Many physicists assume based on the General Theory of Relativity the mass of larger stars that have used up their nuclear fuel will implode to form a singularity or black hole.  (A singularity is defined as region of space in which the mass is concentrated in a non-dimensional point in space whose a gravitational field is so great that neither light nor time can escape.

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 could stop time.

As a star cools and contacts, the gravitational forces at its surface increase as its circumference decrease.  We know this because observations of gravitational forces tell us they are proportional to the square root of the stars mass divided by its circumference.

In 1915, Karl Schwarzschild discovered that according to Einstein’s General Theory of Relativity the gravitational field associated with the mass of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a non-dimension point in space.  He also defined the critical circumference or boundary in space around this non-dimensional point 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 the surface of the mass associated with that stars gravitational field will increase.  At a certain point the contraction of that mass will produce a gravitational field strong enough to stop the movement of time.  Therefore, 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 believe the existence of black holes 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 be 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 (shrinks inward) 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 the external observer because of the time dilatation associated with the relative velocity of the star’s surface with respect to the external observer.  The smaller the 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 the surface of that star.

Therefore, the proponents of black holes say that the contraction of a star can continue until it becomes a non-dimensional point in space because time has not stopped on its surface even though it has stopped to an observer who in 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 instead of in terms of the velocity of the contraction.

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 a star nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because the increasing strength of its gravitational field 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 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 Theory of General 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 the view point of an observer who is at the center of the collapse would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star near its critical circumference because of the increasing strength of the gravitation field at the surface of the star relative to it’s center.  The smaller the star 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 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 the surface of an imploding star will not experience the gravitational forces of the collapsing star.

However, according to the principals of Relativity he will observe the differential gravitational forces caused by an imploding mass with respect to someone who remains at a fixed circumference or is at the center of the collapsing mass.  But according to the Einstein theory of relativity, as a star nears its critical circumference an observer who is on the stars surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame to be increasing.  Therefore, he or she will perceive time as slowing to a crawl with respect to the reference frames that are not on its surface as it approaches the critical circumference.  The smaller the star gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

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 would become infinitely dilated or stop in the reference frames that were not on the surface of a collapsing star as it nears its critical circumference.  Therefore, because motion is not possible in a reference frame or an environment where time has stopped, the collapse of a star’s surface cannot continue beyond the critical circumference.

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 the volume of a collapsing star must maintain a minimum volume which is equal to of greater than the critical circumference defined by Karl Schwarzschild and cannot implode to a dimensionless point as many physicists believe.

This means either the conceptual ideas developed by Einstein are incorrect or the field equations many physicists used to predict the existence a singularity are incomplete because their theoretical predications regarding its existence are contradictory.

Only observations can determine which one is correct because both are based on the validity of the concepts presented in Einstein’s theories and the mathematical equation he developed.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

We have shown through out this blog that it is more consistent with observations to define the universe in terms of a continuous non-quantized form of mass and four *spatial* dimensions instead of four-dimensional space-time.

The following is an excerpt from the address “Aether and the theory of Relativity” Einstein delivered on May 5th 1920 at the University of Leyden Germany.

“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.”

Einstein realized that to unify gravitational and electromagnetic forces or define a gravitational electrodynamics space has to be “endowed with physical qualities” which “may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time.”

Unfortunately, Einstein did not have access to the data concerning quantum “qualities” of mass when developing his theories that we do today, such as the Louis de Broglie observation made in 1924 that all particles have a matter wave component.  If he had he may have chosen to define gravitational forces in terms of four *spatial* dimensions instead of four-dimensional space-time.

The fact that all particles were composed of a matter wave would have confirmed his conclusion that space was composed of a medium which does not consist of “parts which may be tracked through time” because even the smallest particle, according to Broglie observations must have a wave component.  Additional he would have realized this medium must be made up of a continuous non-quantized form of matter or mass because it is the only substance that can “endow” it with “physical qualities” which could not be tracked through time.

However, the properties of this matter wave would also have indicated to him the mass associated with particles and objects like stars or planets would more likely be related to the geometry of a spatial dimension not to a time dimension.

This is because he would have realized the only way to explain and predict the spatial properties of the matter wave Louis de Broglie associated with a particle was in terms of a displacement or curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the peaks and troughs of a wave on that “surface”.

