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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The arrow of time, is the name reason given to the "one-way direction" or "asymmetry" of time by British astrophysicist Arthur Eddington in the macroscopic universe.  Its direction, according to Eddington, is determined by studying the spatial organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world.

However physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet as was just mentioned at the macroscopic level it appears that this is not the case. arrow of time[3]

The question as to why things appear to different on the microscopic level is an unanswered question.

Many explain the observed temporal asymmetry at the macroscopic level, the reason we see time as having a forward direction, ultimately comes down to thermodynamics, the science of heat and its relation with mechanical energy or work, and more specifically to the Second Law of Thermodynamics. That laws uses the states that the entropy of a system either remains the same or increases in every process. This phenomenon is due to the extraordinarily small probability of a decrease or that a system will return to its original configuration, based on the extraordinarily larger number of microstates in systems with greater entropy. In other Entropy  can decrease or a system can return to its original configuration, but for any macroscopic system, this outcome is so unlikely that it will never be observed in the future.

However, entropy can decrease somewhere, provided it increases somewhere else by at least as much. The entropy of a system decreases only when it interacts with some other system whose entropy increases in the process.

Yet, it is difficult to apply that definition to a quantum environment because Schrödinger wave equation that quantum mechanics uses to determine the position component of a particle when observed does so in terms of a probability distribution over the entire universe.  Therefore, to define an arrow of time for a quantum system in terms of entropy one must show there is a physical connection between the macroscopic space-time environments we live in and a particles position in that probability field when it is observed. 

Unfortunately, we define the spatial components of entropy in our macroscopic universe in terms of the space-time concepts defined by Einstein.  Therefore, to define the arrow of time in the probabilistic world associated quantum mechanics in terms of entropy we must show how it is physically connected to the spatial properties of the macroscopic universe defined by him.

Einstein gave us the ability to do this when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time he associated with energy to unit of space.   Additionally, because the velocity of light is constant, he also defined a one to one quantitative correspondence between the both the relativistic and physical properties of a space-time universe and one made up of only four *spatial* dimensions.

Dong so allow will one to physically connect the probabilities associated with Schrödinger’s wave equation to the Thermodynamic laws that governor the entropy in our macroscopic universe.

For example, the article “ Why is energy/mass quantized? ” Oct 4, 2007 showed one can derive the quantum mechanical wave/particle properties of matter in terms of an energy wave on a "surface" of a three-dimensional space manifold with respect to fourth spatial dimension by extrapolating our understanding of a resonant structure created by a wave in a three-dimensional environment.

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

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

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

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

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

In our three-dimensional environment 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 mechanical associates with the particle properties of matter.

Yet one can also define its boundary conditions of its resonate structure in the terms of our perceptions of a three-dimensional environment.

For example, in our three-dimensional world, 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.

It is the confinement of the upward and downward oscillations of an energy with respect to a fourth *spatial* dimension by an observation is what defines the spatial boundaries associated with a particle in the article Why is energy/mass quantized? " Oct 4, 2007.

This shows the reason Quantum Mechanics can define matter in terms of a particle/wave duality and why it only presents its particle or position properties when it is observed is because its wave component is only confined to three-dimensional space when an observation is made.

However, as mentioned earlier it also provides a way to physical connect the probabilistic environment defined by SchrÃdinger wave equation to the physicality of Einstein’s relativistic universe.

The physics of wave mechanics tell us that due to the continuous properties of the wave component associated with a quantum system it 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 outlined above, that quantum properties of matter 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. lenth[4]

(Some may question the fact that the energy wave associated with particle would be simultaneously distributed over the entire universe.  However, the relativistic properties of space-time tell us the 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 energy wave moving at the speed of light, the distance between all points in the universe along its velocity vector is zero.  In other words, because its electromagnetic wave component of a particle is moving at the speed of light as all electromagnetic0 energy must is it would be 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? ” shown a wave/particle duality of matter can be understood in terms of a resonant structure formed wave energy 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.

