We have shown though out this blog observations of our environment suggest that space is composed of a continuous non-quantized form of mass.

This video prepared by the Chandra X-ray observatory team and presented by Scientific Frontline contains some of those observations.

The narration begins:

“Black holes sound wildly complicated.  After all, there are all sorts of bizarre things going on: intense gravity, the warping of the fabric of space, the distortion of time itself.  But when it comes to describing black holes, it comes down to just two numbers: the mass of the black hole and its spin.  That’s right.  Everything you physically need to describe a black hole is found in just these two numbers.”

However, there exists a fundamental theoretical inconsistency between the existence of black holes, these two numbers, and our present interpretation of the composition of space.

The video describes how it is possible to measure the mass of a black hole, which according theory is a result of the gravitational collapse of a mass to an infinitely density one-dimensional point.  This means the mass of a black hole has no volume.

It goes on to explain that they measure its spin by observing how “The black hole’s gravity strips gas from that star, and the gas falls toward the black hole, forming a swirling disk of orbiting matter”.

But according to theory, the mass of a black hole has no volume.  Therefore, it cannot have the properties associated with spin.

However, in the video a black hole is observed to have spin, which means they must be measuring the spin of the volume of space that makes up the black holes gravitational energy boundary and not the spin of its mass.

This fact was recognized in the video when narrator says, “Near the event horizon, the black hole’s spin drags everything around with it, an apple, an astronaut, even space itself, at the dizzying rate of 750 revolutions per second.”

However, our present interpretation of the space or the volume between particles falling into a black hole is that it does not contain any substance that can have the properties of spin.

Therefore, because we can observe the spin of a black hole we must assume either  the mass of a black hole cannot be infinitely dense and have a zero volume or the space between particles of matter must contain a substance that will allow us to assign it a property of spin.

However, mass is the only substance that can be assigned the properties of spin and because a volume by definition is continuous this substance must also be continuous.

Therefore, the observations made in the video “Just two numbers is all you need” means if the mass at the center of a black hole is confined to an infinitely dense one-dimensional point with no volume as theory predict, we must modify our understanding of the composition of space to include a continuous non-quantized form of mass.

Later Jeff

The Shadows of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

Wikipedia defines quantum tunneling as a microscopic phenomenon in which a particle violates the principles of classical mechanics by penetrating or passing through a potential barrier or impedance higher than the kinetic energy of the particle.  A barrier, in terms of quantum tunneling, may be a form of energy state analogous to a “hill” or incline in classical mechanics, which classically suggests that passage through or over such a barrier would be impossible without sufficient energy.  However, on the quantum scale, objects exhibit wave-like behavior.  Therefore, in quantum theory, quanta moving against a potential energy “hill” can be described by their wave function, which represents the probability amplitude of finding that particle in a certain location at either side of the “hill”.  If this function describes the particle as being on the other side of the “hill”, then there is the probability that it has moved through, rather than over it, and has thus “tunneled“.

However, does this behavior really violate the laws of classical mechanics because there are numerous examples of how energy can be relocated or tunneled through what appears to be an impenetrable barrier for the kinetic energy of the mediums associated with the transmission of that energy?

For example, classical wave mechanics tells us that a wave on the surface of water can be transmitted or “tunneled” through a flexible steel plate separating two volumes of water.  This plate acts as a potential energy barrier between the water in each tank because it is “higher than the kinetic energy” of the particles of water in each of the two volumes.

However, because of the spatial properties of the wave its energy can penetrate or be transmitted to other side by the flexing of the steel plate without the particles of water having to go over the potential energy barrier of that steal plate.

As was showed in the Blog “Why is mass quantized?” Oct 4, 2007 it is possible to explain and predict the particle properties of mass in terms of a resonant system or “structure” generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension.