But he would have also realized it would have given him the ability to link gravitational forces to the quantum or particle properties of mass by explaining and predicting them, as was done the article “Gravity“ Dec. 15, 2007 in terms of a similar displacement or curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

He then would have been able to show that a quantum properties of a particle and gravitation forces are, as was shown in the article “Why is mass quantized?“  Oct. 4, 2007 a result of a “compactification” of his “Aether” or a continuous non-quantized form of mass, as we have called it in this blog by a geometric displacement in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Additionally he would have realized that it would be possible to explain and predict the observed properties of electromagnetic energy, as was done in the article “The Photon: a matter wave?“ Oct. 1, 2007 in terms of a curvature or displacement caused by the peaks and troughs of a matter wave in a continuous non-quantized form of mass moving on a “surface” of a three-dimension space manifold with respect to a fourth *spatial* dimensions .

This means that he may have able to geometrical define a Gravitational Quantumelectrodynamics or a link between the gravity, electromagnetic energy and the quantum properties of mass in terms of the existence of an “Aether” or continuous non-quantized form of mass and a fourth *spatial* dimension if he had know about the matter wave properties of a particle before he chose to define gravitational forces in terms of a curvature in four-dimensional space-time.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

(This article is a collaboration between Benny Creemers, a proponent of Super Relativity and Jeff.  Please visit his web site to gain a different perspective on this subject and Mark Fiorentino site for a discussion of the principals of Super Relativity.)

In the article “Reference frames” July-07-08 it was shown the observed properties of all inertial reference frames could be explained and predicted more consistently by defining them in terms of a displacement of a three-dimensional volume with respect to a fourth *spatial* dimension than by defining them in terms four dimensional space-time.

However, it is also possible to explain and predict the properties of gravitational and accelerated reference frames such as those generated by the Kinetic energy of a rockets exhaust in terms of a displacement in a “surface” of a volume with respect to a fourth *spatial* dimension.

In the article “Defining energy” Nov 26, 2007 it was shown gravitational energy could be defined in terms of a displacement in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the Kinetic energy due to a relative velocity in terms of an oppositely directed displacement with respect to a fourth *spatial* dimension of a “surface” of a three-dimensional space manifold.

Additionally observations show the magnitude of the gravitational and kinetic energy of a particle or object is directly related to its mass therefore the displacement with respect to a fourth *spatial* dimension in a “surface” of a volume associated with a mass would be directly related to the mass of a particle or object.

However because mass has volume its energy would be extended with respect to the “surface” of the volume it occupies. Therefore the energy associated with that displacement would be “focused” at a “point” on the axis of the fourth *spatial* dimension.

This means the gravitational “energy surface” of a volume will have a “concave curvature” with respect to the sounding volumes because it would be defined by the radius of a displacement with respect to a point on the axis of a fourth *spatial* dimension.  This curvature in the “energy surface” of a volume with respect to a fourth *spatial* dimension generates a force on each “point” mass interacting with that “surface” causing it to accelerate towards its center.

This “force” is responsible for gravitational accelerations.

Earlier it was mentioned the kinetic energy of relative motion could be defined in terms of an oppositely directed displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension than the one responsible for gravitational energy.

Therefore, the “energy surface” of a volume associated with the relative motion of a mass would have an opposite or “convex curvature” with respect to the one associated with gravitational energy.  This “convex curvature” in the “energy surface” of a volume with respect to a fourth *spatial* dimension would generate an oppositely directed force (from the one that defined gravitational force earlier) on point masses that interact with that “energy surface”.  This will cause an oppositely directed acceleration to a gravitational one.

This defines a physical reason in terms of four *spatial* dimensions why planets orbit stars because it shows how and why the acceleration caused by their kinetic energy counteracts the gravitational accelerations associated with mass.

The fact the interchange between mass and energy is defined by the equation E=mc^2 supports this conclusion.  This is because the law of conservation of mass/energy indicates that if the causality of energy is a displacement in a “surface” of a volume with respect to a fourth *spatial* dimension the energy of a mass due to its relative velocity must be oppositely directed with respect to that dimension than the gravitational energy associated with that mass.

The physical reason why we cannot devise an experiment to determine if someone is occurring a gravitational or accelerated reference frame is that, as mention in the article “Reference frames” 01-07-08 we can only measure movement with respect to three *spatial* dimensions.  Therefore, to determine which type of accelerated reference frame someone was occupying we would have to devise an experiment that could distinguish the directional component of its movement with respect to a four *spatial* dimension . 

However, as was shown in the article “Embedded Dimensions” Oct 22, 2007 this is not possible.  Therefore, we are unable to distinguish between gravitational and accelerated reference frames.

This defines an alternative explanation for Einstein’s Principal of Equivalence in terms of four *spatial* dimensions which is consistent with the explanation of inertial reference frames give in the article “Reference frames” 07-01-08. 