This demonstrates that one can interconnect probabilities associated with Schrödinger’s wave equation to the physicality of the Einstein’s Relativistic universe.

As was mentioned earlier the arrow of time is defined in classical system in terms of entropy or the level of randomness (or disorder) of a system and the Second law of thermodynamics which states that there is an the extraordinarily small probability that a system will return to its original configuration, based on the extraordinarily larger number of microstates in systems with greater entropy even though its. 

Additionally, the above discussion also shows one can use the same definition for the arrow of time in a quantum universe as the one used in a macroscopic one because the position of a particle in a quantum can only be determine with respect to other particles in probability field Schrodinger’s equation.  Therefore, due to the fact that there are infinite number of possibilities in the probabilistic universe of quantum mechanics there an extraordinarily small chance of that universe retuning to is original configuration when an observation is made in the future.  

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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Presently, there is disconnect between our understanding of one of the most mysterious facets of quantum mechanics quantum, that of quantum entanglement and the classical one of separation.

Entanglement occurs when two particles are linked together no matter their separation from one another. Quantum mechanics assumes even though these entangled particles are not physically connected, they still are able to interact or share information with each other instantaneously.

Many believe this means the universe does not live by the law’s classical laws of separation or those derived by Einstein which stated that no information can be transmitted faster than the speed of light.

However, we must be careful not to jump to conclusions because Einstein gave us the definitive answer as to how and why particles are entangled in terms of the physical properties of space-time.

Quantum mechanics assumes that entanglement occurs when two particles or molecules share on a quantum level one or more properties such as spin, polarization, or momentum. This  connection persists even if you move one of the entangled objects far away from the other. Therefore, when an observer interacts with one the other is instantly affected.

There is irrefutable experimental evidence the act of measuring the state of one of a pair of particles can instantaneously effect another even though they are physically separated from each other.

However, before we come to the conclusion it is a result of their quantum mechanical properties, we should first examine the experimental setup and any variables that may allow us to come to a different conclusion.

In quantum physics, it is assumed entangled particles remain connected so that actions performed on one immediately affect the other, even when separated by great distances. The rules of  Quantum physics also state that an unobserved photon exists in all possible states simultaneously but, when observed or measured, exhibits only one state.

One of the experiments that many assume verifies that entanglement is a quantum phenomenon uses (This description was obtained from the Live Science web site) a laser beam fired through a certain type of crystal which causes individual photons to be split into pairs of entangled photons. The photons can be separated by a large distance, hundreds of miles or even more. When observed, Photon A takes on an up-spin state. Entangled Photon B, though now far away, takes up a state relative to that of Photon A (in this case, a down-spin state). The transfer of state (or information) between Photon A and Photon B takes place at a speed of at least 10,000 times the speed of light, possibly even instantaneously, regardless of distance. Scientists have successfully demonstrated quantum entanglement with photos, electrons, molecules of various sizes, and even very small diamonds.

However, Einstein told us there are no preferred reference frames by which one can measure distance.

Therefore he tells the distance between the observational points in a laboratory, can also be defined from the perspective of the photons in the above experiment.

Yet, this tell us (Please see attached graphic) that the separation between the observation points in a laboratory from the perspective of two photons moving at the speed of light would be ZERO no matter how far apart they might be from the perspective of an observer in that laboratory. This is because, as was just mentioned according to the concepts of Relativity one can view the photons as being stationary and the observers as moving at the velocity of light.

Therefore, according to Einstein’s theory all photons which are traveling at the speed of light are entangled no matter how far they may appear to be from the perspective of an observer who is looking at them.

In other words, entanglement of photons can be explained and predicted terms of the relativistic properties of space-time as defined by Einstein as well as by quantum mechanics.

One way of determining if this is correct would be to determine if particles which were NOT moving at the speed of light experience entanglement over the same distances as photon which are.

