make the same quantitative and qualitative predictions regarding them by assuming they are caused by a physical interaction between the third and fourth *spatial* dimension and not one made up of time.

However this article also suggests the reason why scientists are unable physically observe time or a space-time dimension is because its existence is based on the illusion that it is responsible for gravity and the realistic properties of space, time and energy/mass.  

145
The fabric of the Cosmos
Aug 15, 2012

What is the fabric of the cosmos?

Einstein told us that it is made up of a dynamic balance between the properties of space and time.

For example he told us that space is a sort of multidimensional fabric, where the presence of mass causes the fabric of space to curve.  However he did not tell us anything about its composition.  Granted he did tell us what occurs when mass is present however he said nothing about space without mass.  In other words he simply told use how space reacts when mass is present.

The reason may have been because we use the second to measure time while we measure space in units of length therefore, it is very difficult to directly ingrate the properties of time with spatial properties most of us associated with mass.  However, when Einstein derive the equation E=mc^2 and the relationship between mass and energy in a space-time environment based on the constant velocity of light he the provided a method of converting a unit of space associated with mass to a unit of space-time he associated with energy.  Additional because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein's one must assume that energy must also have spatial properties.  However, as mentioned earlier the equation E=mc^2 this gives one the ability to uniquely define the spatial properties of both energy and mass in terms four *spatial* dimensions instead of four dimensional space-time. 

One of the many theoretical advantages to doing this is that it allows one to define the fabric or physicality of space in terms of our experiences. 

The equation E=mc^2 and our experiences tell us there is a dynamic relationship between mass and energy in that when one coverts mass to energy in a closed spatial environment it expands while if one coverts energy to mass in that environment shrinks.  In other words the spatially expansive forces associated with energy oppose or counteract the contractive forces Einstein associated with mass.  However it is difficult to understand how a three-dimensional environment can both expand and contract in a space-time universe because our experiences with time tells us that it only moves in one direction forward.  However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences tell us that spatial environments expand and contract and that one can move in two directions up down or forwards or backwards in it.

Therefore, our experiences with mass and energy indicate that we could define the fabric or physical structure of three-dimensional space based on our experiences in terms of a dynamic balance between contractive gravitational forces of mass, the expansive forces of energy and the geometric properties of four *spatial* dimensions.  This, as mentioned earlier is difficult to do in terms of four-dimensional space-time because our experiences tell us that  time only moves in one direction forward and therefore there is nothing to balance the dynamic interplay of mass and energy with respect to a volume of three-dimensional space.

However because as mentioned earlier the equation E=mc^2 defines a one to one correspondence between a space-time universe and one consisting of four *spatial* dimension the predictive properties of Einstein's space-time universe will not be affected because one can use it to construct one composed of four *spatial* dimensions.

Yet there are other advantages to assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time other than the fact that it would allows us to understand the geometric fabric or structure of three-dimensional space.

One is that it would allow for understanding the origins of Dark Energy or the force that is causing the accelerated expansion of the universe.

The fact that one can use the equation E=mc^2 to show that increasing the energy in a given volume of three-dimensional space causes its expansion towards a fourth *spatial* dimension while decreasing it would result in its contraction is the bases for assuming as was done in the article  “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a displacement in a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.  The qualitative magnitude of this increase or decrease in the volume three-dimensional space with respect to a fourth *spatial* dimension associated with this displacement would be as mentioned earlier by the defined by the equation E=mc^2.

However we know from the study of thermodynamic that energy flows from areas of high density to area of low density very similar to how water flows from and elevated or high density point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to the article  “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe that has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension and similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it. 

Therefore similar how the elevated two dimensional surface of the water in the earlier example accelerated outward towards the three-dimensional environment sounding it our three-dimensional environment will accelerate outward to toward the four dimensional environment surrounding it.

This shows why assuming space is composed of four *spatial* dimensions instead of four dimensional space-time allows one to not only define the fabric or what constitutes the physical structure of space but also why the force called dark energy is causing its accelerated expansion in terms of our experiences with mass and energy.  However it should be remembered this solution can and was derived directly from Einstein's experimentally verified equation E=mc^2

144
Putting the Chromo in
Quantum Chromodynamics

Aug 1. 2012

We have shown throughout "The Imagineer's Chronicles" that there would be many advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow one to understand in terms of classical mechanics the origin of the fractional electrical and color properties Quantum Chromodynamics associates with quarks.

