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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One question that has yet to be answer regarding Einstein relativistic theories is how time and space interact to create the past, present and future.

Einstein side step this question by assuming, as he put it "there exists in this four-dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears Therefore, more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence."

Marina Cort’s, a cosmologist from the Royal Observatory, Edinburgh defined what has come to be called the block universe to help us understand how Einstein may have viewed the past present and future.

Basically, she asks us to imagine a regular chunk of cement. It has three dimensions but we live in four dimensions: the three spatial dimensions plus one time dimension. A block universe is a four-dimensional block, but instead of being made of cement, it is made of space-time. And all of the space and time of the Universe are there in that block."

We can’t see this block, we’re not aware of it, as we live inside the cement of space-time. And we don’t know how big the block universe we live in is: "We don’t know if space is infinite or not. Or time – we don’t know whether it has a beginning or if it will have an end in the future. So, we don’t know if it’s a finite chunk of space-time or an infinite chunk."

In other words, the past, present, and future exist simultaneously and are locked in a non-dynamic, unchanging block of space-time with the rigidity of cement.

However, to understand why Einstein he had to make this assumption one must first define what space and time are.

For example, some define time only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak.  To physicist’s it is a measure of the relative interval between events which is measured in units of time such as seconds.

While space can be defined as the arena where those events occur.  We use the measurements of inch or meter to define the position of those event in that arena.

The problem Einstein with defining how energy causes a dynamic change in a space-time environment that define "happening and becoming" or the future, may have been due to the fact that he mathematically defined it in terms of a melding of time with space which have different units. Therefore, because, in mathematics if the dimensions or units on the left and right-hand sides don’t agree the equation are nonsense it is hard to imagine how the future is created in terms of space-time. This is why he said "It appears Therefore, more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence.

However, the fact he found that definition unsatisfactory is evident when he said that "concepts (or causality) of happening and becoming are indeed not completely suspended, but yet complicated" indicate that he was aware of this.

In other words, Einstein realized that causality of the future in terms of a dynamic process was something that must be considered.

Yet, Einstein gave us an alternative way of understanding "happening and becoming" when he defined the relationship between energy and space-time in terms of the constant velocity of light and the equation E=mc^2 because in doing so he provided a method of converting a unit of time and energy 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 only 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.

In his space-time model he mathematically defined all forms of energy including gravity and the kinetic energy of motion in terms of a curvature or displacement in the "surface" of four-dimensional space-time manifold. However, in his equivalent model consisting of only four *spatial" dimensions he would have defined them in terms of a displacement or curvature in the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As was mentioned earlier, it was evident Einstein realized the difficulty of deriving the future or happenings in terms of his space-time model when he said "no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated.

However, the same is not true of the equivalent model mentioned above consisting of only four *spatial* dimensions because defining the causality of change of the future in those terms would eliminate the problem mentioned above with the incompatibility of space and time.

Yet, before we can define the future in terms of the dynamics four *spatial* dimension we must first explain how it interacts with time to cause it to dilate and shorten length of objects when it is in relative motion with respect to an observer.

For example, one can show as was mentioned earlier by using the Einstein mathematics the kinetic energy of motion can be understood in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension as well one in four-dimensional space-time.

One can understand how this would effect time and the length of objects in relative motion by assuming the perspective of two "2 dimensional creatures are living on the surface of two pieces of paper resting on a desktop.

Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.

If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.

Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.

Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of the three-dimensional curvature in the surface of the paper.

Similarly, because three-dimensional beings could only "view" a three-dimensional translation of a "curvature" or displacement in four *spatial* dimension caused by the motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is not in relative motion to it.

The "movement" of time on both surfaces will also be affected.

Each of the two-dimensional creatures mentioned earlier will view the others time as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two-dimensional translation of those events.  Therefore, it will take longer for events "move" through a curvature in three-dimensional space relative to the time it would take for them to move through two-dimensional translation on the others surface caused by that curvature.

Similarly, time will become dilated in reference frames that are in motion because the curvature generated on its three-dimensional "surface" caused by its relative motion will result the distance between events to be longer than it with respect to the distances measured in reference frames observe on them assumed them to be stationary.  Therefore, they will view time in a reference frame that is in motion relative to them as moving slower than if they were in that reference frame.

As show above both of these models, the one based on the physical existence of four dimensions space-time and the existence of only four spatial dimensions make identical predictions as to the relativistic properties of space and time, therefore which one you chose to define the physical structure of our universe must be based, in part on how you view the future.