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

(This article is a collaboration between Benny Creemers, a proponent of Super Relativity and Jeff.  Please visit his web site to gain a different perspective on this subject and Mark Fiorentino site for a discussion of the principals of Super Relativity.)

We have been suggesting in this blog that space is composed of a continuous non-quantized form of mass and four *spatial* dimensions instead of four-dimensional space-time.

Many believe this implies the Newtonian concept of absolute space and time should be valid.

However, the fact that space is composed of a physical medium such as a continuous non-quantized form of mass does not necessarily imply the existence of absolute space or time.

Einstein realized this because in the address “Aether and the theory of Relativity” he 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 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.”

However, he was careful to define the “quality characteristics” of this physical medium.  Specifically he said that it could not consist of parts, which could be tracked though time.  This would be one of the properties of a continuous non-quantized form of mass because being continuous it would not have parts.

We have shown through out this blog that it is more consistent with observations to define time dilation or the lack of the Newtonian concept of absolute time, gravitational and kinetic energy in terms of displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, since we have defined space in terms of the existence of four *spatial* dimensions, to be consistent with the “qualities” Einstein indicated his Aether (continuous non-quantized form of mass) should have we should define its other quality or “The idea of motion may not be applied to it.” in terms of four *spatial* dimension instead of four-dimensional space-time.

Earlier in the article “Defining space” Sept. 13, 2007, it was shown that the existence of a continuous non-quantized form of mass between particles in a volume is responsible for defining that volume.

(This conclusion is supported by Einstein’s statement that “space without Aether (continuous non-quantized form of mass) 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.)

Therefore, one would think that it would be possible to define the Newtonian concept of absolute space in terms of the physical properties of a continuous non-quantized form of mass.

However, in the article “What is dark matter?” Sept. 10, 2007 it was shown the observed properties of dark matter indicate that it is composed of a continuous non-quantized form of mass and that it causes and is affected by gravitational forces.

But this means that the density of a continuous non-quantized form of mass that define a volume would fluctuate due to variations in the gravitational fields it is exposed to.  However, this also means that an absolute space with respect to an individual particle or object cannot exist because all space is permeated by fluctuating gravitational fields due to the relative motion stars and galaxies that are outside of the volume they occupy.

(Observational evidence of the varying density of Dark Matter can be found on page 39 and 40 of Paul J. Steinhardt and Neil Turok book the “Endless Universe” where they describe how it causes light to bend to form gravitational lenses.)

But the fact that the relative density of a continuous non-quantized form of mass varies in relation to other objects in space would seem to contradict “The idea of motion may not be applied to it.”

However, as mentioned earlier, we have shown through out this blog observational evidence suggests that gravitational energy is caused by a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the only movement a continuous non-quantized form of mass which defines a volume would experience due to a fluctuation in gravitational energy would be in the direction of a fourth *spatial* dimension.

However, we, as three dimensional beings define motion in terms of three-dimensional space.  Therefore “The idea of motion may not (or cannot) be applied to its “movement” with respect to a four *spatial* dimensions because it is not moving with respect to three-dimensional space.

An inertial reference frame is defined as a reference frame in which 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, and if a repulsive force acts between two bodies of the same mass, they will acquire equal velocities in equal amounts of time.

Earlier it was mentioned that kinetic energy can be defined in terms of displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

According to this definition of kinetic energy the continuous non-quantized form of mass defining the volume of an inertial reference frame will be “stationary” with respect to a fourth *spatial* dimension.  Therefore, the continuous non-quantized form of mass associated with that volume would appear to a three-dimensional observer to moving in a straight line at a constant speed with respect to other internal reference frames that occupy different position with respect to a fourth *spatial* dimension.  If two volumes of three-dimensional space occupy the same “position” along the axis in four-dimensional space, they will remain at rest or stationary with respect to each other in three-dimensional space.

The reason a force that acts between two bodies of the same mass in a inertial reference frame causes them to acquire equal velocities in equal times is because, as was shown in article the “Defining energy” Nov. 26, 2007 a force is the result of a movement of a three-dimensional volume with respect to a fourth *spatial* dimension.  Therefore, if an equal force were applied to two masses in an inertial reference frame the three-dimension volume associated with those masses would move with in equal and opposite with directions with respect to a common point in four-dimensional space where that inertial reference frames was located.

This indicates that an accelerated reference frame could be define in terms of the movement of the continuous non-quantized form of mass that defines a volume with respect to a fourth *spatial* dimension.