Quantum Chromodynamics, which is an integral part of the Standard Model of Particle Physics, defines how quarks interact with themselves and each other to form particles such as protons and neutrons. The word quantum stands for the fact that interactions (forces between particles) on this level can be represented as things that occur only in chunks called quarks. The word Chromodynamics stands for the color properties it associates with them.

To this point physicists have identified six types of quarks, called the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3 while the Down, Strange and Bottom have a fractional charge of -1/3.

They assume each quark carries a charge called "color" which like electric charge is always conserved. However, unlike electric charge, the color charge (the chromo in Chromodynamics) comes in three varieties or red, green, and blue and that each quark comprising a particle must have a different color, red, green, or blue.

The reason is because Pauli’s exclusion principle says no particle can be made up of components with identical quantum states.  They incorporate this principal into Quantum Chromodynamics theoretical structure by assigning a color to individual quarks and adopting a rule that says for a stable particle to exist the colors of their components must combine to make a colorless particle.  This requires particles to conform to Pauli’s exclusion principle because colorless or white light only exist if it is made up of one part red, blue, and green light.  Therefore a stable particle can only exist it is made up of three different types of quarks with colors of red blue and green.

However as of yet no one has been able to define a physical mechanism responsible for fractional charge or the color component of quarks.

Yet as was show in the article "The geometry of quarks" Mar. 15, 2009 one can derive a physical reason for their fractional charge and color properties if one assumes as was done in the article “Why is energy/mass quantized?” Oct 4, 2007 that the quantum mechanical properties of energy/mass can be derived in terms of a resonant structure formed by a matter wave on "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly that article showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in four spatial dimensions.

The existence of four *spatial* dimensions would give space (the substance) the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations in space would meet the requirements mentioned above for the formation of a resonant system or "structure" in space.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet energy associated with quantum mechanical systems.

The only way to dampen the frequency of a classically resonating system is to add or remove energy from it, which results in changing the characteristics of that system.

Additionally the energy in a classically resonating system is, as mentioned earlier is discontinuous and can only take on the discrete values associated with its fundamental or harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass and when energy is either added or removed from it, its characteristics changed.

But if space was made up of four *spatial* dimensions one should also be able to explain why quarks have a fractional charge and how their color properties interact to form stable particles in terms of the geometry four *spatial* dimension.

The article  "Defining energy" Nov. 26, 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its "surface" with respect to a fourth *spatial* dimension will be observed by us as being directed along that "surface".  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a "surface" of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that "surface".

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article "Embedded Dimensions" Nov. 22, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the geometric configuration or "colors" of individual quarks may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it may also explain why it takes three quarks of different "colors" to form a stable particle because, as mentioned earlier one can define a particle in terms of a resonant system on a "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not stable.

This shows how one can put the color and therefore the Chromo in Quantum Chromodynamics by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

143
A verifiable alternative to the Higgs Boson
July 15, 2012

We have shown throughout "The Imagineer’s Chronicles" and its companion book "The Reality of the Fourth *Spatial* Dimension" there would be many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

One is that it would allow physicists to understand mass and inertia by extrapolating our experiences in a three-dimensional environment to a fourth *spatial* dimension.

For the past 50 years, the Standard Model of particle physics has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.

But as Charles Seife mentions on page 142 of his book Alpha & Omega "Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless."

In 1964 Peter Higgs showed that one can solve this problem and explain the origins of inertial or rest mass is if one assumes space is permeated by what is called a Higgs field.

He was able to show that if a particle changes its velocity or accelerates, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass.  In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field.  It also assumes the disturbance created by mass as it moves through this field would have to generate the particle called the Higgs boson.

The only problem is that it is has been extremely difficult to identify the Higgs Boson (the particle) the standard model associates with the Higgs field) because of the relatively few times it has been observed in the swam of particles created in modern particle accelerators.

This is problematic for its proponents because the Standard Model tells us it should be created more frequently than it has been in the high energy environments of particle accelerators like The Large Hadron Collider (LHC)

This means that scientists should be careful before saying that the particle they have discovered is the Higgs Boson predicted by the Standard Model.