However, Einstein space-time interpretation did not allow him to define the dynamic changes in our environment that we call the future because he mathematically defined them in terms of a melding of time with space which have different units.  Therefore, he had to assume that the past present and future was locked in a block of cement.

However, as was shown above the same is not true if one interprets his equation in terms of four *spatial* dimensions because all they all have the same units.

Yet, because as was mentioned earlier both of these models are mathematically equivalent and since we cannot physically observe either a time or a fourth *spatial* dimension, we must look to the affects they would have on the ones we can observe or in this case how we perceive the future to determine which one of these physical models is correct.

In other words, if you view it as something that dictates the past and present you will probably chose his space-time model.  However, if you view the future as a dynamic interaction of the past with the present you will most likely choose the model based on only four *spatial* dimensions.

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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A few years after Albert Einstein unified space and time in his (and by now very well tested!) Theory of General Relativity he applied it to the entire universe and found something remarkable. The theory predicts that the whole universe is either expanding or contracting.

Later in 1929 the astronomer Edwin Hubble measured the velocities of a large selection of galaxies and found that the majority of them were moving away from us.  In other words, the universe was expanding.

However, is the universe expanding in space or is it expanding through time? 

To answer this one must first define what time and space are.

Some define time only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak.  To physicist’s it is a measure of the relative interval between events which is measured in units of time such as seconds minutes or hours.

However, space can be defined as the arena where events occur.  We use the measurements of inch or meter to define the position of those event in that arena.

As was mentioned earlier, Einstein’s General Theory of Relativity mathematically define the universe in terms of a melding of time with space.  However, as was mention above they are they have vastly different properties.  For example, one is measure in terms of second while the other is in inches or meters.

Therefore, it is very difficult to understand how time which is measured in seconds can have a dynamic effect on space measured in meters.

To this end Marina Corts, a cosmologist from the Royal Observatory, Edinburgh came up to what has come to be called the block universe.

Basically, it asks us to imagine a regular chunk of cement. It has three dimensions but we live in four dimensions: the three spatial dimensions plus one time dimension. A block universe is a four-dimensional block, but instead of being made of cement, it is made of space-time. And all of the space and time of the Universe are there in that block."block universe

We can’t see this block, we’re not aware of it, as we live inside the cement of space-time. And we don’t know how big the block universe we live in is: "We don’t know if space is infinite or not. Or time – we don’t know whether it has a beginning or if it will have an end in the future. So, we don’t know if it’s a finite chunk of space-time or an infinite chunk."

However, picture this presents a problem for cosmologists because if the merging of space and time causes it to become as ridge as a block of cement how can its spatial component be expanding.

It should be remembered only the spatial component of the universe is expanding not time. 

Additionally, because Einstein defined the universe in terms of only four dimensions, one time and three spatial how can we understand its spatial expansion without adding an additional one because a spatial one cannot expand to one made up of time because, as mentioned earlier they have vastly different properties.

Yet, Einstein gave us an alternative when he defined the mathematical relationship between space and time 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. 

Yet, because both of these models are mathematically equivalent and since we cannot physically observe  either a time or a fourth *spatial* dimension, we must look to the effects they would have on the ones we can observe to determine which one of these physical models is correct.

For example, if we were a two-dimensional creature living on the surface of a balloon that was inflating, we could explain its spatial expansion by assuming we were living in an environment consisting three spatial dimensions because they have the same properties as the two dimension surface of the balloon therefore, it could expand through it.  However, we could not explain it by assuming that we were living in an environment consisting of only time and the two-dimensional surface of the balloon because time as mentioned earlier it does not have the properties of space and therefore could not expand in it. 

Similarly, we can explain why our three-dimensional world was undergoing a spatial expansion by assuming we were living in an environment or universe consisting four *spatial* dimensions because it would have the same spatial properties as the three dimension one we live in.  However, we could not if we assume our universe consisted of four-dimensional space-time because time does not have the properties of space and therefore similar to the surface of the balloon it could not expand in it.

As was mentioned earlier  "A few years after Albert Einstein unified space and time (and by now very well tested! ) in his theory of General Relativity" and showed it can be "applied to the entire universe ." Therefore, he also showed that because of their mathematical equivalence, a physical model based on one unifying three-dimensional space with a fourth *spatial* dimension has also been very well tested and could also be applied it to the entire universe.