But this means the wave properties of a particle could tunnel through a potential energy barrier that had a kinetic energy “higher” than that particle and still not violate the laws of classical mechanics for the same reason as the energy associated with the particles of the wave, in the earlier example could tunnel though the potential energy barrier and not violate the laws of classical mechanics.

The reason this appears to contradict the laws of Classical Mechanics is that classical mechanics defines a particle in terms of a rigid structure associated with its mass.  However, as was shown in the blog “Why is mass quantized?” a particle can be defined in terms of the dynamics of a matter wave on a “surface” of a three-dimensional space manifold with respect a fourth *spatial* dimension.  This is why, as was mentioned in the Wikipedia article “On quantum scale, objects, or particles exhibit wave-like behavior.

This means, on a quantum level the mass of particle does not have the rigid structure classical mechanics associates with a particle but the dynamic spatial structure associated with a wave.  Therefore, its energy can “tunnel” through a potential barrier or impedance higher than the kinetic energy of the particle similar to how the energy of a water wave tunneled through the flexible steal plate in the earlier example.

Therefore, because particles exhibit wave-like behavior on a quantum scale they can penetrate or pass through a potential barrier or impedance higher than the kinetic energy of the particle without violating the laws of classical mechanics.

Later Jeff

The Shadows of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

Probably one of the most prevalent myths regarding black holes is that they are black.  In fact scientist’s have no idea what color they are.  They only assume they are black because according to theory the gravitational forces associated with their mass are so large that light cannot escape or be emitted from them.

However, calling them black is somewhat analogous to calling a light bulb that is turned off black because it is not emitting any light.

Some might say that this analogy is not fare because we determine the color of a light bulb that is not turn on by the light it reflects.  However, a Black Hole does not reflect any light because as mentioned earlier its gravitational field is so strong that light cannot escape from it.  Does that mean it is black or just that we unable to see it?

Another myth about Black Holes is that they are holes in a space-time metric.  But the volume of a hole by definition cannot be made up of the medium in which it resides.  For example, the volume of a hole in sand cannot contain sand.  Additionally one can always fill in that hole and make it smaller by pouring sand in it.

But according to theory, a Black Hole is made up of a space-time metric and these same theories define in mass in terms of curvature in a space-time metric.

Additionally, according to theory when you add mass to a Black Hole it gets bigger.

However, observations of our environment tell us that a hole gets smaller not bigger if we add the material that surrounds it to it.

Why then do we call them Black Holes?

But one of the more mysterious or non-common sense aspects of a Black Hole is how is it possible for an object with a volume bigger than our sun to collapse to a size considerably smaller than the period at the end of this sentence.

In 1915, Karl Schwarzschild discovered that according to Einstein’s General Theory of Relativity the gravitational field of a star greater than approximately 2.0 times a solar mass would cause the matter contained in it to collapse to a one-dimensional point in space after it has used up its nuclear fuel.

This conclusion is based on the fact that the strength of a stars gravitational field increases as it collapses.  Therefore, at a certain point in time the contraction of that star will produce a gravitational field whose energy is strong enough to cause the complete collapse of the matter in that star.  In other words, the energy of its gravitation field becomes stronger than energy that gives atoms and their components, the protons, neutrons and electrons their volume causing them to collapse to a one-dimensional point in space.

However, this assumes that gravitational energy is the only thing that controls the volume of the universe and the mass it contains.

But the discovery of “Dark Energy” indicates their may be another form of energy that contributes to the volume of the universe.

Recent observations of Type Ia supernovae (SNe-Ia) indicate the expansion of the universe is accelerating.  This suggests the existence of an expansive force or “Dark Energy” that opposes the contractive gravitational energy associated with mass.  However, physicists have been unable to define a source or mechanism responsible for this energy.

But they do know that there exists dynamic oppositely directed relationship between mass and energy defined by the equation E=mc^2.  In other words, in a closed system if the mass contained in a volume decreases the energy in that volume increases.