Granted they may have used statistical analysis to determine that a few out of millions particles created in their accelerators has all of its properties however the existence of those particles may be associated with random events.

Therefore they should not only do a statistical analysis to determine if the observed particle has the properties of a Higgs Boson but they should also use the Standard Model to predict how frequently it should appear in the high energy environment they are observing.

If they find that it is not appearing as often as it should one must assume that it may be associated with randomly repeating event which is not connected to the Standard Models predictions.

This is especially relevant because there is an alternative explanation for mass that is based on the observable and therefore verifiable properties of three-dimensional space and does not require the analysis of a few isolated events as is required to verify the existence of the Higgs Field.

Observations of our three-dimensional environment tell us the total potential energy of an object or particle is related to the magnitude of its relative displacement.  For example the potential energy of water in a bucket is in part determined by the height or displacement of its surface relative to the surface of the table it is resting on.  However, its potential energy is greater if one measures it relative to the floor on which the table is resting.

In the following discussion the potential energy of the water in the bucket relative to the table top will represent the rest mass of an object or particle while its energy with respect to the floor will correspond to the energy associated with its relative velocity.

In the article  "Why Space-time?" Sept. 27, 2007 it was showed one can derive the rest or inertial mass of an object or particle in terms of a displacement in a "surface" of a three-dimensional volume with respect to a fourth *spatial* dimension.  Additionally it was shown one can derive the causality of all accelerations including gravitational in terms of an interaction of its mass with the slope of a curvature in a "surface" of a three-dimensional space caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time Einstein theorized was responsible for gravitational accelerations)

However we know from observations that there is an equivalence between mass and energy and that all of the energy, except thermo in a volume of space that is not moving with respect to an external environment is contained in its mass component.  This would be analogous to the fact that all of the potential energy in water in the earlier example is contained in the volume of the bucket on table.

Therefore according to the concepts in the article "Why Space-time?" one could define the inertial or rest mass of an object or particle by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a "surface" of a three-dimensional volume with respect to a fourth *spatial* dimension.  In other words one could define the energy associated with mass in terms of the displacement of a three-dimensional volume with respect to a fourth *spatial* dimension for the same reason as one can define the energy of the water in the bucket as being related to its displacement with respect to the table top.

This shows how one can derive the inertial or rest mass of an object or particle by extrapolating the observable and verifiable properties of three-dimensional space to a fourth *spatial* dimension.

However the article  "Defining energy" derived the energy associated with the relative velocities in terms of a differential displacement with respect to a fourth "spatial" dimension of the three-dimensional environment associated with each object or particle. 

This means the energy associated with momentum or relative velocities would be analogous to the energy created by the displacement of the environment of the table top with respect to the floor in the example mentioned earlier.

Therefore if true one could derive the energy associated with the momentum or velocity of an object or particle in terms of a displacement in of a three-dimensional volume with respect to a fourth *spatial* dimension associated with its rest mass plus that associated with the displacement of its three-dimensional environment with respect to the fourth *spatial* dimension the article  "Defining energy" associated with its relative velocity. (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.) 

This would be analogous to how the total potential energy of water in a bucket would be as mentioned earlier determined by the height or displacement of its surface relative to the surface of the table it is resting on plus the height the table top is above the floor.

The reason mass increases as its velocity approaches that of light is because according to the concepts presented here its magnitude would be equal to the sum of the displacements in a "surface" of a three-dimensional space volume caused by its rest mass and that caused by its relative velocity. Therefore because as was shows in the article  "Defining energy" its displacement with respect to a fourth *spatial* dimension would be directly related to its velocity its mass will increase along with its velocity.

Yet, as mentioned earlier the article  "Why Space-time?" also showed that accelerations are caused by an object or particle interacting with a curved "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Isaac Newton defined inertia or mass as being responsible for why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed.

Yet this is what one would expect if as mentioned earlier the momentum of a particle or object is caused by a "linear" displacement of a "surface" of a three-dimension space volume because it would tend to stay rest or ones in motion would tend to stay in motion unless it interacted with a three-dimensional "surface" that was curved with respect to a fourth *spatial* dimension.