Gravitational acceleration would be defined in terms of the movement of the continuous non-quantized form of mass responsible for the volume of particles or objects towards each other with respect to a fourth *spatial* dimension while kinetic accelerations like a rockets exhaust would be defined in terms of the movement of the continuous non-quantized form of mass responsible for the volume of particles or objects away from each other with respect to a fourth *spatial* dimension

It should be remember that a continuous non-quantized form of mass is not part of a volume, it is the volume that defines reference frames.

Later Jeff

“The “Shadows” of four spatial dimensions“

Copyright 2008 Jeffrey O’Callaghan

Many physicists believe our universe is undergoing a radial spatial expansion based on a discovery made by Edwin Hubble that distant galaxies are moving away from us.  They also believe the universe began with an explosion or big “Big Bang” because if one traces the motion of these galaxies back in time they merge at point in the past.

Alexander Friedmann developed the theoretical foundations for this expansion when he realized a solution to Einstein’s field equations describes a spherical universe, which starts from a point (called a singularity) whose radius expands with time to become the universe, as we know it today.

These observations, that the universe is expanding and Friedmann’s solutions provide the foundation for the Big Bang Theory and the Standard Model of cosmology and particle physics, which for the past 25 years has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with such accuracy the observable microscopic properties of particles and the macroscopic cosmologic properties stars and galaxies that many physicists believe it is the ultimate theory of mass and energy.

One can understand how an expansion of universe could explain the observations made by Hubble by using an analogy of an ant living on a surface of a balloon.  First, one must imagine that the ant can only move on the surface of a huge balloon, which to the ant’s understanding is the total extent of universe.  At an early stage of the balloon-universe, the ant measures distances between separate points on the balloon, which serves as his standard.  As the balloon is inflated, the distance between the same points is measured and determined to be larger by a proportional factor.  The surface of the balloon still appears flat, and yet all the points have appeared to recede from the ant, indeed every point on the surface of the balloon is proportionally farther from the ant than it was earlier.

Similarly, galaxies in our universe would appear to recede from us if the universe was expanding for the same reason that the points on the balloon receded from the ant as his or her universe expands.

As mentioned earlier the Standard Model successfully answers many of the questions regarding the cosmological structure of the universe and the creation of subatomic particles based on the existence of an expanding universe.

However, for all of it successes it has one very obvious shortfall in that it does not answer the question “What is the universe expanding into and how do the physically properties of the spatial dimensions interact to generate the particles and forces in our world?”

But there are some who say that it would not make any sense to ask what our universe is physically expanding towards for the same reason that it would not make any sense for the ant in the earlier example to ask what his “universe” is expanding towards.  This is because the ant is confined to the two-dimensional surface of the balloon; the existence of a universe outside of that surface would not affect him.

Similarly, many feel that it would not make any sense for us to ask what our three-dimensional universe is physically expanding towards because we are confined to a three-dimensional universe and the existence of a universe outside of that three-dimensional universe would not affect us.

This would be true if physicists and cosmologists had not used the concepts of the dimensional interactions they associate with a physically expanding universe to develop the abstract mathematical basis for Standard Model of cosmology and particle physics.  Therefore, their existence, according to the assumptions on which the Standard Model is based must have a physical along with an abstract effect on our universe.

However, even though we are confined to our three-dimensional universe we can get an understanding of some of the properties of the dimension it is expanding towards by observing the effects of this expansion on our universe. 

For example, we know that it must have the properties of a spatial dimension because the observations made by Hubble that the universe is undergoing a spatial expansion with time indicate that three-dimensional space is expanding towards a higher dimension or dimensions.

Presently, we understand very little about the physical properties of these higher dimensions due, in part to the fact many scientists seem to be satisfied with defining them in only in terms of their abstract mathematical properties instead of attempting to understand them in terms of how and why their physical interactions with three-dimensional space can explain and predict the forces that shape our world.

However, history has shown us that the greatest advancements in civilizations have been the result of looking beyond what we can see or “To boldly go where no one has gone before.”

Later Jeff

The *Shadows* of four *spatial* dimensions

Copyright 2008 Jeffrey O’Callaghan

Modern science owns much of its success to its ability to define a common causality of related events.

For example, Newton discovered law of gravity when he realized the casualty of events like the moon orbiting the earth and objects falling to the earth were related.  He then defined a common causality for both of these events that could be applied to similar events in other parts of the universe.

A 14th-century English logician and Franciscan friar Occam defined the underlying principles that Isaac Newton and most other modern scientists use to guide them in the understanding of our universe.  This principal, called “Occam razor” states that the explanation of any phenomenon should be based on a casualty which is common to other phenomenon so as make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory.

However, most scientific investigations of the “law” of cause and effect assume that all events or phenomenon are caused by other events or phenomenon.