Therefore, due to the symmetry between the quantity of mass and energy in a closed system we should expect a symmetry between the quantity of forces those systems contain.  In other words, we would expect a force to be generated that is oppositely directed with respect to the gravitational forces when we convert mass to energy.  This force has been give the name Dark Energy and is responsible for the accelerated expansion of the universe.

However the “concentration” of Dark Energy relative to gravitational energy is also defined by the equation E=mc^2c were “c” equals the speed of light.  This means its “concentration” and therefore its strength is 1/c^2 weaker than gravitational forces.

The reason why we have only just observe Dark Energy or the force that opposes gravity is because until recently we have not had the technology to such detect the extremely small effects it has on its environment relative to gravitational forces.

However, this means a star could not collapse to a one-dimensional point but only to the point where the compressive forces due to the gravitational forces of its mass equals the oppositely directed or expansive forces associated with the Dark Energy contained in that mass.

In other words, it would collapse to the non zero volume where the “concentration” of expansive forces associated with Dark Energy equal the concentration of the contraction forces associated with gravity.

(In the article An alternative to a singularity?  Aug. 15-08 a similar result was obtained in terms of the time dilation Einstein’s Theory of relativity predicted would be caused by a gravitational field.)

This suggests our common sense feeling that it is not possible for the entire mass of star to collapse to a volume no bigger that the period at the end of this sentence is valid.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan 

We have shown in this blog their is significant observational evidence suggesting that the universe is composed of four *spatial* dimensions instead of four-dimensional space-time.

However, there are also several purely theoretical advantages to the defining the universe in these terms that is not based on observations.

For example it would enable physicists to define a theoretical model that could explain and predict the uncertainty principal and probability functions of quantum mechanics in terms of the observable properties of a classical Newtonian world.

In 1924 Louis de Broglie theorized that all particles are, in part composed of a matter wave.  In his paper “Theory of the double solution“ he attempted to define a causal interpretation for the wave properties of particles in the classical terms of space and time.  He later abandoned it in the face of the almost universal adherence of physicists to the theories presented by Born, Bohr, and Heisenberg regarding the uncertainties and probabilistic interpretation of quantum particles.

However, his theories still serve as the basis for the development of the general theory known today by the name of wave mechanics.  

One of the difficulties he may have faced in defining a causal interpretation of the wave properties of particles is that he assumed that the wave properties of matter were a result of its probabilistic properties.  However, it is possible their probabilistic properties are a result of it wave properties.

In a classical Newtonian world, a resonant system or “structure” will be formed when the transverse spatial movements of a wave interact to reinforce themselves.

For example, the three-dimensional transverse displacements of a two-dimensional surface of water will form a resonant system when the oscillations of the water interact to reinforce each other.

Therefore, if Louis de Broglie had assumed that space was composed of four *spatial* dimensions instead of four-dimensional space-time he may have been able to define a causal interpretation of the quantum properties Born, Bohr and Heisenberg associated with particles in terms of a classical resonant “structure” formed by a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This would be very difficult to do if one defines the universe in term four dimensional space-time because the spatial properties of a transverse of the matter wave he associated with particles is not compatible with a universe consisting of four dimensional space-time.

However, a resonant system or “structure” on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension formed by a matter wave would have many of the properties Born, Bohr and Heisenberg associated with particles. They would appear to have finite boundaries on a macroscopic level however, on a microscopic level their volume would be defined by the wavelength of the matter wave responsible for their resonant “structure”.  Therefore, the uncertainty or probability of finding a particle in a specific volume would be related where one sampled the matter wave or wave function that defines that particle.

In other words, if Louis de Broglie had assumed the existence of four *spatial* dimensions instead of four dimensional space-time he may have be able to theatrically define the particle properties of mass in terms of a resonant system or “structure” formed by a matter wave that had the uncertainties and probabilistic characteristics found in Born, Bohr and Heisenberg theories.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

Sometimes it can be just as important to understand what makes a theory valid, as it is to understand what it predicts.

