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But not simpler. 

One of the difficulties in merging quantum mechanics with Einstein’s Relativistic Theories is its predictive powers are based on the assumption the physical evolution of space and time determines the future while quantum mechanics defines it only in terms the evolution of the mathematical properties of the wave function.

To begin we should start with one of the most basic aspects of the wave function that defines Quantum reality

The physicist John Wheeler asked how can one best define that reality in five words or fewer? he determined the best answer was given by Aatish Bhatia “Don’t look: waves. Look: particles.” That’s quantum mechanics in a nutshell.”

This suggests that we must explain why Don’t look: waves. Look: particles defines the reality of a quantum environment in terms of the physical evolution of space and time.

On way of doing this is to use the fact that both their evolutions are controlled by a wave. For example, Relativity defines it in terms of the energy propagated by electromagnetic wave while Quantum Mechanics defines it in terms of the mathematical evolution of the wave function.

(Einstein provided a mechanism for the propagation an electromagnetic wave through space-time when he defined gravitational energy in terms of a curvature in it.  This means one can define the propagation of energy associated it in terms of the alternating curvatures of the peak and valleys of one as it moves it.)

This suggests the wave function that governs the evolution of a quantum environment may be mathematical represented by the electromagnetic wave that governs evolution in the world of Relativity. This means we may be able understand why Don’t look: waves. Look: particles describes quantum reality by looking at how an electromagnetic wave evolves in the space-time environment of Relativity

For example, the science of wave mechanics and Relatively tells us wave energy would move continuously through space-time unless it is prevented from by moving through time by someone observing or something interacting with it. This would result in its energy being confined to three-dimensional space. The science of wave mechanics also tells us the three-dimensional “walls” of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause its wave energy to be concentrated at the point in space where a particle would be found. Additionally, wave mechanics also tells us the energy of a resonant system, such as a standing wave which this confinement would create can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

In other words, this shows one can use the established science of wave mechanics and physical world of Relativity to show why when some looks at quantum existence it appears as a particle because that act creates boundaries required to create the resonant system which defines it.

This also shows how one can merge the explanation of quantum mechanics given above of Don’t look: waves. Look: particles” in terms of the evolving space-time environment of Relativity.

For example, it explains why the act of looking at a quantum environment creates the confinement required for the creation of a standing energy wave in three-dimensional space which, as shown above is responsible for the quantize properties of particles in a quantum world.

Yet, if no one is looking the wave properties of that environment will be predominant because it is free to move until they are observed and then they will revert to the back their particle properties.

This shows how one can understand the validity of describing quantum mechanics as “Don’t look: waves. Look: particles” in terms of a deterministic evolutionary processes in a space-time environment.

Copyright Jeffrey O’Callaghan 2020

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What makes gravitational force different from those of electromagnetism is that gravity acts along the perpendicular axis of space-time while electromagnetic forces acts in the two-dimensional plane that is perpendicular to gravity.  This is the reason why gravity only acts in one direction attractive while that of electromagnetic can act in two directions, attractive and repulsive because it has the freedom to move along that two dimensional plane.

Einstein had difficulty in understanding how derive to the forces of electromagnetic as they moved through space in terms of his space-time model as was documented by the American Institute of Physics.

From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his theory of relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explaneed as aspects of some broader mathematical structure. The quest for such an explanation — for a unified field theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einstein’s years than any other activity.

However, the reason is NOT that his theories could not support electromagnetism but more likely because time moves only one direction forward similar to how gravity only moves in one direction attractive.  However, electromagnetism "moves" in two direction attractive and repulsive therefore it is difficult to understand how one directional properties of time could be responsible for it.

Yet Einstein gave us an easier way to see how and why his space time model can be linked to the positive and negative forces associated with electromagnetism when he used the constant velocity of light to define geometric properties of forces in a space-time environment  This is because that would allow one to convert a unit of time in his four-dimensional space-time universe to a unit of space in a universe consisting of only four *spatial* dimensions.  Additionally, because the velocity of light is constant it is possible to define a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of define the time-based components in terms of its equivalent in only four spatial dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the displacement associated energy in a space-time environment in terms of four *spatial* dimensions is one bases for assuming, as was done in the article  Defining energy? Nov 27, 2007 that all forms of energy including gravitational and electromagnetism can be derived in terms of a spatial displacement in any "surface" or plane of three-dimensional space with respect to a fourth *spatial* dimension.

This allows one to form a physical image of how electromagnetic forces can be both attractive and repulsive in terms of the differential force caused by the "peaks" and "toughs" of an energy wave moving in the three-dimensional plane with respect to a fourth *spatial* dimension that is perpendicular to gravity’s.

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

Similarly, it tells us an energy wave on the three-dimensional plane with respect to a fourth *spatial* dimension that is perpendicular to gravity would cause a point on that plane to become displaced or "elevated and depressed" with respect to the equilibrium point that existed before that wave was present.

However, it also tells us a force will be developed by those differential displacements in the plane that was perpendicular to gravity that will result in its "elevated and depressed" portions moving towards or become "attracted" to each other as the wave moves through space.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic field in terms of the force developed by the differential displacements of a point on the three-dimensional plane that is perpendicular to gravity.

However, it also provides a classical mechanism for understanding repelling forces of electromagnetism because observations of water show that there is a direct relationship between the magnitude of a displacement in its surface to the magnitude of the force resisting that displacement.

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

One can also derive the magnetic component of an electromagnetic wave in terms of the horizontal force developed by the horizontal displacement caused by its peaks and troughs.  This would be analogous to how the perpendicular displacement of a mountain generates a horizontal force on the surface of the earth, which pulls matter horizontally towards the apex of that displacement.