This would also explain the resistance of an object or particle to an acceleration and why it would be directly proportional to its mass because as the article  "Why Space-time?" showed the magnitude of the curvature in four *spatial* dimensions caused by mass would be directly proportional to it and since the causality of all accelerations are a result of an interaction of mass with the slope of a curvature in a "surface" of a three-dimensional space and it would be directly proportional to its mass.  Therefore a mass will interact with the curvature in space that article also associated with an acceleration in proportion to its mass.  In other words there should according to these concepts outline above be a one to one correspondence between the mass of an object or particle and the acceleration it experiences for a given force. 

However this is exactly what Isaac Newton's Second law of motion tells us that "The acceleration of a body is directly proportional to the net force F acting on the body, and is inversely proportional to the mass m of the body, i.e., F = ma.

This not only provides an consistent explanation for the existence of mass based on verifiable observations made in our three-dimensional environment but also solves one of the major conceptual problems associated with the Higgs field and Newton's first law of motion or an object at rest will remain at rest unless acted on by an unbalanced force while an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

If one assumes the origin of mass is an interaction between a particle and the (nonzero) Higgs field and "that a disturbance created by mass as it moves through this field generates the particle called the Higgs boson" one also must assume that mass exchanges energy with the environment associated with the Higgs field.  However this means that all objects will experience an unbalance force as it moves through that environment because that is the only way it can cause a disturbance in it.

Yet this contradicts Newtown's laws of motion and the observation that objects and particles maintain a constant velocity as they move through space because if it was true that mass is a result of an unbalance force or interaction between it and the Higgs field we would observe that they do not maintain a constant velocity while moving through space.

However according to the concepts outlined above mass and velocity are a result of an unchanging "linear" displacement in a "surface" of a three dimensional volume with respect to a fourth *spatial* dimension.  Therefore these concepts conceptually agree with both observations of the movement of particles or objects and Newton laws because as just mentioned the displacement in the "surface" three dimensional space associated with both mass and velocity is unchanging and therefore does not require an interaction with its environment.

This demonstrates that one does not have to assume the existence of the Higgs field or Boson to explain why particles have mass and inertia because it can be explained by extrapolating observations made in our of a three-dimensional environment to a fourth *spatial* dimension.

142
The “reality” of Faraday’s fields
July 1, 2012
 

We have shown throughout the “The Imagineer's Chronicles” and our book "The Reality of the Fourth *Spatial* Dimension" there would be many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is it would allow one define the "reality" of Faraday's field and the strong, weak, electromagnetic, and gravitational forces by extrapolating properties of a classical three-dimensional environment to a fourth *spatial* dimension.

There are presently two methods science uses to define how forces are propagated.

The first assumes that all forces both attractive and repulsive are propagated by particles.  For example it is assumed that electromagnetic forces are propagated though space by photons that are both real and virtual.

It is easy to understand how particles can be responsible for repulsive forces because our every day experiences tell us that a force is generated when two objects collide that causes them to move apart or repel each other.

However this is not the case with attractive forces because no one has ever observed two objects moving towards or being attracted to each other after a collision.

Therefore scientists have to create or imagine what are called "virtual particles" which by their own admission do not exist, except in the math to explain attractive forces in terms of particle interaction.

Granted they assume that virtual particles exhibit some of the properties that "real" particles do, such as obedience to the conservation laws however they differ in that they when they collide or interact with "real" particles they cause them to attract instead of repulsing each other as is the case when two real particles interact.

When you ask a scientist how they know this all they can do is point to some abstract mathematical equations that they say demonstrates they have the physical properties associated with a repulsive field.

One problem with assuming this is that no has or ever will observe a virtual photon because as mentioned earlier by definition they do not exist.  Another more damaging one is that it is very difficult to devise a realistic mechanism based on observations that can account for how something that does not exist in the real world can interact with something that does to cause the observed properties of a repulsive force. 

The second assumption uses the concept of a field to explain how and why forces are propagated through space.

The only problem with this assumption is that no one has been able to define the physicality or reality of these fields in terms of four dimensional space-time.

However as mentioned earlier one can define their "reality" and that of strong, weak, electromagnetic, and gravitational forces by extrapolating observations of a classical three-dimensional field to a fourth *spatial* dimension.