This may be why we found Karl Poppers book “The Logic of Scientific Discovery” so interesting because he describes how the advance and growth of science rests on a doctrine of falsifiablity and only those theories that are testable and falsifiable by observations add value to a scientific community.

The copy we read was an English translation of the original German text, which means the clarity of some of his ideas may have been lost in the translation.  However, we feel that they are interesting enough to paraphrase some of them here for our friends.

On page 39, he writes:

“To give a casual explanation of an event means to deduce a statement which describes it, using as a premise of the deduction one or more universal laws together with certain singular statements, the initial conditions.”

He later goes on to define two different types of statements and how they are related.

The first or as he calls it the “universal statement of laws” apply to the entire universe.  These are more commonly called laws of nature.  Newton’s law of gravity would be an example of a universal statement because it can be applied through out the universe.

The second or singular statement is defined as statements that apply to specific events.

Karl believes that, for a theory to be valid these singular statements must be deducible from the universal statements and a set of initial conditions which are usually assumed to be the cause of an effect.

This may seem simple however, as Karl points out defining how these parameters are related is not.

Most modern scientists believe in the principal of cause and effect or “the assertion that any event can be causally explained can also be deductively predicted.”

However, the fact that an event can always be causally explained can have two different meanings depending on your interpretation of the word can.

One can, by using deductive logic define the “reality” or causality of an individual event by analytically observing that event.  However, because the prediction is based on observations of that individual event it is always possible to find a set of statements and initial conditions that will satisfy that prediction.

Therefore, this definition of cause and effect is unfalsifiable because the causality of each is based on individual parameters of an event and therefore will always be true for that event.

However, one can also define the causality of an event in terms of what Karl calls a “synthetic” reality or theory based on inductive logic by saying the “world is governed” by strict laws that are constructed so that every single event has a “universal regulation”.

This definition of cause and effect is also unfalsifiable because if an event was discovered that did not fall into its definition of “universal regulation” it is possible to redefine it because it is based on a “synthetic” reality which does not have a rigid structure of its own.

We feel Karl Pepper dismisses the validity of “principal or theory of casualty” and most other theories, because they are based on what he calls the “synthetic” reality of inductive mathematical logic.  For example, the predictive powers of the Standard Model of Particle Physics are based on defining their properties in terms of the “synthetic” reality of inductive mathematical logic.

He would consider this to be a “synthetic” reality because it is based on the abstract or inductive logic of mathematical equations and not on the deductive logic derived from observing how particles interact in a “real” or non-abstract environment.  According to Karl this makes them unfalsifiable because it is always possible to insert new equations in a theory to validate any observation because they (the equations) are not physically connected to the environment they define.

However, as this NASA video of the Snow Flake Cluster shows our ability to make detailed analytical observations of our environment has increased significantly in recent years.  This means, we should now be able to define theories based on deductive observational logic and not on the “synthetic” reality of abstract mathematical equations.

According to Karl, theories developed in this way would add value to scientific community because they would be testable and falsifiable by observations whereas ones based on abstract mathematical logic are not.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright Jeffrey O’Callaghan

We have shown in this blog and the paper at http://www.theimagineershome.com/shadows.html that observations of the environment indicate that a vacuum contains a measurable quantity of a continuous non-quantized form of mass.

One of these observations is called the Casimir effect.

The Casimir effect is a small attractive force, which acts between two close parallel-uncharged conducting plates, which many physics believe is due to quantum vacuum fluctuations of the electromagnetic field.

According to modern physics, a vacuum is full of fluctuating electromagnetic waves of all possible wavelengths, which imbue it with a vast amount of energy.  Casimir realized that between two plates, only those electromagnetic waves whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy.  As the gap between the plates is narrowed, fewer waves can contribute to the vacuum energy and so the energy density between the plates falls below the energy density of the surrounding space.  The result is a tiny force trying to pull the plates together.  This force, which has been measured, provides proof of the existence of the quantum vacuum.  This is because Quantum theory requires that each of these vibrations be quantized and therefore the field, at each point in space would be a simple harmonic oscillator that has the energy of the particle associated with the force that Casimir observed to be pushing the plates together.