This is because, the degree of relativistic shortening of the distance between the end points of the observations of two particle is dependent on their velocity with respect to the laboratory were they are being observed.

Therefore, all photons no matter how far apart they are from the perspective of a lab will be entangled because Einstein tells due to the fact that they are moving at the speed of light that distance will be Zero from their perspective.

However, he also tells us that for particles moving slower than the speed of light the distance between will be greater than zero and how much more would depend on their the relative speed with respect to it. In other words, the slower with respect to the lab they are moving the less that distance will be shortened.

Therefore, if it was found that only photons experience entanglement when the observation points were separated by large distances it would support the idea that it is caused by the relativistic properties of space defined by Einstein.

However, one must remember the wave particle duality of existence as defined by Quantum mechanics tell us that before a particle is observed it has an extended length equal due to its wavelength. Therefore, all particles will be entangled if the reduction in length between the endpoints of the observations when adjusted with respect to their relative velocity is less their wave length as defined by quantum mechanics.

A more conclusive argument could be made for the idea that entanglement is a result of the relativistic properties of space if it was found that entanglement ceased when the relativistic distance between the end points of observation when viewed from the perspective of particle moving slower than the speed of light was greater than its wavelength as defined by quantum mechanics.

Some have suggested that “There are inertial frames for every speed less than light – speaking informally – but there is no inertial frame for light speed itself. Any attempt to generate one actually generates a degenerate frame which can cover only an infinitesimal fraction of space-time.” However the argument that there are “There are inertial frames for every speed less than light”

because they would create an infinitesimal fraction of space-time is invalid, because Special Relativity WITHOUT EXCEPTION defines an inertial frame reference as one which is not undergoing acceleration.  Therefore, even though using a photon as a reference frame may create infinitesimal 2 dimensional  fraction of space-time the conceptual foundations formulas for length contractions of reference frames in relative motion define by Einstein tells us that one can exist. One reason that all of the mass which is contained in it is not undergoing acceleration.Therefore, the  fact that it may define a degenerate frame would be irrelevant to the conclusion draw above because as that post showed it is the distance between the end points of the observation when viewed from a photon that determines whether or not it will be entangled.

Copyright Jeffrey O’Callaghan 2020

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 A Quantum Singularity is a misnomer because it owes it existence to classical one created by a black hole not to its quantum mechanical properties.black_hole_singularigy 

Even so many physicists assume it is the key to unifying Quantum mechanics with Einstein’s General and Special Theories of Relativity because they believe the gravitational collapse of matter in a black hole, predicted by his theories also predicts, with equal certainty the existence of a singularity, which by definition is infinitely small and quantum mechanical in nature. Therefore, due to the fact that they are caused by gravitational forces a theory of quantum gravity would be required to define its formation.

Its existence is based on a mathematical interpretation of General Theory of Relativity which tells us that when star starts to collapse after burning up its nuclear fuel and forms a black hole the gravitational forces of its mass become large enough to cause matter to collapse to zero volume or one that is governed by quantum mechanics.

However, even though there is observational evidence for the existence of black holes there never will be any for a singularity because according to the General Theory of Relativity nothing, including light can escape form one.

For example NASA’s Hubblesite tells us that "Astronomers have found convincing evidence for a black hole in the center of our own Milky Way galaxy, the galaxy NGC 4258, the giant elliptical galaxy M87, and several others. Scientists verified its existence by studying the speed of the clouds of gas orbiting those regions. In 1994, Hubble Space Telescope data measured the mass of an unseen object at the center of M87. Based on the motion of the material whirling about the center, the object is estimated to be about 3 billion times the mass of our Sun and appears to be concentrated into a space smaller than our solar system."

However, as mentioned earlier we will never be able to observe a singularity because they only exist inside black hole.  Therefore to determine their reality we must rely solely on the predictions of the General Theory of Relativity regarding their formation.