However, as was shown above his physical model based on four *spatial* dimensions pass an additional test which his space-time model cannot, that of explaining the spatial expansion of our three-dimension environment. 

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 share information with each other instantaneously seemingly breaking one of the most hard-and-fast rules of classical physics and Einstein theories: that no information can be transmitted faster than the speed of light.

Even though it may be hard for some to accept the instantaneous sharing of information over what appears to be long distances has been proven time and time again over the years.

For example, when researchers create two entangled particles, separate them and independently measure their properties, they find that the outcome of one measurement influences the observed properties of the other particle.

This was made possible in 1964, when John Bell showed there is a theoretical limit beyond which correlations can only be explained by quantum entanglement, not classical physics.

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 even though he was so upset to what he called this  "spooky action at a distance." that in 1935 he along with Podolsky Rosen proposed the following thought experiment which came to be called the EPR Paradox.

In 1935, Einstein co-authored a paper with Podolsky and Rosen highlighted a problem that they felt showed that Quantum Mechanics could not be a complete theory of nature.  This thought experiment came to be called the EPR Paradox. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a "hidden variable" that would allow Quantum Mechanics to become a complete theory of nature.

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

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

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

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

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

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

Since then there have been many experiments using the properties of paired of photons and other particles that verify without any doubt that two photons and others particles that are spatially separated can be entangled.

In quantum mechanics it is assumed that the act of measuring the state of one of a pair of entangled particles instantly affects the other no matter how far they are apart.

However, Einstein in his Special Theory of Relativity gives us a classical explanation in terms his theory for the entanglement of two particles.

For example, with regards to the polarized photons mentioned earlier that Allen Aspect used to verify the quantum mechanical interpretation of entanglement his theory tells us that because photons must always be moving at the speed of light they can never be separated with respect to an external observer no matter how far apart he or she perceives them to be.

This is because he tells that that there are no preferred reference frames by which one can measure distance. Therefore, one must not only view the separation of a photon with respect to an observer who was external to them but must also look at that separation from a photon’s perspective.

However, his theory tells the distance between the two photons A and B would be defined by their relative speed with respect to an observer.

Specifically, he told us that it would be defined by

Yet, this tell us that the separation between two photons moving at the speed of light from their perspective would be zero no matter how far apart they might be from the perspective of an observer in a laboratory because 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 with all other paired photons no matter how far apart or "spacelike" separated they may appear to be to ALL observers.

In other words, the inequities in the measurements made on ALL REPEAT ALL pairs of photons should be violated in a world containing the physical reality of Einstein’s theories because they will influence each other no matter how far they may be separated when viewed from a reference frame other than a photon’s, such as a laboratory.

Up until now we only have addressed the entanglement of photons that are moving at the speed of light.  However, the same the relativistic properties of motion can be applied to explain the entanglement of other particles that are not moving at that speed.

This is because quantum mechanics defines the composition of matter in terms of its wave particle duality.  More specifically, as was shown in the previously article  "Quantum mechanics in a nutshellt look: waves. Look: particles" Dec. 1, 2015 it assumes that before an observation is made matter is propagated though space in terms of its wave properties and only after being observed does it present its particle properties.

In other words, in Quantum Mechanics matter has an extended volume while moving through space which is directly related to the wavelength associated with its particle properties.

This means the wavelengths of two particles in motion will overlap and be entangled if the separation between the end points of an observation as measured from their perspective is less that the wavelength of those particles.

However, as mentioned earlier Einstein tells us that we must use this theory to derive the separation of two moving particles from their perspective and not from the prospective of observers in a laboratory.

Therefore, even though particles may appear to be separated from the view point of a laboratory observer they may not be separated from the view point of the particles that are moving with respect to those observers because of an overlap of their wave properties..

In other words, one does not have to break one of the most hard-and-fast rules of classical physics and Einstein theories: that no information can be transmitted faster than the speed of light because one can use his classical theories to explain how and why particles that appear to be separated can communicate instantaneously. REVIEW BUTTON

The illusion is not that entanglement of two spatial separated particles from the perspective of the observers in Allen Aspect experiment mentioned earlier does not exist.  The illusion is that entanglement is not the result of the quantum mechanical properties of matter but instead is the result of the physical reality of Einstein’s Theory of Relativity because it tells us that the separation of particles must be measured from their perspective and not from the perspective of an observer in a laboratory.