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

This shows that one can use Einstein’s General theory of Relativity to derive the physical properties of both electromagnetism and gravity.  Additionally it defines the reason why the force of gravity only acts only by attracting objects is because it is confined to the perpendicular axis of space-time or its equivalent in four *spatial* dimensions while electromagnetism can both, attract and repulse objects because it has the freedom to move objects or particles two directions in the two dimensional plane that is perpendicular to gravity’s .

It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.

Later Jeff 

Copyright Jeffrey O’Callaghan 2020

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As was mentioned in the Scientific American article "Is Gravity Quantum?"

"All the fundamental forces of the universe are known to follow the laws of quantum mechanics, save one: gravity. However, finding a way to fit gravity into quantum mechanics would bring scientists a giant leap closer to a “theory of everything” that could entirely explain the workings of the cosmos from first principles. A crucial first step in this quest to know whether gravity is quantum is to detect the long-postulated elementary particle of gravity, the gravitron. In search of the graviton, physicists are now turning to experiments involving microscopic superconductors, free-falling crystals and the afterglow of the big bang."

When Einstein was asked about the consequences of not being able to observe the graviton he replied "It seems as though we must sometimes use one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do"

However, there is a way of fitting gravity into quantum mechanics that does on involve observing the gravitron.

Quantum mechanics assumes all forces are defined by a particle wave dichotomy while Einstein General Theory of Relativity tells us that gravity causes ripples or waves in the fabric of space-time.  However, if one can use the concepts developed by Einstein to show that those gravity waves also exists as a particle wave dichotomy similar to the particle wave dichotomy of quantum mechanics one may be able define a physical connection between his theories and quantum mechanics.

But before we begin, we must first define the relationship between how that particle wave dichotomy manifests itself in the quantum world.

The physicist John Wheeler said the best answer was given by Aatish Bhatia “Don’t look: waves. Look: particles.” That’s quantum mechanics in a nutshell."

In other words, quantum mechanics tells us when a force is observed to interact with an object such as a proton or electron the particle component of its dichotomy becomes predominate while its wave properties only present themselves as it moves unhindered through space.

As was mentioned earlier one may be able to bridge the gap between Quantum Mechanics and General Relativity if one can define how and why the wave in space-time Einstein associated with gravity exist as a particle wave dichotomy similar to the other forces that quantum mechanics defines in those terms.

One of the problems we face in doing this is that his theory defines the force of gravity with respect to time while Quantum theory defines all forces in terms of the spatial properties of position when interacting with objects.

However, Einstein gave us a way to transform his time based definition of gravity into a spatial one which is more consistent with Quantum Mechanics spatially oriented definition of a particle when he defined gravities geometric properties in terms of the constant velocity of light.  This is because it allows one to convert a unit of time in his four-dimensional space-time universe to a unit of a space in one consisting of only four *spatial* dimensions which would be more consistent with quantum mechanics position orient definition of a particle.  Additionally, because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, he provided a qualitative and quantitative means of redefining his space-time universe in terms of an equivalent one in only four *spatial* dimensions.

However, redefining the time based geometry of gravity in terms of its equivalent in four *spatial* dimensions also allows one to not only understand why all forces, including gravity exist as a particle wave dichotomy but also, as mentioned earlier the interaction or non-interaction of a force with anything determines which of those "realities" becomes predominate.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive particle properties of the wave component of gravities dichotomy by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

These oscillations would be caused by an event such as the decay of a subatomic particle or the collision of two black holes. This would force the "surface" of a three-dimensional space manifold to oscillate with the frequency associated with the energy of that event.

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

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

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

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy quantum mechanics associates with the particle component of its particle wave dichotomy.

Yet, it also allowed one to derive the physical boundaries of the particle component of its dichotomy in terms of the geometric properties of four *spatial* dimensions.

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

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

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension by the interaction of forces with "things" in three-dimensional space is what defines the spatial boundaries of the resonant system of the particle component of it particle wave dichotomy defined in the article “Why is energy/mass quantized?” Oct. 4, 2007.

In other words, Einstein theories tell us the particle component of the particle wave dichotomy of gravity would appear or become reality when it confined to three-dimensional space by its interaction with "something" in three-dimensional space.

This is similar to the particle wave dichotomy quantum mechanics associates with all forces in that they manifest themselves as waves until the interact with another quantum system.

Not only that but it allows one to form a direct connection between the General Theory of Relativity and Quantum Mechanic’s assumption that reality is defined in terms of a particle wave dichotomy because the same logic used above can be applied to all forces to explain why, if a force is allowed to move uninhibited through space the wave reality of its dichotomy will be predominate and why if it interacts with anything its particle ones will be predominate.

In other words, we do not have to observe the Gravitron to bring quantum mechanics and its particle wave dichotomy into the Theoretical environment of General Relativity because the physical reasons for that dichotomy are inherent in its theoretical structure.

Additionally, it gives consistent explanation of why one can sum up quantum mechanics in these words "Don’t look: waves. Look: particles" by extrapolating the "single" physical picture provided by the General Theory of Relativity to all quantum systems.

It should be remembered that Einstein’s genius and the symmetry of his mathematics allows us to choose whether to define the reality of a quantum system in either a space-time environment or one consisting of four *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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Physics is an observational science and therefore we must be careful to base our theoretical models directly on observations and not allow the members of our community to ignore them when submitting their theories.

For example, many feel the most reliable way to determine the age of the universe is by measuring its expansion rate base on the radial velocities of galaxies determined by the redshift in their light. Using that value, they imagine Schrodinger’s the universe to the point where everything was contained in a singularity, and calculate how much time must have passed between that moment (the Big Bang) and the present. Doing so tells us the universe is approximately 13.77 billion years.