However, the Casimir effect also provides observational support for the assumption that a vacuum contains a measurable quantity of a continuous non-quantized form of mass because its existence could explain how simple harmonic oscillations can be responsible for the force that pulls or pushes the plates together in terms of classical mechanics.

Classical wave mechanics tell us that all waves must have a physical medium made up of some form of mass to enable them to propagate.  Additionally observations of waves in a classical environment indicate the number of simple harmonic oscillators that can be established in a given environment is dependent on the distance or “gap” between the “ends” of the environment that contain those oscillators.

These classical observations are similar to those Casimir observed when he narrowed the gap between plates in that the number of possible simple harmonic oscillations or quantum fluctuations that can be formed between them decreases.

However, as was shown in the article “Why is mass quantized?” Oct. 04, 2007 the quantum properties of all mass can be explained and predicted in terms of simple harmonic oscillations generated by electromagnetic waves in a continuous non-quantized mass component of a vacuum.

Therefore, the number of simple harmonic oscillators in space between the plates would, according to classical wave mechanics decrease as the gap between them decreases.  In other words, the smaller the gap between the plates the fewer number of quantum fields that gap could support.

This means there will be a greater number simple harmonic oscillators or quantum fields impacting the plates from the outside of the gap than between it.  This will cause a force that will push the plates together because the energy density associated with harmonic oscillations or quantum fluctuations outside of the gap would be greater than inside of it.

Therefore, the Casimir effect provides observational evidence that a vacuum contains a measurable quantity of a continuous non-quantized form of mass because it would explain how the simple harmonic oscillators that modern physicists associate with particles and quantum fluctuations can generate it in terms Classical Wave Mechanics.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

Most will agree the goal of Physics is to provide an understanding of the why laws of the universe are what they are.  However, there is some disagreement on how to approach it.

For example, a classical approach would be to observe how matter and energy interact in our environment and then attempt to define a mechanism, based on those observations that will explain and predict the causality of those interactions.

This was the method was used Newton to develop the laws of gravity.

Newton observed the orbits of many planets and realized they had something in common in that their positions could be predicted if one assumed that they were a result of force emanating from mass itself.  This observation was reformulated into Newton’s gravitational theory. 

This method gave him the ability to check, through observations the validity of his theory because he could observe how the planets physically interact with their spatial environments to define their positions.

However, Newton was unable to define the casualty of the force associated with his law of gravity.

That was left to Einstein.

He realized the causality of the force of gravity could be explained and predicted by assuming that time and space is physically connected.  This idea was became know as “The General Theory of Relativity”.

However, Einstein had to use a different approach than Newton to verify his theory because the physical properties of a time or space-time dimension cannot be directly observed.

He had to assume, instead of observing how planets interacted with a space-time environment to define their positions because its physical properties of are unobservable.

However, this approach, unlike the one used by Newton does not give physicists the ability to verify through observations how the existence of a space-time dimension can explain and predict the orbits of planets and gravitational forces because, as mentioned earlier physicists cannot directly observe how a planet interacts with a space-time environment.  Therefore, they must rely on how they think they would interact in a space-time environment for verification of Einstein’s theory.

Physics is an observational science because, as it name implies it is devoted to the understanding of how and why matter and energy physically interact to create the structure of the universe.  Therefore, physicists should use caution when assuming the existence of a parameter, such as a space-time dimension that is unobservable because there is no way for them to quantify it observationally.

It has been shown throughout this blog that it would be more logical and consistent to define the causality of gravitational force in terms of four *spatial* dimensions than four-dimensional space-time as was done by Einstein.