Copyright Jeffrey O’Callaghan 2020

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Richard Feynman the farther of Quantum Electrodynamics believed Thomson’s double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability and provides a mechanisms for understanding how it is propagated through space.

The wave-particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.  Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

The reason the above-mentioned experiment is so important is because it provides a mechanism for understanding how electromagnetic energy is propagated and why the particle wave dually exists purely in terms of Einstein’s Theory of Relativity.

But before we begin, we must first understand how the electromagnetic wave component of a particle’s duality is propagated through space and time.

One of the difficulties involved in doing so is that we define its movement though space in terms Maxwell’s equations which are based on the interaction between its electric and magnetic components with respect to time not space.  This presents a problem because the particle component of its duality must always be defined by its spatial position when observed. Therefore, to understand how they are related we should attempt to define its movement through space and time in term of its spatial properties.

Einstein gave us the ability to do this purely in terms spatial properties of its electromagnetic wave components when he used the constant velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to an equivalent unit of space in an environment consisting of only four *spatial* dimensions.  Additionally, because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

This gives one the ability to derive the properties of an electromagnetic wave and understand its movement in terms of the spatial displacement that would be created by its observed transverse wave characteristics. 

For example, a transverse wave on the two-dimensional surface of water moves through water because it causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force is developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water. This results in a wave to move on the surface of the water.

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

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

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

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

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

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

However, this means that one can define a physical model for the propagation of an electromagnetic field in terms of Einstein’s space-time theory because, as was shown above when he mathematically defined its geometric properties in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his theory in terms of the geometry of four *spatial* dimensions.

Yet, viewing it in terms of its spatial components also allows one to understand the mechanism responsible for the wave particle duality of a photon as observed in the Thomson’s double slit experiment and why electromagnetic energy always presents itself as a particle when it strikes the detector in the that experiment.

For example, the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the Einstein’s theories to explain the quantum mechanical properties of an electromagnetic wave 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.

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 the energy wave associated with a photon 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 would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

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

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for the particle called a photon.

However, one can also use Einstein space-time theories when viewed in their spatial equivalent to explain how the boundaries of the standing wave responsible for creating the resonant system that article indicated was responsible of a particles formation are created.

In classical physics a standing wave is created when the vibrational frequency of a source causes reflected waves from one end of a confined medium to interfere with incident waves from the source.  This interference of the wave energy causes their peaks troughs to be reinforce in the volume they are occupying thereby creating a standing wave.

The confinement required to create a standing wave in space-time or its equivalent in four *spatial* dimensions can be understood by comparing it to the confinement a point on the two-dimensional surface of paper experiences when oscillating with respect to three-dimensional space.  The energy associated with the wave motion of that point would be confined to its two-dimensional surface and would be reflected and interfere with the incident wave when reaches three-dimensional space at its edge. Therefore, a standing would be created by its interaction with three-dimensional space.

In other words, when a wave on the surface of a piece of paper encounters the third *spatial* dimension at its edge it is reflected back allowing a standing wave to be formed on its surface.

Similarly, an electromagnetic wave moving on the surface of three-dimensional space would be confined to it and reflected back to that volume, similar to the surface of the paper if it was prevented from oscillating with respect to a four *spatial* dimensions or four-dimensional space-time.

In other words, the interference caused by the confinement of an electromagnetic wave to three-dimensional space, which is caused by it striking the detection screen in the Thomson’s double slit experiment results in the resonant standing wave to be formed in space called a photon.

That experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes it wave component to interfere after passing through both slits, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light "is always found to be absorbed as discrete particles, called photons".

When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detail.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygen ‘s Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

However, the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.   This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

Even more puzzling is why any attempts to measure which slit that electron passed through cause the interference pattern to disappear.

Yet, as mentioned earlier one can derive the outcome of this experiment by assuming that electromagnetic energy is propagated by a wave on the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension instead of four-dimensional space-time

For example, the reason why the interference patterns remain when only one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as was just shown it has an extended spatial volume which is directly related to the wavelength.

This means a portion of its energy can simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern.

Additionally, one can also explain why the interference pattern disappears when a detector is added to determine which slit a photon has passed through.  The energy required to measure which slit it passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit   Therefore, the energy passing thought that slit will not be able to interact, with the energy passing through the other one to form an interference pattern on the screen.