But there is a problem because there are other things which would affect the redshift which were not taken into consideration when calculating its age.

For example, an observer watching an event like a star orbiting a black hole would notice that light coming from it is redshifted by its intense gravitational field.

In other words, since we can observe how gravity influences redshift, we also know that not taking its effects into account would make radial velocity of galaxies appear to be higher than it was thereby making the universe appear younger than it is.

This discrepancy is amplified by the fact most if not all evolutionary models of our expanding universe assume its gravitationally density increases as one goes back in time because its decreasing size causes its matter component to become more concentrated.

As was mentioned earlier, it has been observed light emanating from just above the event horizon of black hole is redshifted by its intense gravitational field. This means we know from direct observations the magnitude of the redshift coming from galaxies will increase as we go back in time due to the differential gravitational potential between the universe’s past and the present. However, this also means if we don’t take that into account we will overestimate the speed of the the universe expansion and therefore underestimated its age.

In other words, because the gravitational differential between the past and the present was not taken into consideration the universe MUST be older than 13.77 billion years when determined by the redshift.

There can be no other conclusion if one accepts the observations which verify a redshift can be caused by gravity and the fact that the gravitational density must have been greater in the past than it is now due to its expansion.

Some might say that because the density of the gravitational field expands along with the universe it would not affect redshift of light. However, Einstein’s theory of Relativity tells us all change, including that associated with the universe expansion is not a result of anything moving in time but through time. This concept is sometime represented by what is called a block universe where each event would be represented by a ridge block of space-time which never changes.

In other words, the changes that occur in the universe as it expands are a result of movement though each ridge block of space-time and not by changes in that block . Therefore, if one accepts Einstein theory the gravitational density of the early universe is still there exerting its influence on light from when it was emitted from the galaxy used to determine it age.

Note: we are not only taking about the gravity of a galaxy that existed when the light was emitted but the total gravitational potential of the universe that light is required to overcome as it travels from the past to the present.

One could make a better estimate of the universe’s age than the one we have now have if one could determine the total gravitational potential the universe had in the beginning. This would help us to determine how much of the redshift is a result of the radial velocity of galaxies and how much was a result of gravity.

The Cosmic background radiation may give us a way to do this because most assume the slight temperature variations across it tells how matter was distributed at the time it was emitted.  One can use the magnitude those density differentials to determine how each part interacted with its neighbors to produce that distribution. This may permit us to estimate how much matter is represented by one of these temperature variations and by using Einstein’s field equations get an approximate value for the total mass and gravitational potential of the universe had at that time.

This would allow one to subtract the redshift caused by the differential gravitational potential at its origin of the visible universe with respect to what it is now to determine actual the radial velocity of galaxies and thereby a more accurate measure of its age.

However, the fact the universe MUST be older than 13.77 billion years based on observation of how gravity effects the redshift presents problems for some of the proponents of the inflationary big bang model because they have said that observation of the Cosmic background radiation have confirmed that is exactly how old it is.

To put it in the words of the European Space Agency.

Planck’s superbly precise new picture of the CMB (below) shows remarkable agreement with theoretical work, confirming that observations fit a simple cosmological model defined by just six numbers. (Take that in for a moment: the whole physical universe is described by six numbers.) (and) "When combined with other types of measurements, the that data homes in on an age for the universe of 13.798 billion years, give or take a mere 0.037."

Additionally, they tell us "Our inflationary model makes specific predictions about what this complex graph should look like. As you can see, Planck’s observations (red dots) trace nigh perfectly the theory (green line). My colleague Alan freaked out when he saw the tight fit at the graph’s far right” you don’t appreciate the wonders of scientific progress until you have a 6-foot-3 man jumping up and down in your office.

However, as was shown above the universe must be older than 13.77 billion years because the effects gravity has on the redshift were not taken into account when considering its age.

In other words, very fact that those (red dots) trace perfectly Alan’s theoretical prediction that the universe is 13.77 billion years old invalidates it because as was just mentioned it MUST be older than that.

As was motioned earlier, Physics is an observational science and therefore we, in the physics community must not allow our members to ignore ones that we know will eventually will invalidate their theories. This is because their inevitable downfall not only reduces our creditability but also slows the progress to a better understanding of how the universe really functions.  This is in part because governments and the public will be less willing to fund the research of those who have a chance to succeed after spend large sums of money on those that are doomed to failure because their authors chose to ignore the observations that WILL eventually invalidate their theories.

Later Jeff

Copyright Jeffrey O’Callaghan 2020.

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One of the biggest problems is cosmology is accurately determining how far distance objects are away from us.

In 1998 researchers discovered the repulsive side of gravity when they discovered a discrepancy in apparent brightness of light from type 1A supernovae, which exploded billions of years ago suggested that it had traveled a greater distance than theorists predicted it should. From that they concluded that the expansion of the universe is actually speeding up, not slowing down. This was such a radical finding that some cosmologists suggested that the falloff in supernova brightness was the result of other affects, such as intergalactic dust dimming the light. In the past few years, though, astronomers have solidified the case for cosmic acceleration by studying ever more remote supernovae.

But there is something else other than dust which would affect the measurement of their distance.

For example, Einstein tells us and observations of black holes confirm that light losses energy and becomes dimmer as it exits or "climbs" out of a gravitational field.

In other words, the assumption that one can accurately determine the distance of an object based solely using its luminosity and its apparent brightness is simply wrong.

Most of if not all theoretical models of the universe assume that it evolved from a gravitationally denser environment than it is it now.