For example, Newton defined the causality of an object falling towards the earth in terms of a force originating in mass called gravity but he did not define the causality of gravitational force.

However, there is a limiting factor to our ability to explain and predict the causality of the first event in a series of events because the causality of that event is caused by a previous event, which in tern must have a casualty.  This means the first event in a series of events cannot be explained or predicted in terms of a causality because if it could it could not be the first event in that series.

Presently scientists use two very different methods to define the casualty of events.  The first is based on physically observing how components of an environment interact while the other on using abstract mathematical equations.

The first assumes that all events are caused by a physical interaction.

Many scientists attempt to define the casual of an event in an unobservable environment by extrapolating the properties of an observable environment to that event.

For example, Louis de Broglie theory that all particles were composed of a matter wave allowed scientists to apply the observable properties of wave interactions in the macroscopic world to the interactions of electrons in the unobservable world of chemical bonding.

This gives Wave Mechanics, as this scientific discipline came to be called the ability to successful explain the causality of chemical bonding in terms of the observable properties of waves in the macroscopic world.

Therefore, one could consider the science of wave mechanics an example of a physical theory in the sense that it can explain the unobservable causality of chemical bonding in terms of the observable properties of wave interaction in the macroscopic world.

The second method assumes existence of an abstract causality.

Scientists can write a series of abstract mathematical equations defining a similarity between two events based only on observing the event itself and not on observing environment in which the event took place.  They then hypothesize a casualty for those events based on the structure of those abstract equations and not on observations of the environment where those events occurred.

String Theory would be an example an abstract theory because it mathematically defines the causality of particle formation in terms of vibrations in a one-dimensional component of space.  However, no one has ever physically observed the existence of a one-dimensional component of space or the environment where it could vibrate.  Therefore, its theoretical predictions are abstract in the sense that it does not explain the causality of events in terms of physically observable vibrations in a one-dimensional component of space.

Both of these methodologies are valuable tools that can be used to advance our understanding of our world however the first or physical method posses a greater degree of scientific credibility than the second or abstract method because its explanations of the causality of events can be corroborated by observation of similar events in different environments.

For example, the wave mechanical explanation of the causality of the chemical bonding of atoms can be “externally” or independently corroborated by correlating it to the observable properties of waves in a classical environment.  Whereas, the causality of events defined by the mathematical equations of String Theories cannot be independently corroborated because they are based only on the “internal” abstract logic of the equation and therefore do not have an external source that can be used to verify the accuracy.

Therefore, how one defines the causality of a casualty depends on how one defines casualty.  

If one feels that causality of an event is a result of a physical interaction of a component of an environment he or she will most likely embrace the philosophy that it should be defined in terms of the observation of the environment where the event occurs.  However if one feels that causality is related to only to the event and not to the physical interactions of the components of an environment then she or he will most likely aspire to the philosophy that it can be defined in terms of abstract mathematical equations.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

The article “What is energy?” Nov. 26, 2007 showed it is more consistent with observations to define gravitational and kinetic energy in terms of a curvature or displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* than defining them terms of a curvature in a four-dimension space-time manifold.

However, that article did not explain why it is also possible to define the casualty of electrical energy in terms of a similar displacement in a “surface” of a three-dimensional space manifold.

In the Blog “The Photon: a matter wave?” Oct 1, 2007 it was shown the particle properties of photon could be explained and predicted in terms of a resonant “system” formed by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension

(Louis de Broglie was the first to theorize that all particles including a photon were composed of a matter wave.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

However, it can be shown the displacement caused by the peaks and troughs of a matter wave on a “surface” of a three-dimensional space manifold are responsible for the electrical energy of a photon.

A wave on the two-dimensional surface of water causes a portion of 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 a spatial displacement of the surfaces, which will cause the elevated and depressed portions of the wave to move towards or become “attracted” to 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 portions of that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present on that “surface”. 

Therefore, according to the concepts developed in the article “What is energy?” Nov. 26, 2007, the causality of the electrical energy of a photon would be definable in terms of the displacement caused by the peaks and valleys of a matter wave on a “surface” of a three-dimensional space manifold. 

This is because if one defines a displacement above the equilibrium point on a “surface” of a three-dimensional space manifold caused by the peak of a matter wave as being responsible for positive electrical energy one could define a the displacement caused by the trough of that matter wave as being responsible for negative electrical energy.

The causality of the attractive forces of unlike charges would then be definable in terms of the force developed by the spatial displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This force would be analogous to the force developed by a spatial displacement in the surfaces of water, which as mentioned earlier causes the elevated and depressed portions to move towards or become “attracted” to the surface.