However, as was shown earlier one can also show the reason the interference pattern appears as a particle when electromagnetic wave contacts a detection screen is because striking it results in it being confined to three-dimensional space instead of four-dimensional space-time or four spatial dimensions, thereby creating a standing wave in either four spatial dimensions or four dimensional space-time to be created.

In other words, it clearly shows the reason all forms of energy exhibit both wave and particle properties are because they are physically made up of waves in terms of Einstein’s Theory of Relativity.

The above discussion shows that Richard Feynman was right in assuming that Thomson’s double slit experiment provided a mechanism for understanding the  wave particle duality of energy/mass because it clearly demonstrates their inseparability.

Additionally, it also provides an explanation how and why energy  is propagated through space because it shows the quantum mechanical and wave properties of energy displayed in the double slit experiment can be understood if one assumes they are made up of a resonant system in a moving in a four dimensional space-time manifold or on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms Einstein theories. 

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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Absolutely not, because those laws as proposed by Einstein prevent that from happening.

The existence of a singularity at the center of a black hole is often taken as proof that the theory of general relativity has broken down, which is perhaps not unexpected as it occurs in conditions where quantum effects should become important. time_dialiton12

In the center of a black hole many believe a gravitational singularity occurs which contains a huge mass in an infinitely small space. In other words density and gravity become infinite while space-time curves infinitely. This would result in the laws of physics as we know them cease to operate. As the eminent American physicist Kip Thorne describes it, it is "the point where all laws of physics break down".

Unfortunately, everyone including Kip Thorne is wrong because as was just mentioned the laws proposed by Einstein governing the existence of space-time tell us that a singularity can never repeat never exist in a black hole.

The existence of a singularity is based on a mathematical solution developed in 1915, by Karl Schwarzschild who proposed based on Einstein theories the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time.  Additionally, it is assumed that his solution identified a radius for any given mass, known as the Schwarzschild radius, where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity or black hole. Thus, where the radius of the body is less than its Schwarzschild radius, everything, even photons of light, must inevitably fall into the central body called a singularity or a one-dimensional object in space-time.

However, the according to the relativistic laws Einstein proposed for his space-time universe the time dilatation it associated with a gravitational field would prevent matter form collapsing beyond the event horizon of a black hole to form a singularity .

In other words, the very theory is used to predict the existence of a black hole also prevents the formation of a singularity and the laws of physics, as defined by Einstein from breaking down in its space-time environment.

To understand why one must analyze how he define the relativistic properties of space-time and how it interacts with matter in a gravitational field.

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

However, the existence of a singularity mentioned earlier is based on the assumption that time continues to move for matter even after it has past the event horizon of a black hole.

However, this is a direct contraction of the relativistic properties of time as described in Einstein theories.

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, it also tells us, the laws of physics developed by Einstein for a space-time environment are not violated in black hole with respect to all external observers because the time dilation associated with its gravitational field would not allow the collapse of matter beyond its critical circumference to a singularity.

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 also 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 is at the center of the clasping mass and the contraction cannot continue from their perspectives.

However, it also tells us, the laws of physics developed by Einstein for a space-time environment are not violated in black hole with respect to an observer who is  at the its center because the time dilation associated with its gravitational field would not allow the collapse of matter beyond its critical circumference to a singularity.

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.

However, it also tells us, the laws of physics are not violated in black hole with respect to all riding on the surface of a star because the time dilation associated with its gravitational field the collapse of matter beyond its critical circumference to a singularity.

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 as many physicists believe because it causes time to freeze at its critical circumference with respect to all observers and therefore must maintain a quantifiable minimum volume which is equal to the one defined by Karl Schwarzschild.

However, this means the laws of physics as defined by Einstein do not break done when a singularity forms at the  center of a black hole because as was shown above those laws tell us its formation is not supported by those laws.  Therefore it cannot be taken as proof that the laws as defined by General Theory Relativity has broken down, because those same laws prevent that from happening Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

There can be no other conclusion if one accepts the validity laws as defined by Einstein Relativistic Theories and of the physical observations of the time dilation associated with a gravitational field.

Later Jeff

Copyright 2020 Jeffrey O’Callaghan

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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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because it can stop the collapse of matter no matter how massive an object is.

Einstein told us a gravitational field causes time to dilate and 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 stop the movement of time.  Additionally, it is assumed that his solution identified a radius for any given mass, known as the Schwarzschild radius, where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity or black hole. Thus, where the radius of the body is less than its Schwarzschild radius, everything, even photons of light, must inevitably fall into the central body called a singularity or a one-dimensional object in space-time.