Therefore, we would expect light that was emitted from an exploding star billions of years to grow fainter due the differential gravitation potential as it leaves the past and enters the instruments used by today’s researchers to measure its apparent brightness.

Note: we are not taking about the gravity of the star that exploded billions of years in the past but the total gravitational potential of the universe that light is required to overcome as it travels from the past to the present.

Some might say that the because the density of the gravitational field expands along with the universe it would not affect apparent brightness of light from the type 1A supernovaes use in the above study. However, Einstein tells us all change, including that associated with the universe expansion is not a result of anything moving through time but in time. This concept is sometime represent by what is called a block universe where each event would be represented by a ridge block of space-time which never changes and the changes that occur in the universe as it expands are a result of movement though each ridge block and not by changes in in that block of space-time. Therefore, if one accepts Einstein theory the environment were1A supernovae exploded billions of years is still there exerting its gravitational influence from billions of light years away when observed in1998.

This means the discrepancy in the light found in 1998 may not only be due to the distance it traveled but to the energy lose it experiences is due to the differential gravitational potential that exits between its point of origin and where is was observed.

The simple fact is that the conclusion the universe expansion is accelerating must be reconsidered if they did not take into account the effect of the differential gravitational density between then and now had on light as it moved through space.

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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Physics is an observational science and therefore we must be careful to base our theoretical models on those observations and make sure the theoretical predictions we make using them conform to them.

For example, the "Big Bang" the most widely accepted theoretical model of the universe’s beginning assumes it was an extremely hot dense environment which cooled as it expanded making conditions just right to give rise to the building blocks of matter, the quarks and electrons of which we are all made and later quarks aggregated to produce protons and neutrons. Within minutes, these protons and neutrons combined into nuclei. As the universe continued to expand and cool, things began to happen more slowly. It took 380,000 years for electrons to be trapped in orbits around nuclei, forming the first atoms. These were mainly helium and hydrogen, which are still by far the most abundant elements in the universe. Present observations suggest that the first stars formed from clouds of gas around 150 to 200 million years after the Big Bang.

But there is a problem because that estimate is based on the assumption that the passage time is constant throughout the universe’s evolution while Einstein and observations tell us that moves slower wherever gravity is stronger.

For example, an external observer watching an event like an object falling into a black hole would notice that its motion toward it slows as it approached its event horizon due to the density of its gravitation field.

As was just mentioned, the big bang model assumes based on observations that the first stars formed from clouds of gas around 150 to 200 million years after the Big Bang.

However, that assumes time was moving at the same speed for both the evolution of those passed events and for those who are observing it from the present.

Yet, Einstein and the observation of events happening near a black hole, regarding the affect gravity has on time tell us something different.  They tell us the timing of events must have moved faster when the universe young than it does from the perspective of present-day observers because, due to its expansion the matter and gravitational density was greater back then than it is now.

In other words, defining the time between events at the beginning of our universe must be based not only on the observations made today but on relative strength of gravity between present day observers and what it was at the time they are observed.

This tells us an event that appears to a 150 to 200 million years to occur from the perspective of an observer in the present would not have taken that long if viewed by someone who was present when it occurred.

It is important to remember this slowing of the timing of events is not related to the velocity of the expansion of the universe but directly to relative strength of gravity between the observed and what he is observing at the time the event occurred.

Some might try to claim that this would not be the case because gravity was also expanding at the same rate the universe and therefore it would not effect how long it would take for events to occur. However, if we are truly looking back in time to when the event occurred, we must assume that the conditions we observed are not change by its expansion because that would mean the future can change the past.

As was mentioned earlier the big bang model tells the first stars formed from clouds of gas around 150 to 200 million years after the Big Bang.

However, as was shown above they could not have taken long if they were observed in the environment where they were forming because of the effect’s gravity has on time. This means, for the big bang model to remain a viable explanation of the universe evolution it must not only revamp the time line for their formation but the time lines for the future events that were based on the theoretical model suggesting they formed 150 to 200 million years after the Big Bang.

Some proponents of the Big Bang model may try to deny that there any difference between the timing of events from the perspective of an observer looking them from present and past even while telling us that the gravitational density was stronger in the past.

That would be hard for them justify that conclusion because we have observed, as was mentioned earlier a denser gravitational field cause time and therefore the timing of events to move slower from the perspective of an outside observer. Additionally, it is one of primary predictions of the General Theory of Relativity which they used to define the formation and evolution of stars and the large-scale structures we observe in today’s universe.

This means they would have to not only deny that gravity has been observed to effect time but the validity the General Theory of Relativity because it unequivocally states that it must. However, as was just mentioned they used it to define the theoretical structure of the Big Bang model.

In other words, the only way they can justify the validity of Big Bang model of the universe’s evolution would be to show that it can explain the observable structures of the present universe in terms of the formation of the first stars occurring in something other than 150 to 200 million years after the Big Bang.

Unfortunately, there are no other choices.

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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Quantum mechanics defines the position of all particles in the universe only in terms of the probabilistic values associated with Schrodinger’s wave equation.  In other words, it tells us that because they are defined in terms probabilities they are randomly distributed throughout the entire universe before being observed.

 However, Einstein disagreed.  He felt one could explain those probabilities in terms of the observable properties of the physical universe.  In other words, he felt because it would be more natural or probable to observe a particle or objects to be located at, or, at the very least, near where it’s found a moment later instead of assuming they are spread out over the entire universe as Quantum mechanics does.  If that is the case, a deeper understanding of physics should provide that information which will contradict that aspect of quantum mechanics. 

The most logical way to determine if this is possible would be to integrate the observable properties of particles with those of our physical universe to see if one can explain them.