However, another advantage of defining it in terms of four *spatial* dimension is that it would give physicists an observational based for defining its properties because they can observe the individual properties of the three spatial dimensions and then extrapolate them a fourth *spatial* dimension

Therefore, even though, as was shown in the article “Embedded Dimensions” Oct. 22, 2007 physicists may never be able to directly observe the properties of a fourth *spatial* dimension they can use observations of three-dimensional space as a basis for the defining its properties.

This would still require physicists to assume the existence of a fourth *spatial* dimension to define the causality of gravitational force found in this blog however, it would give them an observational bases for defining its properties.  Therefore, it would require one less assumption to define its existence because one would not have to assume what its physical properties are along with its physical existence.

This would placate the English logician Occam because the principal he proposed in 14th-century called “Occam’s razor” which has provided guidance for many theoreticians since then states that “the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory”.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

One of the more important unanswered questions of modern physics and cosmology is what is Dark matter made of.

Fritz Zwicky first theorized the existence of Dark matter in 1930 after measuring the rotational speed of individual galaxies in several galactic clusters.  He found their rotational velocities could not be predicted by Newton laws of gravity based on mass of all of the visible objects in them.  Therefore, he concluded that these clusters must contain an invisible or a dark form of matter.

Later observations of gas clouds in the outer parts of disklike galaxies independently confirmed the fact that approximately 90 percent of the mass in the universe is invisible or undetectable with today’s technology.

However, since the discovery in 1930 by Fritz Zwicky that 90 percent of the matter in the universe is invisible physicists have not be able to determine or agree on it’s form.

For example on page 92 of Mario Livio book “The Accelerating universe“, he lists the three forms that many scientists feel this invisible or dark matter can have.

The first is that it could consist of ordinary non-luminous matter such as planets, brown dwarfs, or black holes.  The second possibility is that it could be composed of neutrinos.  A third candidate is some exotic elementary particle that is a relic of the early universe.

He then goes on to explain the problems with each of these scenarios.

The existence of enough non-luminous matter to make up the invisible matter in the universe is not supported by observations based on gravitational microlensing events.

Relativity tells us that light bends as it moves through a gravitational field. Therefore, we should expect to see the effects of gravitational microlensing of any non-luminous matter that is situated between us and the light coming form stars we are observing.  However, to this date we have been unable to detect any gravitational microlensing effect that could be attributed to non-luminous matter.

There are some who say that this may be because of none of the non-luminous matter in our universe happens to be situated between us and a star.  However, as Mario Livio points out in his book the shear number of non-luminous objects that would be required to make up the missing mass of the universe is so large that this seems likely.

The second possibility or the existence of neutrinos has been confirmed though observations.  This makes them prime candidate for dark matter along with non-luminous object because observations indicate they do have mass.

However, On page 98 of Mario Livio book “The Accelerating universe” he explains that neutrinos are probably not the dominate component of dark matter because the existence of enough neutrinos is not supported by the observed structure of our universe.

Neutrinos because of their mass are characterized by high random speeds in the early universe.  However observations of the early universe indicate the matter that condensed to form individual galaxies was not hot enough to support the high random speeds that would have been required to create the large number of neutrinos necessary to make up the observed quantify of dark matter that is known to exist.

The third and finial possibility according to Mario Livio is that it may be made up of some exotic elementary particle such as WIMPs.  However, the existence of these particles are not based on observations but only on theoretical perditions and therefore there is no way to either confirm they existence or that they are responsibly for the gravitational force associated with dark matter.

However, as we have shown in this blog there are many observations that support the existence of a continuous non-quantized form of mass.

For example, in 1924 Louis de Broglie 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.  However, this means that a continuous non-quantized medium must exist because his theories indicate that even the smallest possible particle must have a wave component.  But, macroscopic observations of waves indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists because wave component of the smallest particle must be made up of a continuous medium.