 

However, according to Einstein there is one "force or degeneracy pressure" that will stop it from continuing to collapse into a gravitational singularity and that is time.

To understand how and why one must analyze how he defined the relativistic properties of space-time and how it interacts with matter in a gravitational field.

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

However, the existence of a singularity mentioned earlier is based on the assumption that time continues to move for matter even after it has past the event horizon of a black hole.

Yet, this is a direct contradiction of the relativistic properties of time as described in Einstein theories.

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, it also tells us, the force of time is stronger that the gravitational forces of a black hole with respect to all external observers because when it freezes it prevents the further gravitational collapse of matter beyond the critical circumference with respect to them.

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 than another towards its center it could not be consider an inertial reference frame because it would be pushed or pulled due to the differential gravitational force cause be its uneven collapse.  But the laws governing time dilation in his 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 also 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 time 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.

However, it also tells us, the force of time is stronger than the gravitational forces of a black hole with respect to all observers located at its center because when it freezes with respect to them it prevents the further collapse of matter beyond the critical circumference.

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 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.

However, it also tells us, the force of time is stronger that the gravitational forces of a black hole with respect to an observer who is riding on it because when it freezes with respect to its external environment it prevents further the collapse beyond the critical circumference.

This means, as was just shown according to Einstein’s concepts because time and movement stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of 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 the gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe because it causes time to freeze at its critical circumference with respect to all observers. Therefore it must maintain a quantifiable minimum volume which is equal to the one defined by Karl Schwarzschild.

This tells us either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations based on the General Theory of Relativity that many physicists used to predict the existence of a singularity because as has just been shown the theoretical predications made by them with respect to the  time dilation associated with a gravitational field tell us it cannot exist. Therefore, according to his theories a black hole must have a solid surface at the event horizon which is made up of matter in its most basic form because it cannot be compacted any more.

However, it also tells us time is a force more powerful than the gravitational field of a black hole because it has the ability to freeze the collapse of matter at its event horizon no matter how massive it is.

In other words, time is the most  powerful in the universe because it can stop the collapse of matter in a black holes.  Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

There can be no other conclusion if one accepts the validity Einstein Relativistic Theories and of the physical observations of the time dilation associated with a gravitational field.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

Superposition, in the quantum world means that on a quantum scale, particles can be thought of as waves that can exist in different states or positions at the same time.  Like all waves they can overlapping or be superimposed on each other and because it assumes that particles are waves, they can also exist in a superimposed state.  However, this means a particle can be in two places at once and in the quantum world only “decides” where it is and its “what” to be when it is observed.   This doesn’t make intuitive sense but it’s one of the weird realities of quantum physics.

Many fell it is the only way to explain the experimental observations that support the superposition and wave particle duality is the non-classical non-intuitive one given by quantum mechanics.

However, Einstein unknowing may have able to define the classical “reality” of Superposition by extrapolating the rules of classical mechanics to the physical properties of 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 he associated with energy in space-time to unit of space one can associate with four *spatial* dimensions.  Additionally, because the velocity of light is constant, he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This would allow one to understand the validity of quantum mechanics assumption that particles can be defined in terms of waves and how they can be superimposed or simultaneously be in multiple positions before being observed. 

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 a matter 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 a matter wave moving in four *spatial* dimensions.  

The existence of four *spatial* dimensions would give a matter 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 these resonant systems in four *spatial* dimensions are responsible for the particle properties of matter.  

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 when the matter energy wave 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 structure formed matter 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 an 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 effected 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 far they may be from their perspective is zero with respect to that wave.  Therefore, its energy exists at every point in between them.  

This gives us an explanation in terms of physical properties of Einstein’s space-time universe for the VALIDITY of quantum mechanics assumption that a photon and its wave packet can 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 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 tells how a particle “decides” where it wants to be when observed 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 classical mechanism in the article “Why is energy/mass quantized?” which define a particle as result of resonant system created by 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.

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

I like to think the moon is there even if I am not looking at it is one of the more famous quotes attributed to Einstein when confronting the Quantum mechanical assumption that objects do not exist is space and time until they are observed.

Quantum mechanics assumes that one cannot define the position of particle in terms of where is has been but only in terms of the probabilistic values associated with its wave function.  This is in stark contrast to the Classical “Newtonian” assumption that one can assign precise values of future events based on the knowledge of their past.