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

Similarly the magnitude of the force generated by 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 electrical charge.  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.

The difference between gravitational and electrical energy would then be definable in terms of the relationship of the displacement with respect to a “surface” of a three-dimensional space manifold.

For example, gravitational energy was defined in the article “What is energy?” Nov. 26, 2007 in terms of the force developed by a “depression” in a “surface” of a three-dimensional space, which results in the force always being attractive.

While electrical energy is defined in this article to be the result of a spatial separation or displacement in the equilibrium of a common “surface” of a three-dimension space manifold with respect to a fourth “spatial” dimension which explains how and why, as this article shows electrical forces can have both attractive and repulsive properties.

This indicates that it is possible to define a common unifying mechanism responsible for gravitational and electrical energy in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

We have shown in this blog that there is significant observational evidence suggesting that space is composed of a continuous non-quantized form of mass.

However, there are several purely theoretical advantages to assuming this that is not related to observations.

One is that it would allow physicists to theoretically define a mechanism that is responsible for the formation of particles based on processes that occur in the macroscopic world.

In the macroscopic world, it is possible to define a resonant system or “structure” in terms of oscillations in a continuous medium even though that medium is made up of particles called atoms.  This is because the size of most resonant systems in the macroscopic world is so much greater then the size of atoms that their supporting mediums can be treated as being continuous.

Additionally observations of resonant systems indicate their physical properties are determined by the oscillatory or vibratory frequency of the medium that makes up that system and that they are stable only when oscillating at its fundamental or a harmonic of its fundamental frequency.

Particle physicists have made very similar observations in that the physical properties of a particle are determined by the frequency of a component of that particle.

This suggest that because they display prosperities similar to a resonant system in continuous medium the properties of particles may be the result a resonant system made up of oscillations in a continuous medium.

(Louis de Broglie was the first to theorize that particles have a wave or oscillating component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for these waves to be propagated on because even the smallest possible particle must have a wave component.  Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle.)

There are several other indications that suggest that particles are made up of resonant systems in a continuous medium.

For example, physicists have discovered relativity few stable particles compared to the unstable ones.

However, this is what one would expect if particles were composed of a resonant system because as mentioned earlier, a resonant system is only stable when it is oscillating or vibrating at its fundamental or harmonic of its fundamental frequency.  Therefore, if particles were composed of a resonant system in a continuous medium there should be relatively few stable particles compared to unstable ones because there are an infinite number of frequencies that a continuous a medium can be made to oscillate at but only a few that will support resonance.

Additionally the observations that unstable particles decay into a few stable ones indicates that the properties of all particles may be related to the existence of a continuous medium.  This is because, observations made in the macroscopic world show it is possible to add or subtract almost any amount of energy from a continuous medium creating very large number of vibrating systems each with a different energy.  But these systems will lose or gain energy from their environment until they begin to vibrate or osculate at the resonant frequency or a harmonic of the resonant frequency of the supporting medium.

However, this is precisely what physicists observe when they add or remove energy from particles in particle accelerators.  They can add or subtract virtually any quantity of energy to a particle in particle accelerators.  This results in the creation of a very large number of particles with different physical characteristics but similar to resonant systems in the macroscopic world these particles decay by losing or gaining energy from their environment until they have the energy of the resonant frequency or a harmonic of the resonant frequency of the medium supporting that resonance.

These similarities between the properties of resonant systems and particles provide a theoretical basis for defining them in terms of a resonant system in a continuous medium.

It is also possible to make a theoretical prediction of the physical characteristics this medium based on the success of Louis de Broglie theory that all particles are, in part composed of a wave.  If his theory is valid, even the smallest possible particle must be made up of a wave, which means as mentioned earlier, that a continuous non-quantized medium must exist to support the wave of the smallest possible particle.  However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass.  Therefore, the success of Louis de Broglie theory indicates that if the physical properties of particle are made up of a resonant system a continuous medium that that medium must be made up of a continuous non-quantized form of mass.

This compliments the observational evidence presented in this blog for the existence of a continuous non-quantized for of mass because it shows that its existence can be predicted on a purely theoretical bases.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

In the Imagineer’s article Why is mass quantized? Oct. 4, 2007 it was shown that the observed properties of all particles could be explained and predicted in terms resonant system in continuous non-quantized form of mass.

However, it is also possible to determine the outcome of particle interactions based on the existence of this resonant system.

On pages 59 and 60 of Brian Cregg book “The God Effect” he describes experiments that show how photons interact with different polarizing filters.