Additionally it has been experimentally verified that energy in itself is not quantized because a photon can have any frequency and therefore any energy greater than zero or less than infinity and the equation defining the relationship between mass and energy, E=m*c^2, also indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.

This means that a continuous non-quantized form of mass must exist to support the continuous properties of the electromagnetic spectrum and its interchangeability with mass.

A continuous non-particle form of mass would have all of the properties of Dark Matter.  Its mass could define the casually of the gravitational forces associated with dark matter and it would undetectable to all forms of detection equipment presently available to science because they are only calibrated to detect mass in a particle format.

Therefore, one of the most important questions for modern cosmologists might not be “What is dark matter made up of?” but why haven’t they considered the possibility the it is made up of a continuous non-quantized or non-baryonic form of mass.

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

Just because something can happen does not mean that it will.

For example, the wind can blow a stack of papers off a desk into a disorganized pile on the floor but it can also pick up a disorganized stack of papers and organized them on a desk.

However, common sense tells most of us that we should not open a window and wait for a breeze to come in to pick up our report and reorganize for us even though it is possible to mathematical define such and event.

However, many physicists assume that if mathematics predicts that an event can happen it will even if the occurrence of that event does not agree with our common sense understanding of the process it is defining.

For example in Chapter 5 of Kip S. Thorne book Blacks Holes & Time Warps “Implosion is Compulsory” he describes how Oppenheimer and Snyder predicted that a star with a mass approximately 2.0 times greater that of our sun must implode at the end of their lives to a singularity or a dimensionless point in space based on a solution of Einstein’s field equations.

We do not disagree with the fact that based on Einstein’s field equations it is possible for the mass of a star to implode to form in a singularity however; we disagree with those that say that this must occur.

Common sense is based on humans ability observe their environments and to conceptually extrapolate them to new environments.

For example, observations of our environment tell most of us that it is highly unlikely that the wind will pick a report up off the floor and reorganize it on a desk for us even though it is mathematically possible.

Similarly, observations of our environment tell most of us that it is unlikely the mass of a star can be concentrated in a single one dimensional point in space even though it is mathematically possible.

Why then do some scientists tell us not only that it can but must happen?

The reason is that many physicists have a tendency to focus only on the mechanistic attributes of mathematical equations defining a theory and not on their conceptual implications.

As was mentioned earlier many physicists believe the implosion of a star into a singularity or black hole is mandatory based on a solution of Einstein’s field equations.  Additionally they tell us the gravitational forces inside of a singularity are so great the relativistic field equations that the define their creation cannot be apply to their internal structure after they are formed.

However, the most fundamental and experimentally verified concept of Einstein’s theory is that the laws of physics are the same in all inertial reference frames which he defined as being “one which 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 should be able to view the collapse 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.)

Therefore, not only does the existence of a singularity defy most peoples “common sense” understanding of their environment but the theoretical basis for its existence is logically and mathematically in consistent with physicist’s theoretical observations of their environment.

This is because physicists have never made an observation in any environment that indicates that Einstein’s prediction that the laws of physics are not the same in all reference frames.  However, they use the field equations derived from the conceptual content of his theories to predict an environment where those laws of physics do not apply.  This indicates the purely mathematical arguments for the existence of black holes or singularities used by physicist’s is logically and mathematically inconsistent with physicists theoretical observations of the relativistic environment on which they are based.

We are not saying that a singularity does not exist.  What we are saying that physicists should use some common sense and spend a portion of their time looking at the conceptual aspects of a theory instead of only the mechanistic attributes of its equations before using them to make predictions.

And above all they should remember “just because something can happen does not mean that it will.”

Later Jeff

The “Shadows” of four spatial dimensions

Copyright 2008 Jeffrey O’Callaghan

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 mass is concentrated in a one-dimensional point in space and whose 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 one-dimension point in space.  He also defined the critical circumference or boundary in space around this one-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 these 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 one dimensional 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 of 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