For example in a quantum system Schrödinger wave equation plays the role of the classical Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution by assuming that it simultaneously exists everywhere in three-dimensional space before it is observed. 

This accentuates the fundamental difference between quantum and classical mechanics because the latter tells that a particle and the moon do not exist in specific position until observed where as Classical mechanics tell us that it does.

However, Einstein unknowing may have provided a way to define the classical “reality” of quantum probabilities by extrapolating the laws of a 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 the probability function of quantum mechanics address the spatial properties of position whereas he chose to define the universe in terms of the time properties of four dimensional space-time.  In other words understanding the physical connection between the spatial properties of quantum mechanics 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.

Yet, he gave us the solution to this problem when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of particle in a space-time universe because that provided a method of converting a unit of time he associated with energy to unit of space one can associate with position 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.

However, as was just mentioned this change in perspective allows one to define a physical connection between Einstein theories and the probability functions of quantum mechanics in terms of their common spatial properties.

For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can derive why the energy associated with the probability wave of quantum mechanics appears as a particle when observed by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a energy 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 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 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 associated with quantum mechanical systems.

Yet one can also define the boundary conditions responsible for a creating a particle 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.

The confinement of the “upward” and “downward” oscillations of an electromagnetic wave with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with the resonant system the article “Why is energy/mass quantized?” Oct. 4, 2007 associates with a particle.

This give us explanation of why, in a quantum system the intervention of an observer forces it to “choose” a state or how it “knows” when someone is observing it because if a particle is free to move it will display its wave characteristics while in every case, observing it requires one to confine its energy to the specific volume associated with the observing equipment. Therefore it will always display its particle “reality” when someone looks or observes it.

 

However one of the most advantageous results of viewing the relativistic properties of Einstein’s theories in terms of their spatial instead of their time components is that it allow for the integration of one of most perplexing aspects of quantum mechanics; that of how and why a particle’s position when observed is based on probabilities and how it can exist simultaneously exists everywhere.

The physics of wave mechanics tell us, due to the continuous properties the energy waves the article “Why is energy/mass quantized?” Oct. 4, 2007 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 that wave function of quantum mechanics represents vibrations or oscillations in a “surface” of three-dimensional space, as was mentioned earlier is correct these 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.

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

Yet 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 the resonant structure that article associated with 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.

In other words the position in space and time of a single particle could only be defined in terms of the probabilities associated with quantum mechanics.

Additionally Einstein theory also gives us the answer as to why a particle simultaneously exists everywhere in three-dimensional space. 

That theory tell us all energy waves such as that the article “Why is energy/mass quantized?” Oct. 4, 2007 defined as being responsible for a particle travel at the speed of light.

However it also tells the length of an object relative to another is effected by its relative velocity and that that there is 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 distances from the wave’s perspective.

 

Yet he 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?” (mentioned earlier) was showed responsible for a particle, the distance or length between the end point of the entire universe is zero.

In other words from the perspective of the energy wave responsible for a particle the physical length of the universe is zero, therefore it exists at every point in it.  In other words Einstein theory tells it must simultaneously everywhere when observed by an observer who is not moving at the speed of light.  This gives us an explanation in terms of physical properties of Einstein’s space-time universe for the validity of quantum mechanics assumption that a particle simultaneously exists everywhere in three-dimensional space 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.

There can be no other interpretation if one accepts his Theory of Relativity.

 

Finally one can definitively answer Einstein’s question “Is the moon there even if I am not looking at it” in terms of his Theory of Relativity

 

As was shown earlier a individual particle would most probably be found were the magnitude of the vibrations associated with it’s wave packet is the greatest.  Therefore the position of the mass components of all objects that consist of multiple particles such as the moon would be the point in space where the energy of their individual wave packets overlap which would result that point having a larger energy concentration than the sounding space.

However he did not define the location of a mass, such as the moon in terms of it’s quantized properties but in terms of how energy is concentrated at the apex of a curvature in the continuous properties space-time.

This tells us the moon is there when we are not looking because the overlapping of its individual energy wave components causes their energy to be concentrated in a specific volume of three-dimensional space and not because of the probability it’s individual particle components will be at that specific spot in space.

This shows that one can define why the quantum probability function gives us an accurate description of nature and why the moon is their when no is looking by extrapolating the laws of a classical mechanics to the physical properties of the space-time environment defined by Einstein.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

 

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