The concept of a field was developed when physicists learned that they could simplify the calculations of the forces involved in planetary motion by assuming or imagining the existence of a continuous gravitational field. They defined this field in such a way that if another planet were put at any point in that field the resulting force between any other planets would be exactly the Newtonian one. This simplified the calculations of planetary motion because it allowed them to isolate and analyze the forces of one planet on another instead of trying to analyze the forces exerted on a planet by the others at the same time.

Originally, many thought this was just a trick to simplify calculations.

But Michael Faraday, while researching electromagnetism discovered that a continuous field has real physical properties and therefore was able to convince others that is was more the just a calculating device.

However unlike a virtual particles which cannot be defined in terms of their physicality one can define the physicality of faradays fields and the four forces of nature if one does, as mentioned earlier assume the existence of four *spatial* dimensions instead of four dimensional space-time.

For example the article "What is electromagnetic energy" Sep 27, 2009 showed one can physically derive the propagation of electromagnetic forces in by extrapolating the physical properties of a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space with respect to a fourth *spatial* dimension.

This would enable one to define the physicality of both the attractive and repulsive properties electromagnetic forces in terms of observable field properties of a three-dimensional environment instead of the imaginary one of virtual particles.

For example a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force will be developed by the differential displacement of the surface which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly a matter wave on the "surface" of a three-dimensional field with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become "attracted" to each other.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the fluctuations in the four dimensional field associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement.

This cannot be done in terms of four dimensional space-time because time is only observed to move in one direction only forward and therefore could not support the bi directional movement required to account both attractive and repulsive forces.

This shows how and why a theoretical model based on the physical properties of a field consisting of four *spatial* dimension instead of four dimensional space-time would allow one to derive both the attractive and repulsive properties of faraday's electromagnetic field.

However the article "The “Relativity” of four spatial dimensions" Dec. 1, 2007 showed that one can also derive gravitational forces in terms of the same field properties the article “What is electromagnetic energy" associated with four *spatial* dimensions

Briefly it showed one can derive all forms of energy in terms of a displacement in a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension.

Therefore, because mass is a form of energy it should, according to the concepts contained in that article cause a displacement in the field properties of three-dimensional space and objects interacting with it will experience a differential force directed towards the apex of that displacement. This force is called gravity.

Therefore the articles "What is electromagnetic energy" and “The “Relativity” of four spatial dimensions" define the physicality of the field properties of gravitational and electromagnetic force terms of a displacement in the "surface" of a three-dimensional field by extrapolating the physical properties of classical fields in a three-dimensional environment to a fourth *spatial* dimension.

However it also provides a method of linking electromagnetic and gravitational forces to their quantum mechanical properties because as the article "Why is energy/mass quantized?" Oct. 4, 2007 showed one can derive them by extrapolating resonant properties of a field in classical a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical field, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in an environment consisting of four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional field (the substance) to oscillate with respect to a fourth *spatial* dimension at the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant field to be established in four *spatial* dimensions.

Observations of a three-dimensional environment tell us that the energy of a resonant field can only take on the discrete or quantized values associated with the fundamental or a harmonic of its fundamental resonant

Similarly the energy of a resonant system in an environment consisting of four *spatial* dimensional environment could only take on the discrete or quantized values associated with the fundamental or a harmonic of a resonant system in that environment.

These resonant fields are responsible for the quantum mechanical properties the energy/mass.

Yet one can also derive the Strong and Weak forces by extrapolating the resonant properties of a three-dimensional field to a fourth *spatial* dimension

The weak force manifests itself in the transmutation of a quark from one flavor or color to another when nuclear particles decays and is responsible for changing one quark to another quark, or a lepton to another lepton,

The mechanism responsible was for this was derived in the article  "The geometry of quarks" Mar 15, 2009.

Observations of particles indicate they are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3. The Down, Strange and Bottom have a fractional charge of -1/3. Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green

The mechanism responsible for the fractional charge of quarks can be found in article "Embedded dimensions" which showed it is possible to define all forms of forces including electrical in terms of a displacement of the field properties of a three-dimensional space with respect to a fourth *spatial* dimension.

However, we as three-dimensional beings can only observe three of the four *spatial* dimensions. Therefore, the forces associated with a displacement in that field with respect to a fourth *spatial* dimension will be observed by us as being directed along its "surface".

However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a "surface" of a displaced three-dimensional field with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that "surface".

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 is be because, as was shown in the article "Embedded dimensions" there are three ways the individual axis of three-dimensional field can be oriented with respect to a fourth *spatial* dimension. Therefore, the configuration or "colors" of each quark may be related to how its energy is distributed in a three-dimensional field with respect to a fourth *spatial* dimension.

However, it also explains why it takes quarks of three different "colors" to form a particle because, as mentioned earlier a particle is defined in terms of the resonant field properties of three-dimensional space.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate field would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space. A stable particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis. Therefore, a particle consisting of anything but quarks of three different colors would not be stable.

As mentioned earlier the weak force manifests itself in the transmutation of a quark or lepton from one flavor or color to another when particles decay.

However this is what one would expect if their stability was related, as shown above to the geometric configuration of their central axis because the only thing that distinguishes their color or flavor is how their central axes in the fourth *spatial* dimension orientated with respect to three-dimensional space. If the individual quark components of a particle were not in the lowest energy configuration they would rotate around that axis until they were.

Therefore the weak force could be derived in terms of the force required to produce the lowest energy configuration possible by the transmutation or the change of a quark or lepton from one flavor or color to another by the rotation the central axis of the field properties of three-dimension space with respect to a fourth *spatial* dimension.

This suggests that the stability of the energy/mass components of particles such as a proton and neutrons are related to a resonant interaction between the field properties of three-dimensional space and a fourth *spatial* dimension.

However, the fact the resonant interaction between the components of a three-dimensional field and fourth *spatial* dimensions is strong enough overcome the repulsive electrical energy of the two up Quarks in a proton also defines the causality of the strong force and the stability of a nucleus.

The strong force is a result of the spatial separation between the protons in a nucleus becoming small enough so the excess resonant binding energy associated with their individual field properties can interact. The sharing of this excess binding energy allows the up quark of one of the adjacent protons to be replaced with a down quark resulting in the formation of a neutron consisting of one up quark and two down quarks

However, the addition of a neutron to a nucleus adds the excess binding energy associated with its resonant field without the repulsive effects associated with of the positive charge of a proton.

Therefore, the existence of neutrons in a nucleus allows for creation of larger ones consisting of multiple positively charged protons because they add the binding energy associated with their resonant fields without adding any repulsive electrical charge.

Yet this indicates that the magnitude of the strong nuclear force would be related to the size of the nucleus.

The size or diameter of a nucleus increases as is the atomic weight increases.

However, after a certain atomic weight is reached a nucleus will become physically too large for the individual resonant fields associated with the protons and neutron to uniformly share the energy require to maintain its structure. This will result in that nucleus expelling the energy/mass required to reduce its physical size to a point where a stable nucleonic structure can be maintained. Therefore, any nucleus that is physically larger than this critical value will be unstable and radioactive.

Additionally, the nucleus of atoms that have an atomic weight less than the critical value would increase its weight and size by "absorbing" energy/mass from an external source. This will result in increasing the size and atomic number of that nucleus.

This indicates that the effectiveness of the strong nuclear force in absorbing or emitting energy/mass would drop rapidly off as the distance from the nucleus increases.

This shows how one can derive physicality or the "reality" of the field properties of the strong nuclear and weak forces by extrapolating the classical laws governing fields in a three-dimensional environment to one consisting of four *spatial* dimensions.

However it also provide a physical link between them, gravitational and electromagnetic forces because it defines them in terms of a common mechanism associated with displacements in a three-dimensional field with respect to a fourth *spatial* dimension created by either the rest mass of an object or a matter wave moving is a three-dimensional field with respect to a fourth *spatial* dimension.

Briefly the article "The “Relativity” of four spatial dimensions" extrapolated the laws of classical fields to derive gravitational forces in terms of a displacement in a of a three-dimensional field with respect to a fourth *spatial* dimension while the article "What is electromagnetic energy" Sep 27, 2007 derived electromagnetic forces in terms of the differential displacements in the field properties of three-dimensional space created by a matter wave moving on a "surface" of a three-dimensional field with respect to a fourth *spatial* dimension.  Additionally the article "Why is energy/mass quantized?" showed one can also derive their quantum mechanical properties and those of energy/mass by extrapolating the laws governing resonance in a classical three-dimensional field to a matter wave in four *spatial* dimensions while as was just shown the strong and weak forces can also be derived in terms of a resonant properties associated with a matter wave on in that same a three-dimensional field.