In the first experiment, photons in their natural randomized polarization state are passed through a 45-degree polarizer set halfway between the source of the photons and a vertical polarizer.  Observations of this experimental setup show that 50 percent of the photons passing through the 45-degree polarizer pass through the vertical polarizer.

A classical interpretation of this experiment is that a component of the energy associated with the vertically and horizontally polarized photons defined by Pythagoras’ theorem should pass through the 45-degree polarizer.  Therefore, every photon passing through the 45-degree polarizer will have a 50 percent probability of having a vertical or horizontal component.  This means that 50 percent of the photons that passed through the 45-degree polarizer should also pass through the vertical polarizer.

The Quantum mechanical explanation of this is that every photon simultaneously exists in both in the vertical and horizontal polarization at the same time.  Therefore, every photon that passes through the 45-degree polarizer will have an equal or 50 percent probability of passing through the vertical polarizer.

The second part of this experiment involves photons passing through two polarizing screens one vertical and one horizontal.  In this case, 50 percent of the photons pass through the first vertical polarizer and none pass through the second polarizer.

The classical interpretation of this is that the perpendicular orientation of the vertical and horizontal polarizers completely blocks the passage of all photons through the horizontal polarizer.

However, these results contradict the quantum mechanical explanation for why 50 percent of the photons that passed through the 45-degree polarizer passed through the vertical polarizer.  This is because if all photons simultaneously exist in both a vertically and horizontally polarized state, 50 percent of the ones that passed through the vertical polarizer should also pass through the second horizontal polarizer.

In another experiment, if one places a third polarizer between the vertical and horizontal polarizing screens and turns it so that it is 45-degree angle with respect to them, 50 percent of the photons will pass through the first vertical polarizer and 50 percent of those will pass through the 45-degree polarizer while 50 percent of those photons pass the third polarizer.

But if the 45-degree polarizer worked by only letting through vertically or horizontally polarized photons no light should get through the third polarizer because all of the photon entering it were vertically polarized therefore, they should not get through the third horizontally polarized screen.

Again, the Quantum mechanical explanation for this is each photon that was vertically polarized when entering the 45-degree polarizer exists in both states (vertical and horizontal polarization) when leaving it.  Therefore the photons that passed through the first vertical polarizer have and 50 percent probability of being either vertically or horizontally polarized after passing through the 45-degree polarizing screen and therefore they will have a 50 percent chance of passing through the final horizontal polarizer.

However, Quantum mechanics cannot provide a consistent explanation why photons that pass through a vertical polarizer in the second experiment existed only in a vertical state while those same photons after passing through a 45-degree polarizer exists in both a vertical and horizontal state.

In the article  Why is mass quantized? Oct. 4, 2007 it was shown the properties of all particles including a photon are the result of a resonant system or “structure” established in four *spatial* dimensions by a matter wave moving in three-dimensional space.

However, this also means that the matter wave responsible for generating the resonant system associated with a photon can have amplitude variations along each axis of three-dimensional space.

Therefore, it would be possible for photons that were vertically polarized after passing through a vertical polarizer to have there polarization shifted as they passed through a 45-degree polarizer.  This shift could be caused by the reflection or interference of the wave properties of photons as they encounter the 45-degree polarizer.

However as was shown earlier photons that pass through a 45-degree polarizes will have both a vertically and horizontally polarized a component defined by Pythagoras’ theorem.  Therefore, every photon passing through the 45-degree polarizer will have a 50 percent probability of having a vertical or horizontal component.  This means that 50 percent of the photons that passed through the 45-degree filter should also pass through the vertical polarizer.

This does not mean the photons that pass through the 45-degree polarizer exits simultaneously in both a horizontal and virtual state at the same time it means that the angle of their energy vectors has a component in both the vertical and horizontal plains.

Therefore, the 50 percent of the photons leaving the 45-degree polarizer will have a horizontal polarization component while 50 percent will have a vertical polarization component so 50 percent of the photon leaving the 45-degree polarizer will pass through the third vertical polarizing filter.

(This shifting would not occur when vertically polarized photons encountered the horizontal polarized screen in the earlier experiment because, as mentioned earlier the particle properties of a photon are the result of a resonant structure established by a matter wave moving in three-dimensional space.  Therefore, the refection or interference of the matter wave responsible for their particle properties would be 180 degrees out of phase and would cancel.  However, the interference of matter wave of the vertically polarized photon with a 45-degree polarizer would not cancel because of the angle it makes with its wave front.  This interference would cause a shifting in the orientation of the matter wave responsible for the particle properties of the photon.  It would allow its wave energy to pass through the 45-degree polarizer and reestablish the resonant “structure” on the other side of the polarizer.  Additionally due to the resonant properties of the matter wave, the energy of a photon emerging from the 45 degree polarizer would have to be identical to the ones entering it.)

would allow its wave energy to pass through the 45-degree polarizer and reestablish the resonant “structure” on the other side of the polarizer.  Additionally due to the resonant properties of the matter wave the energy of a photon emerging from the 45 degree polarizer would have to be identical to the ones entering it. )

By defining a photon in terms of a resonant system generated by a matter wave in four *spatial* dimensions allows one to define a deterministic mechanism that can define the interactions of photons with a polarizing environment.