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

However this would only be true if the mathematics used to predict both a black hole and its singularity conform to the conceptual arguments associated with Einstein General Theory of Relativity because its existence is based solely on that mathematics of that theory and not on observations, as is the case of black holes.

In other words the fact that we can observe a black hole tells us the mathematics used to predict its existence has a valid basis in ideas of General Relativity. 

However the same cannot be said about the existence of a singularity because the conceptual arguments found in that theory tells us that we cannot extrapolate the mathematics associated with it to the formation of a black hole.

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

Einstein in his General Theory of Relativity predicted time is dilated or moves slower when exposed to gravitational field than when it is not.  Therefore, according to Einstein’s theory a gravitational field, if strong enough it would stop time.

In 1915 Karl Schwarzschild discovered that according to it the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a singularity.  He also defined the critical circumference or boundary in space around a singularity where the strength of a gravitational field will result in time being infinitely dilated or slowing to a stop.

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

This critical circumference is called the event horizon because an event that occurs on the inside of it cannot have any effect on the environment outside of it.

Yet many physicists, as mentioned earlier believe the existence of a singularity is an inevitable outcome of Einstein’s General Theory of Relativity.

However, it can be shown using the concepts developed by Einstein; this is not true.

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

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

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

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star from the reference frames of all observers as Einstein tells we must because they are all equivalence.

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

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

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

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

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

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

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

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

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

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

There are some who claim that irregularities in the velocity of contractions in the mass forming the black hole would allow it continue to collapse beyond its event horizon. However Einstein’s theories tells us that time would move slower for the faster moving mass components than the slower ones thereby allowing the them to catch up with their faster moving onew so they will be moving at the same speed when they reach the event horizon.

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

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

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

This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations that many physicists used to predict the existence of singularities because, as has just been shown the mathematical predications made by it regarding their existence is contradictory to conceptual framework of his theories.   Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

As was mentioned earlier many physicists think the key to unifying Quantum mechanics with Einstein’s General and Special Theories of Relativity is the singularity that some of the mathematical models say exists in black holes.   However, as was show above their existence is not supported by his theories.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

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In quantum mechanics, wave function collapse is said to occur when a wave function, initially in a superposition of several states appears to reduce to one due to interaction with the external world.  This interaction is called an observation.

The measurement problem in quantum mechanics involves understanding how (or whether) wave function collapse occurs. The inability to directly observe such a collapse has given rise to different interpretations of quantum mechanics and poses a key set of questions that each interpretation must answer.

Quantum mechanics assumes it evolves deterministically according to the Schrödinger equation as a linear superposition of different states. However, when observed it is always found in a definite state.  Its future evolution is based on the state the system was discovered to be in when the measurement was made.  In other words, the measurement "did something" to the system that is not obviously a consequence of Schrödinger evolution. The measurement problem is describing what that "something" is, and how a superposition of many possible values becomes a single measured value.

To express matters differently, (paraphrasing Steven Weinberg) Schrödinger wave equation determines the wave function at any later time. If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities? As a general question: How can one establish a correspondence between quantum and classical reality.

However, Einstein unknowing may have able to define what happens to the wave function when observed by extrapolating the rules of classical mechanics to the physical properties of the space-time environment he defined.

One of the reasons he may have been unaware of this possibility is because superposition involves the spatial properties of position where as he chose define the universe in terms of time or the properties of four-dimensional space-time.  In other words, understanding the physical connection between the spatial properties of position and the time properties of Einstein space-time universe is extremely difficult for the same reasons as one would find it difficult to define a physical connection between apples and oranges.

However, Einstein gave us a way around this when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass and energy in a space-time universe because that provided a method of converting a unit of time in space-time environment to unit of space in one made up of 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.

This would allow one to describe what happens to the linear superposition of different states when an observation is made and why it becomes a single measured value.