This demonstrates that if one assumes as was done here that space is composed of four *spatial* dimension instead of four dimension space-time one can theoretical unify the four forces of nature by extrapolating the observable field properties of our three-dimensional environment to fourth *spatial* dimensions.

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Is time eternal?
June 15, 2012

Is time an eternity or does it have a beginning and end?

This question is very difficult to answer because current theories are only able to describe what happened after the beginning of our universe.  In other words how the universe came about and whether there is any meaning to a "before" or "after" is unknown and perhaps unknowable.  Therefore many believe it is not possible to determine if time began at the moment of its inception or if it had its beginnings in a previous epic.

The reason is because the most popular theories of its origin assume that it emerged from a singularity or one dimensional point and is expanding from the tremendously hot dense plasma environment associated with it.  This Big Bang theory, as this concept has come to be called assumes the momentum generated by the heat of that environment is sustaining the expansion.

Unfortunately for those looking for an answer to the question as to the eternity of time, the laws of physics cannot be applied to a singularity therefore it is impossible to use them to understand what may have happened in the period before the universe was formed.

However this may not be true because using the currently accepted laws of physics one can project observations made in our present time backwards to the show that it may not have had its beginning in a singularity.

For example observations in "our time" tell us when a star supernova explodes it expels hot gas.  However scientists know that a star existed before that event occurred because they can project the laws of physics governing the expanding hot gases backwards to define a period before it took place.  In other words they can determine what existed before an event occurred such as a supernova by projecting their understanding the process that happened after it backwards to the period before it took place.

Yet there are many observations like those associated with the expanding gases of supernova that suggest that our universes expansion did not begin form a one dimensional point or a singularity as the Big Bang models assumes but from an extended three-dimensional volume of space.

The difference between a theoretical model based on these "real time" observations and the mathematical model supporting the existence of a singularity is because, as mentioned earlier science cannot project the laws of physics beyond a mathematically predicted singularity but can through a three-dimensional volume.

Therefore using a theoretical model based on observations of a three-dimensional environment means that science could predict the existence of time before the beginning of our universe by projecting the currently accepted laws of physics beyond the three-dimensional volume that it suggests its expansion began from.

For example one of the most fundament and verifiable observations in science is that the total quantity of energy/mass in a closed system is conserved and that it cannot be created or destroyed.  Since, by definition our universe is a closed system according to its energy/mass cannot be created or destroyed in it.

Yet we know from observations the equation E=mc^2 defines the equivalence between mass and energy in an environment and since mass is associated with the attractive properties of gravity it also tells us the kinetic energy associated with the universe's expansion also possess those attractive properties. Therefore the law of conservation of energy/mass tells us that in a closed system the creation of kinetic energy cannot exceed the gravitational energy associated with the total energy/mass in the universe.

However, not all of the energy of associated with the universe’s expansion is directed towards it because of the random motion of its energy/mass components.  For example, observations indicate that some stars and galaxies are moving towards not away us.  Therefore, not all of the energy present at the time of its origin is directed towards its expansion.

As mentioned earlier the law of conservation of energy/mass tells us that gravitational contractive properties of the universe's energy/mass cannot exceed its kinetic energy equivalent at time the expansion of the universe began. However because some of the kinetic energy of its components is not directed towards its expansion the total gravitational contractive properties of its energy/mass must exceed the kinetic energy of its expansive components. Therefore, at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as just mentioned not all of its kinetic energy is directed towards its expansion. Therefore at that point, in time the universe will have to enter a contractive phase.

We also know from observations that heat is generated when we compress a gas and that this heat creates pressure that opposes further contractions.

Similarly the contraction of the universe will create heat which will oppose its further contractions.

Therefore the velocity of contraction of our universe will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of its contraction.

At this point in time the total kinetic energy of the collapsing universe would be equal to the radiation pressure associated with the heat of its collapse. From this point on its contraction will be maintained by the momentum associated with the remaining mass component of the universe.

However, after a certain point in time the radiation pressure generated by it will become great enough to ionize its mass component and to cause it to reexpand.

This