This would be true even though we cannot observe an individual quantum particle because there are properties of it that we can observe.

For example, as was mentioned earlier quantum mechanics defines the structure of the universe in terms of the abstract probabilities associated with Schrodinger’s wave equation which only become physical or non-abstract when observed.  This is why it assumes that our universe has a dual existence; the physical one associated with particles and the non-physical or probabilistic one associated with Schrodinger’s wave equation.  Additionally, it assumes that when an observation is made that equation and the probabilities associated with its "collapse" to create physical universe as we know it at the time of the observation.

But the physicality of its wave component was confirmed in 1927 by Davisson and Germer by the observation that electrons and later all particles can be diffracted by crystals. This provides observational verification of physicality of the wave/particle duality of Quantum Mechanics associates with both particles and the universe because the only way to explain the diffraction pattern produce is to assume that that they are made up of electromagnetic waves.

However, it showed the successes of Schrodinger’s wave equation may not be based purely on the mathematics of probabilities but on the physical properties of the energy wave observed by Davisson and Germer.

Yet, before we can understand why, we must first view the universe in terms of the spatial properties of position to understand how the physical properties of that wave interacts with it to define its position when observed. In others words to show why "it would be more natural or probable to observe a particle to be located at, or, at the very least, near where it’s found a moment later one must define the universe in terms of its spatial instead of its time properties, as Einstein had done in his Special and General theories of relativity.

Einstein gave us the ability to do this when he defined the geometric properties of space-time in terms of the constant velocity of light because that provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions. Additionally, because the velocity of light is constant, he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

Doing so allows one to understand how the randomness of a particles position, as defined by quantum mechanics is not dependent on the abstract properties of Schrodinger’s wave equation but on the physical properties of the universe as define by Einstein.

For example, the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the spatial equivalent of Einstein’s theories, defined above to explain the quantum mechanical properties of an electromagnetic wave by extrapolating the rules of classical resonance in a three-dimensional environment to the energy wave discovered by Davisson and Germer moving on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

The existence of four *spatial* dimensions would give an energy of the wave, mentioned earlier Davisson and Germer discovered the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established on a surface of a three-dimensional space manifold.
Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where "E" equals the energy of a particle "h" equal Planck’s constant "v" equals the frequency of its wave component.
Yet it also allowed us to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

In physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly, an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article "Why is energy/mass quantized?".
In other words, the energy wave in four *spatial* dimensions associated with the dual particle/wave properties of existence define by quantum mechanics will maintain its wave properties unless it is confined to three by an observation, then it will be observed as particle

This suggests that it is not the abstract properties of Schrodinger’s wave equation that collapses when an observation is made but instead it is the collapse of the wave energy observed by Davisson and Germer when confined to three-dimensional space by an observation.e

The physics of wave mechanics also tells us that due to their continuous properties the energy waves the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example, the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

Similarly, if the assumption that quantum properties of energy are a result of vibrations or oscillations in a "surface" of three-dimensional space is correct those oscillations would be distributed over the entire "surface" three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

(Some may question the fact that the energy wave associated with particle would be distributed over the entire universe.  However, the relativistic properties of space-time and four *spatial* dimensions tell us that distance perceived by objects or particles in relative motion is dependent on their velocity which become zero at the speed of light.  Therefore, from the perspective of an electromagnetic wave moving at the speed of light, the distance between all points in the universe along its velocity vector is zero.  In other words, its energy is distributed or simultaneous exists at every point in the universe along its velocity vector.  There can be no other conclusion if one accepts the validity of Einstein’s theories.)

As mentioned earlier the article “Why is energy/mass quantized?â” shown a quantum particle is a result of a resonant structure formed by an energy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

Yet, observations of the physical world around us tell that point will most likely not be very different from where it was a moment ago.

However this also tell us because of the physicals properties of the wave/particle component of the universe they will have a definite position relative to each other.

As was mentioned earlier, the probabilistic interoperation of Schrodinger’s wave equation tells us that all the particles in the universe are randomly disturbed before being observed.

However, as was show above, one could argue it only defines the probability of finding the position were the collapse of the wave associated with each individual particle occurs.  In other words, contrary to currently accepted Quantum Mechanical interpretation, the individual particle/wave components of the universe are not randomly disturbed because, as was shown above they would have a definite position relative to each other before it is observed.

Therefore, Einstein assumption, mentioned earlier that "it would be more natural or probable to observe a particle to be located at, or, at the very least, near where it’s found a moment earlier would be consistent with that probabilistic interpretation of Quantum Mechanics. Because, as the above discussion shows one cannot, in a universe governed by its wave/particle duality and Relativity know exactly were a particle will be when observed.

in other words, "The Reality of the Quantum Universe" can be understood in terms of is wave/particle duality and the space-time environment defined by Einstein.

It should be remembered Einstein’s genius allows us to choose whether to define the probabilities in Quantum Mechanics in either a space-time environment or one consisting of only four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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A fundamental issue in Einstein Theory of Relativity is if all motion is relative how can we measure the inertia of a body? Einstein and many others assumed we must measure it with respect to something else. But what if a particle is the only thing in the universe, how can we measure it.

Mach, an Austrian physicist and philosopher developed a principle which some have interpreted as the motion of such a particle’s has no meaning if it was alone in the universe.

In Mach’s words, "the principle is expressed as the investigator must have knowledge of the immediate connections, say, of the masses of the universe. There will hover before him as an ideal insight into the principles of the whole matter, from which accelerated and inertial motions will result in the same way."

Einstein considered Mach prospective so important to the development of General Relativity that he christened it Mach’s principle and used it to explain why inertia originates in a kind of interaction between bodies.

For example, according to General Relativity, the benchmarks for all motion, and accelerated motion in particular, are freely falling observers who have fully given in to gravity and are being acted on by no other forces. Now, a key point is that the gravitational force to which a freely falling observer acquiesces arises from all the matter (and energy) spread throughout the cosmos. In other words, in general relativity, when an object is said to be accelerating, it means the object is accelerating with respect to a benchmark determined by matter spread throughout the universe. That’s a conclusion which has the feel of what Mach advocated. So, in this sense, general relativity does incorporate some of Mach’s thinking.

However, he provided another way of defining inertia that does not require the existence of any other objects but relies only on the geometric properties of space defined in his General Theory of Relativity. In other words, geometry of space itself provides an absolute baseline for inertia.

In physics inertia is the resistance a physical object to a change in its velocity. Therefore, one can define a baseline for its measurement if one can find a universal starting point for it based on objects velocity.

One of the most logical ways to do that would be to use the observable differences between the two types of motion; velocities and accelerations.

For example, velocities transverse the same space or distance in a given time frame while accelerations transverse an exponentially increasing distance over that same time period.

This tells us the primary difference between them is a component of space not time because if one uses the same time frame for both the only thing that distinguishes them is the distance they transverse.

However, Einstein defined the geometry of space and our universe in terms of time therefore, because space not time is, the variable that distinguishes velocities from accelerations, we should look for a way to define motion and it energy purely in terms of its spatial properties.

Einstein gave us the ability to do this when he defined the mathematical relationship between space, time and energy in terms of the constant velocity of light because in doing so, he provided a method of converting a unit of time in a space-time environment to its equivalent unit of space in four *spatial*  dimensions. Additionally, because the velocity of light is constant, he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, Einstein’s mathematics actually defines two mathematically equivalent physical models of the universe, one consisting of four-dimensional space-time and one of only four *spatial* dimensions.

This allows one to define the energy associated with both accelerations and velocities, in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in four-dimensional space-time.

In other words, using the spatially equivalent model of Einstein space-time theories one could define the energy associated with velocities in terms of a linear displacement in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension because it remains constant as an object moves though space.

While one would define accelerations both gravitational and non gravitational in terms of a non-linear displacement or curvature in that "surface" because, as was mentioned earlier it increases as a object move though space.

In other words, if one defines gravitational accelerations in terms of a positive non-linear displacement or curvature in that "surface" one would define all other forms of accelerations in terms of an oppositely directed displacement or curvature in that "surface".

Additionally, the magnitude of the linear displacements associated with relative velocities is dependent on the energies associated with their movement or momentum while the degree of the non-linear displacement associated with accelerations would also be dependent on the magnitude of the energy required to cause them.

In other words, the greater the relative velocities or accelerations the greater the displacement or curvature in the "surface" of the three dimensional space manifold with respect to fourth *spatial* dimension associated with their motion.

What makes accelerated motion different from velocities is that they do not create an energy gradient in space necessary to activate the human senses or measuring instruments because, as was just mentioned the displacement they create is linear with respect to the "surface" of the three dimensional space manifold with respect to a fourth *spatial* dimension

Therefore, the reason it only makes sense to say that this is moving with respect something is because referencing it to that something provides an energy gradient or differential which can activate measuring equipment or human senses.

However, because Einstein tells us the displacement in the "surface" of a three-dimensional space manifold with respect to fourth *spatial *dimension associated with accelerated motion is non-linear it will intrinsically create an energy gradient between two points space.

This also allows one to define a universal baseline for the measurement of inertia in terms of the linear displacement in that "surface" because as mentioned earlier it defines the energy level of all constant motion.Â

As was mentioned earlier, in physics inertia is a measure of the resistance or force (over a given time period) required to the change the velocity of a physical object. Therefore, to define an absolute benchmark for measuring it one must first define a starting point for the energy gradient that, as mentioned earlier is responsible for acceleration. Additionally to make it universal benchmark that point must be the same of all objects and particles.

Therefore, a universal baseline for the measurement of the inertia in all objects is the linear displacement in that "surface" with respect to a fourth spatial dimension associated with their velocity before a measurement was taken . In other words, one can measure the inertia of all objects by measuring the energy difference (in a given time frame) between its starting displacement in space and its displacement at the end points. In other words, it defines a universal starting point or baseline the measurement of inertia for all objects.

Some have said that one cannot measure the inertia of a particle or object that exists alone in the universe because one cannot reference its movements to anything.  However, referencing its velocity with respect to the universe is not relevant to its measurement because Einstein tells us that the energy of velocity is made up of two parts.  One is the energy of associated with its velocity and the other is that of the energy of it’s rest mass defined by the equation E=mc^2.  Therefore, because the displacement that defines a object is made up of two parts the energy of its rest mass and that of its velocity does not need to be reference to any other object or particle. In other words the mass of the object provides the displacement or baseline for measuring the inertia of a particle or object at rest. Therefore, its movement or velocity or lack of it with respect to the entire universe will not effect that measurement because it is determined only by the energy required to produce a change in its velocity or the displacement the "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension that is responsible for that change.

This shows how one can derive a universal baseline for measuring the inertia of all particles and objects in terms of the physical geometry of space as defined by Einstein.

It should be remembered that Einstein, by defining the universe’s geometry in terms of the constant velocity of light allows us to choose whether to define inertia either a space-time environment or one consisting of four *spatial* dimension.

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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Is it an intrinsic property of space that cause velocities to make sense only by saying that this is moving with respect to something while accelerations or changes in velocity don’t require comparisons to give them meaning?

Newton came to conclusion it was based an experiment involving a bucket of water.

Greene, Brian describes his book "The Fabric of the Cosmos" (Knopf Doubleday Publishing Group) why he though space
this by observing a spinning of a bucket hanging from rope filled with water.  At first, after it is allowed to unwind the bucket starts to spin but the water inside remains fairly stationary; the surface of the stationary water stays nice and flat. As the bucket picks up speed, little by little its motion is communicated to the water by friction, and the water starts to spin too. As it does, the water’s surface takes on a concave shape, higher at the rim and lower in the center,

"Why does the water’s surface take this shape? Well, because it’s spinning, you say, and just as we feel pressed against the side of a car when it takes a sharp turn, the water gets pressed against the side of the bucket as it spins. And the only place for the pressed water to go is upward. This reasoning is sound, as far as it goes, but it misses the real intent of Newton’s question. He wanted to know what it means to say that the water is spinning: spinning with respect to what? Newton was grappling with the very foundation of motion and was far from ready to accept that accelerated motion such as spinning is somehow beyond the need for external comparisons.

A natural suggestion is to use the bucket itself as the object of reference.  As Newton argued, however, this fails. You see, at first when we let the bucket start to spin, there is definitely relative motion between the bucket and the water, because the water does not immediately move. Even so, the surface of the water stays flat. Then, a little later, when the water is spinning and there isn’t relative motion between the bucket and the water, the surface of the water is concave. So, with the bucket as our object of reference, we get exactly the opposite of what we expect: when there is relative motion, the water’s surface is flat; and when there is no relative motion, the surface is concave.

Newton explained the terrestrial bucket experiment in the following way. At the beginning of the experiment, the bucket is spinning with respect to absolute space, but the water is stationary with respect to absolute space. That is why the water’s surface is flat. As the water catches up with the bucket, it is now spinning with respect to absolute space, and that is why its surface becomes concave. As the bucket slows because of the tightening rope, the water continues to spin spinning with respect to absolute space”and that is why its surface continues to be concave."

However, Einstein demonstrated, in his Theory of Relativity that absolute space does not exist, therefore their must exist another reason for the concavity of the water in Newton’s
Bucket.

One of the most logical ways to find it would be to use the observable differences between the two types of motion; velocities and accelerations. 

For example, velocities transverse the same space or distance in a given time frame while accelerations transverse an exponentially increasing distance over that same time period. 

This tells us the primary difference between them is a component of space not time because if one uses the same time frame for both the only thing that distinguishes them is the distance they transverse.

However, Einstein defined the geometry of space and our universe in terms of time therefore, because space not time is, as was just mentioned the variable that distinguishes velocities from accelerations, we should look for a way to define motion purely in terms of its spatial properties.

Einstein gave us the ability to do this when he defined the mathematical relationship between space, time and energy in terms of the constant velocity of light because in doing so, he provided a method of converting a unit of time in a space-time environment to its equivalent unit of space in four *spatial* dimensions.  Additionally, because the velocity of light is constant, he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, Einstein’s mathematics actually defined two mathematically equivalent physical models of the universe, one consisting of four-dimensional space-time and one of only four *spatial* dimensions.

This allows one to define the energy associated with both accelerations and velocities, in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in four-dimensional space-time.

In other words, using the spatially equivalent model of Einstein space-time theories one could define energy associated with velocities in terms of a linear displacement in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension because it remains constant for a given time interval. 

While one would define accelerations both gravitational and non gravitational in terms of a non-linear displacement or curvature in that "surface" because, as was mentioned earlier it increases for as it moves through time.

In other words, if one defines gravitational accelerations in terms of a positive non-linear displacement or curvature in that "surface" one would define all other forms of accelerations in terms of an oppositely directed displacement or curvature in that "surface". 

Additionally the magnitude of the these displacements for both accelerations or a those associated with relative velocities is dependent on there energies associated with there movement.

In other words, the greater the relative velocities or accelerations the greater the displacement in the "surface" of the three dimensional space manifold with respect to fourth *spatial *dimension
associated with their motion

What makes accelerated motion different from velocities is that they do not create an energy gradient in space necessary to activate senses because, as was just mentioned the displacement they create on the "surface" of the three dimensional space manifold with respect to a fourth *spatial* dimension is linear.

Therefore, the reason it only makes sense to say that this is moving with respect something is because referencing it to that something provides an energy gradient or differential which can activate measuring equipment or human senses.
 
However, because Einstein tells us the displacement in the "surface" of a three-dimensional space manifold with respect to fourth *spatial *dimension associated with accelerated motion is non-linear its movement will intrinsically create an energy gradient between two points space which can activate measuring equipment or human senses.

In other words, the reasons it only make sense to say that this is moving with respect something while changes in velocity or accelerations don’t is because acceleration intrinsically cause energy gradients between different points in space where as velocities do not.

This would also explain the observations Newton made in his bucket experiment because the energy or velocity of the water is different at each point in the bucket.  In others word, because the water near the bucket’s edge is moving faster or is accelerated with respect its center it has more energy and therefore will create a larger displacement in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension resulting in its "surface" becoming a concave.  In other words, the concavity of the surface of the water in Newton bucket is not caused by an interaction with space or the bucket but due to direct effects Einstein showed the energy associated with the velocity of the water has of the geometry of space.             

However, this also tells us that what makes space space is energy.

For example, what makes the space in a house and its rooms is not a property of that space but is a property of the geometric structure created by its foundation and walls

Similarly, Einstein tells us that what makes space space in our universe is not a property of space but of the geometric structure created by energy.

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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Is there lower limit to the size of our universe.  In other words, how many times can the universe and its mass components be divided up into smaller and smaller chunks until it can divided no farther.

The answer would most likely be found in the two dormant theories, Quantum Mechanics and Einstein’s Theories of Relativity which are used by cosmologists and particle physics to define its evolution.

For example, Einstein’s theories say very little about its origins but it does say a lot about how its components interact to create its observable structures and while doing so tells a lot about how they interact to define the lower limit of its size. 

While on the other hand, a few Quantum Mechanical Theories define its evolution and the lower limit to its size in terms of an infinitesimally small point in space-time.  However, it is unable to providing any details about how its components, after its beginnings interact to create the universe, we can observe around us.

For example, one theory called the Big Bang, which is based on the mathematics of Quantum Theory defines its beginnings and the lower limit to its size in terms of the expansion of a point in space-time called a quantum fluctuation while defining its evolution not in terms of how its component interact but in terms of points in space-time that represent positions of all of the particles it contains at the time they are observed.

This technique of using a one-dimensional point to represent a particle or an objects position is similar to how NASA defines the orbits of planet and its space probes. 

For example, they do not use physical size or the volume of a planet to calculate position and interactions with its orbiting components, instead they use a one-dimensional point at its center called the center of gravity to represent those interactions.

Similarly, quantum mechanics does not need to use physical size of a particle to define its position because similar to how NASA can use a point at the center of an object to represent it, it can use a point in space-time that is in the center of a particle to represent its position.  In other words, the fact that Quantum mechanics describes the microscopic environment of particles in terms of one-dimensional points does not mean that they do not have size.

As was mentioned, earlier Quantum Mechanics assumes the universe began as quantum fluctuation which is a mathematically defined as point in space-time.  In other words, it assumes the size of the universe could be, at its beginning smaller than the period at the end of this sentence.

However, Einstein theories tell us a completely different story of its beginning.

For example, it tells us that matter can only compacted so much before the forces of gravity and time stop it from going any further.

This is true even though in 1915, Karl Schwarzschild proposed based on Einstein theories the gravitational field of a star greater than approximately 2.0 times a solar mass would collapse to form a black hole whose which is a region where time stops and neither light nor particles can escape from it.  However, many assumed that the collapse continues until is compacted into a one-dimensional point or singularity in space-time.

One can understand why those that believed that came to the wrong conclusion by analyzing how those forces interact to create a black hole as was done in the previous article "Time is a force more powerful than those of a black hole" published on Aug 31, 2019

Briefly

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

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

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

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

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

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

Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

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

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

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

(However, some have suggested that a singularity would form in a black hole if the collapse of a star was not symmetrical with respect to its center.  In other words, if one portion of its surface moved at a higher velocity that another towards its center it could not be consider an inertial reference frame because it would be pushed or pulled due to the differential gravity force cause be its uneven collapse.  But the laws governing time dilation in Einstein’s theory tell us that time would move slower for those sections of the surface that are moving faster allowing the slower ones to catch up.  This tells us that every point on the surface of star will be at the event horizon at the exact same time and therefore its center will not experience any pushing or pulling at the time of its formation and therefore could be considered an inertial reference frame.)

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

Therefore, because time stops or becomes frozen at the critical circumference for all observers who are at the center of the clasping mass the contraction cannot continue from their perspectives.

Yet, 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 reaches the critical circumference.  Therefore, an observer on the surface of that 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 it will not experience the gravitational forces of the collapsing star.

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

Therefore, time would be infinitely dilated or stopped with respect to all reference frames that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

However, the contraction of a star’s 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 in its external environment would become infinitely dilated or stop when the surface of a collapsing star reaches its critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference with respect to the external environment of an observer who riding on its surface the contraction cannot continue because motion cannot occur in an environment where time has stopped.

This means, as was just shown according to Einstein’s concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces the collapse of matter must stop at the critical circumference.

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

In other words, based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity or a one-dimensional point as many physicists believe because it causes time to freeze at its critical circumference with respect to all observers.  Therefore, a universe whose evolution is governed by his theories must maintain a quantifiable minimum volume which is greater than the one defined by Schwarzschild radius because if it were smaller matter could not move through that boundary in space time and it could not evolve any further." 

However. the same principle must be applied to the size of the universe at its beginning.  In other words, if time stops at the Schwarzschild radius any object or component of a universe smaller than that could not move through it and evolve to form the structures we observed today.

Additionally, Schwarzschild radius also defines the lower limit to size of all subatomic particles because it defines where time would stop at their surface.  Therefore, if they were smaller or even equal to that radius they could not interact with the other particles because time would stop as they approached each other and interaction with other particles would never happen.

In other words, in a universe governed by Einstein’s theories the lower limit to the size of both the universe and the particles it contains is defined by Schwarzschild radius.

Yet this would seem to contract the quantum mechanical description of a particle as being represented as point in space-time without an extended volume.

HOWEVER, THIS IS NOT THE CASE because, as was mentioned earlier the point in space-time that quantum mechanics defines as the position of a particle could be interpreted as the center of wave component of its duality similar to how NASA uses the point at the center of mass of an extended object to determine its position in space-time as was shown in the article published on Jan. 1, 2020 "Particles as standing waves in space-time"

Yet, it is possible that someone with better mathematical skills than me may be able to unify the Quantum universe with Einstein’s by mathematically describing a environment in which the point description of a particle defines the energy center of its wave component of its wave particle duality while showing how that point interacts with their environment based on those properties similar to how NASA uses the center of the energy or gravitational components of planets to how they interact with other each other.

Latter Jeff

Copyright 2020 Jeffrey O’Callaghan

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