Additionally, it would also allow one to understand the validity of quantum mechanics assumption that particles can be defined in terms of waves, how they can be superimposed or simultaneously be in multiple positions before being observed and why their interaction with the external world must be describe in terms of probabilities.

For example, the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the Einstein’s theories to explain and understand the physicality of the wave properties of particles by extrapolating the rules of classical resonance in a three-dimensional environment to an energy wave moving on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.

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

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

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

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

As was shown in that article the ossifications of these resonant systems in four *spatial* dimensions are responsible for the wave properties quantum mechanical particles.

However, one can also explain how the boundaries of a particle’s resonant structure are defined.

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

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

It is the confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension which allows the resonate structure the article "Why is energy/mass quantized?" Oct. 4, 2007 showed was responsible for a particle to exist. \

In other words the reason it becomes a single measured value when observed is because when the energy wave moving through space either space-time or four spatial dimensions is confined by an observation to three-dimensional space the interference between waves reflected back and forth by that confinement sets a resonant standing wave in space which is called a particle.

In other words, Einstein give us a classical validation of the quantum mechanical assumption that particles can be thought of as waves because it shows they are made up of resonate structures formed by energy wave and why when someone observes its wave component it always appears as a particle.

Additionally, one of the most advantageous results of viewing the relativistic properties of Einstein’s theories in terms of their spatial instead of its time components is that gives us the answer to one of the most perplexing aspects of quantum mechanics; that of how and why a particle can simultaneously exists anywhere in the universe before being observed.

This is because it tells the length of an object relative to another is affected by its relative velocity and that there are no preferred reference frames by which one can measure that length. Therefore, one must not only view the distance traversed by the wave with respect to an observer who was external to it but one must also view the distance between observers from the wave’s perspective. Yet it also tells us that the length of everything including the universe from an object or wave moving at the speed of light is zero as can be seen from his formal on the right for length contraction.

Therefore, from the perspective of the energy wave the article "Why is energy/mass quantized?" showed was responsible for a particle which is moving at the speed of light with respect to all observers the distance or length between all observers no matter where they are in the universe is zero with respect to that wave.  Therefore, it exists at every point in between.

This gives us an explanation in terms of the four spatial dimensional equivalent of Einstein space-time universe for the VALIDITY of quantum mechanics assumption that a photon’s wave packet simultaneously exists everywhere in in the universe before being observed. In other words, it only "decides" where it wants to be in space when it is prevented from moving at the speed of light relative to an observer by an observation.

However, viewing Einstein theories from the perceptive of their spatial instead of their time components also allows one to derive the classical reason why one must use probabilities to determine a particles position will be before being observed.

The fact that one can, as was show in the article mentioned earlier “Why is energy/mass quantized?” derive the particle properties of an energy wave as the result of a resonant structure formed on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension also allows one to understand how a particle "decides" where is want to be in terms of our classical understanding of the world around us.

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 one accepts the validity of Einstein’s theories and the theoretical model that the quantum properties of a particle are a result of vibrations or oscillations in a "surface" of three-dimensional space, those oscillations as was shown above would be distributed over the entire "surface" three-dimensional space with respect to all observers while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

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 found were the magnitude of the vibrations in a "surface" of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This shows how one can make intuitive "sense" of Quantum Superposition and why the wave packet of a particle decides what and where it wants to be when observed by extrapolating the rules of a classical mechanics to the spatial equivalent of Einstein’s theories.

In other words it solves the the measurement problem because it provides an understanding what happens to the wave function when it interacts with the  external world by describing what and how the superposition of many possible values becomes a single measured value when an observation is made.   Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

It should be remembered Einstein genius allows us to view his theory in either four-dimensional space-time or its equivalent in only four *spatial* dimensions.  As was shown above changing one’s perspective on his theory from time to its spatial equivalent allows one to form an intuitive understanding of quantum Superposition based on our experiences in a three-dimensional world.

Latter Jeff

Copyright Jeffrey O’Callaghan 2019

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