This also shows that there is a logical and consistent physical explanation for these interactions other than the indeterminism of quantum probabilities.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

Modern Quantum theory assumes that it is only possible to define the probability of a particles state when it is measured but not the state the particle was in before a measurement is made.  Therefore, according to quantum mechanics all possible states of a particle must be superposed over each other.

However, the conclusion of quantum mechanics that particles exist in all possible states before a measurement is made in not supported by experimentation.

This can be shown by integrating the results of several experiments involving the transmission of photons through a polarizing filter.

In the first experiment, photons in their natural randomized polarization state are passed through a 45-degree polarizer set halfway between the source of the photons and a vertical polarizer.  This experimental setup shows that 50 percent of the photons passing through the 45-degree polarizer pass through the vertical polarizer.

The Quantum mechanical explanation of this is that every photon exists in a superposed state or simultaneously in both a vertical and horizontal polarization.  Therefore, every photon that passes through the 45-degree polarizer will have an equal or 50 percent probability of passing through the vertical polarizer. 

The second experiment involves two polarizing screens one vertical and one horizontal.  In this case, 50 percent of the photons pass through the first vertical polarizer and none pass through the second polarizer.  This indicates that none of the photons that passed through the vertical polarizer was horizontally polarized because if any of them were some would have passed through that polarizer.

However, these experimental results contradict the quantum mechanical assumption that photons simultaneously exist in both a vertical and horizontal state.

In another experiment if one places a third polarizer between the vertical and horizontal polarizer and turns it so that it is 45-degree angle with respect to them, 50 percent of the photons will pass through the vertical polarizer and 50 percent of those will pass through the 45-degree polarizer while 50 percent of those photons pass the horizontal polarizer.

However, if the 45-degree polarizer worked by only letting the vertically polarized photons no photons should pass through the horizontal polarizer because all of the horizontal photons should have been blocked by the vertical polarizer.

The Quantum mechanical explanation of this is that every photon exists in a superposed or simultaneously in both a vertical and horizontal polarized state.  Therefore, every photon that passes through the 45-degree polarizer will have an equal or 50 percent probability of passing through the vertical polarizer

However, as the earlier experiment showed the photons that passed through the vertical polarizer were not in a superposed state because if they were 50 percent of them would have passed through the horizontal polarizer.

Therefore, if Quantum theory is valid it should be able to explain, in context with its theoretical structure why the photons after passing though a 45-degree polarizer are superposed and after passing though a vertical polarizer are not.

Some will point to the “Copenhagen Interpretation” of quantum mechanics to resolve this conflict.

It states that the act of observing a particle causes it to lose its superposition.  This could explain why the photons that passed through the vertical polarizer did not pass through the horizontal polarizer because the act of “observing” them caused them to exist only in the vertical state so they would be blocked by the horizontal polarizer. 

However, the Quantum mechanical explanation of why 50 percent of the photons in the first experiment passed through the vertical polarizer after passing through the 45-degree polarizer is because they were in a superposed state.

But according the Copenhagen Interpretation these photons would not be in a superposed state because they were “observed” by the 45-degree polarizer.

We all know that wherever there are probabilities there are alternative outcomes of experiments and tests in any given environment.

However, this discussion shows that the environment were a test takes place is also responsible for some of the alternative the probabilities that occur when an experiment is preformed.

For example, the probability that a photon will pass through a horizontal polarizer was determine by the “state” of the environment were the test was preformed.  In the test environment without the 45 degree polarizer between the vertical and horizontal polarizer a photon had a different or alternative probability of passing though a horizontal polarizer than when a 45 degree polarizer was placed between them.  This indicates the “state” of a test environment has a role in determining the probability that photon will pass through a polarizer.

However, the probabilistic predictions of quantum mechanics are not based on the “state” of an environment so therefore they cannot be used to ascertain the probability that they will be applicable in any given environment.

Therefore, scientists should remember when tying to use Quantum Mechanical probabilities as the basis for defining a “Theory of Everything” that those probabilities cannot be used to predict probability of encountering environments in a “state” in which its probabilistic predictions are invalid.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan