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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Latter Jeff

Copyright Jeffrey O’Callaghan 2020

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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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One cannot deny that Quantum mechanics, the theory that defines the tiny world of particles and Einstein’s theories, the one that defines what we see through a telescope have been the most successful scientific theories of modern times However, attempts to bring these two theories together and define "A Theory of Everything" have been unsuccessful.

However, the fact that we have been unable to do so suggests that one or both of these theoretical models does not describe the true nature of reality because the world we see through a telescope must have its foundations in the world of the very small therefore they must be connected.

There can be many reasons for this.  One is that foundational assumptions of either or both of them is incorrect.  In other words, the world of the tiny may not be governed by probabilities as quantum theory suggests or the world, we see though a telescope may not be ruled by relativistic properties of four dimensional space-time.

However, there is another possibility that many have over looked is that even though their mathematics makes very accurate perditions of experimental observations they do not accurately define reality of their operating environments.

For example, Einstein mathematically defined the physical structure of the universe in terms of the geometry four dimensional space-time.

However, when using the constant velocity of light and the velocity of objects that do not move at that speed to define its geometric properties he provided a way of mathematical converting a unit of time in a space-time universe to unit of space in one physically consisting of only four *spatial* dimensions.

In other words, their is an equally valid interpretation of his mathematics in terms of only four spatial dimensions.

Since both of these solutions that of four dimensional space-time and four spatial dimensions would yield the same numerical results it gives one a different way of connecting his theories to those of Quantum mechanics based on the physical properties of four spatial dimensions instead of four dimensional space-time.

Quantum Theory on the other hand defines tiny world of particles in terms of the non physical probabilities associated with Schrödinger wave equation which as mentioned earlier no one has been able to physical connect to the space-time universe define by Einstein.

However, the fact that Einstein provided an alternative solution to his mathematics in terms of four spatial dimensions suggests it may be possible to make that connection and therefore define a Theory of Everything by using the alternative solution of four spatial dimension that his theory provides instead of one based on four dimensional space-time.

For example the article "Why is mass quantized?" Oct. 4, 2007 showed one could derive the quantum mechanical properties of energy in terms of a resonant "system" or structure formed by a energy wave on the surface of a three-dimensional spatial manifold with respect to a fourth *spatial* dimension.

Briefly that article showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate can be meet in one consisting of terms of four spatial dimension.

Its continuous properties would allow an energy wave on a "surface’ of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for 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.

Therefore, these oscillations in a continuous non-quantized field of energy would meet one of the requirements mentioned above for the formation of a resonant system or "structure" in space.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in a space-time environment would be responsible for the incremental or discreet energy associated with quantum mechanical systems.

Another requirement for a resonate system to be formed is that the wave must be confined to specific volume of space.

However, one can also define the confinement of the resonant component of a particle and therefore establish a physical connection to the wave particle duality quantum mechanics associates with energy in terms of the relativistic properties of four *spatial* dimensions.

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

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

The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article "Why is energy/mass quantized?".

In other words, an energy wave in four *spatial* dimensions will maintain its wave properties unless it is confined to three by an observation, therefore it it always be view as a particle when an observation is made and any energy left over from the formation of its resonate structure will be radiating from the point of observation in the form of light or an energy wave.

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

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

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

(Some may question the fact that the energy wave associated with particle would be distributed over the entire universe.  However, the relativistic properties of space-time and four spatial dimensions tell that distance perceived by objects or particles in relative motion is dependent on their velocity which become zero at the speed of light.  Therefore, from the perspective of an energy wave moving at the speed of light, the distance between all points in the universe along it velocity vector is zero.  In other words, it’s energy is distributed or simultaneous exists at every point in the universe along its velocity vector.  There can be not other conclusion if one accept the validity of Einstein’s theories.)

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

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

Similarly a particle would most probably be 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, by interpreting Einstein space-time theories in their equivalent four spatial dimension one can connect the non physical probabilities associated with Schrödinger wave equation to the reality of the world defined by him.  Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

Additional it shows, by changing our interpretation of Einstein’s theories from four dimensional space-time to it equivalent in four spatial dimensions allows one to clearly understand the physical connection between the probabilistic world of quantum theory and the relativistic world of his theories, thereby allowing one to form a Theory of Everything.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

Quantum entanglement is the name given to quantum mechanical assumption that all particles remain connected so that actions performed on one affect the other, even when separated by great distances.

The rules of quantum physics state that an unobserved photon exists in all possible states simultaneously but, when observed or measured, exhibits only one state.  

Entanglement occurs when a pair of particles, such as photons, interacts physically. For example a laser beam fired through a certain type of crystal can cause individual photons to be split into pairs of entangled photons even when they are separated by a large distance, hundreds of miles or even more.

In other words when observed, Photon A takes on an up-spin state. Entangled Photon B, though now far away, takes up a state relative to that of Photon A (in this case, a down-spin state). The transfer of state between Photon A and Photon B takes place at a speed of at least 10,000 times the speed of light, possibly even instantaneously, regardless of distance.

The phenomenon so riled Albert Einstein he called it “spooky action at a distance.” and in 1935 he along with Podolsky Rosen proposed the following thought experiment which came to be called the EPR Paradox.

Its intent was to show that Quantum Mechanics could not be a complete theory of nature. 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 Schrödinger 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.

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 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.

In other words the measurements made by Allen Aspect made on the polarized photon verified that Bells inequity was violated by finding a correlation between the probabilities of each particle being in a given configuration based on the concepts of quantum mechanics. When this correlation was found many assumed that somehow photons must be entangled or physical connected even though they were in different local realities

Many took this as verification of quantum mechanics assumption that all particles are entangle no matter how far apart they are.

However Einstein, Podolsky, and  Rosen specified in the description of their experiment “two systems, A and B (which might be two free particles)” not just a photons because they knew  that Special Relativity gives a reason why they would entangled which were different from those give by quantum mechanics.

As was mentioned earlier according to quantum mechanics act of measuring the state of a pair of entangled photons instantly affects the other no matter how far they are apart. However Einstein Special Theory of Relativity tell 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.

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

However Einstein tells us that a photon traveling at the speed of light does not experience the passage of distance relative to an observer because as is shown by putting its velocity in his equation for length contraction along its velocity vector the physical distance between them becomes zero.

Therefore one cannot use photons to verify that Bell’s inequity is violated because even though they appear to be at different points when measured by an observer who is not moving at the speed of light they are not because according to Einstein the distance between those points from the perspective of all photons is always zero and therefore they must always be entangled.

This suggests the reason Bells inequity is and MUST be violated for all photons is because Einstein tells us the length contraction associated with the fact that they are they are moving at the speed of light means they are physically entangled or connected at the time of measurement no matter how far apart they appear to be to an observer.  However this is not the reason defined by quantum mechanics.

In other words the “hidden variable” that Einstein was so sure existed that would allow Quantum Mechanics to be complete theory of nature at least for photon is his Special Theory of Relativity.  However Quantum Entanglement may exist for particles other than photon but as we have just seen it cannot be verified by using them as test subjects.

Later Jeff

Copyright 2019 Jeffrey O’Callaghan

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What is the origin of kinetic energy and why should we care?

Einstein was able to define the origins of gravity and potential energy associated with rest mass in terms of curvature or the changing geometry of a space-time manifold but he did not tell us anything about the causality of kinetic energy.

For example he told us that gravity is caused by curvature or distortion in a space-time manifold however he did not due the same for kinetic energy associated with constant relative motion.

Yet its casualty is central to our understand of our universe because it along with gravity and Dark Energy are assumed to be responsible for evolution of the universe.

However one reason may be because kinetic energy of relative motion is constant with respect to both distance and time.  In other words the energy of an object in constant motion always moves the same distance in a given time interval.

As was just mentioned one of the difficulties in defining the kinetic energy in terms of the space-time environment defined by Einstein is that its magnitude is determined only by the distance an object moves through space within a constant time interval.  In other words it is only dependent on the spatial not on time parameters of its movement.

However redefining Einstein’s space-time universe in terms of its spatial properties would allow one to define the energy of constant motion in terms of those spatial properties.

Einstein gave us the ability to do this when he define the displacement or curvature he associated with the potential energy of rest mass in terms of the equation E=mc^2 and the constant velocity of light because that gave us the ability to redefine a unit of time in his space-time universe to an equivalent unit of space in a universe consisting of only four *spatial* dimensions.

This fact is the bases for assuming as was done in the article “Defining energy” Nov. 26, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Using those concepts one could define the energy of rest mass in terms of magnitude of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension cause by a objects mass while defining the kinetic energy of two masses in relative motion in terms of the spatial displacements cause by that motion. 

In other words the “surface” of three dimensional space associated with objects in relative motion would exist on different three dimensional plains with respect to a fourth *spatial* dimension.

For example magnitude of kinetic energy of two masses would be defined the relative magnitude of their displacement in “surface’ of three dimensional space with respect to a fourth *spatial* dimension 

In other words it allows one to mathematically derive the causality of relativistic motion in terms of the geometry of either four *spatial* dimensions or four dimensional space-time space because when Einstein’s defined his space-time universe in terms of energy/mass and the constant velocity of light he allow to chose one or the other and get the same end results.

Einstein in his General Theory of Relativity derived the causality of gravity in terms of a curvature or displacement in a space-time manifold however in his Special Theory of Relativity he only told us the effects of relative motion has on an environment not what caused the energy of that motion.  However as was shown above one can use his theoretical concepts to mathematically define its casual in terms physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension thereby give a more complete understanding of the relativistic environment encompassed by his theories.

This is significant because understanding the spatial properties of relative motion is the first step in understanding how Newton’s laws of motion are physically connected to Einstein’s space-time environment.

Later Jeff

Copyright 2018 Jeffrey O’Callaghan

Einstein was often quoted as saying “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”

For example in his General Theory of Relativity he derived the causality of gravity in terms of a curvature in the geometry of space and time.

One can understand how in terms of the physical image of a marble on a curved surface of a rubber diaphragm.  The marble follows a circular pattern around the deformity in its surface. Similarly planets revolve around the sun because they follow a curved path in the deformed “surface” of space-time.

In other words he was able to integrate the physicality of gravity into our consciousness in terms of a physical image based on observing a marble moving on a curved surface.

However he was unable to do the same for electrical forces as was documented by the American Institute of Physics.

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

In other words because time is only observed to move in one direction forward, a space-time universe can only support a force that cause movement in one direction towards an object such as gravity. 

However, it would be easier to form a physical image of electrical forces if one converts or transposes Einstein’s space-time universe to one of only four *spatial* dimensions the because of the bidirectional symmetry of the spatial dimension.

In other words because time is only observed to move in one direction forward, a space-time universe can only support a force that cause movement in one direction towards an object such as gravity while one made up four *spatial* dimensions could support the towards and away or bi-directional movement associated with electromagnetism. Therefore because of the bidirectional symmetry of a spatial dimension it would be easier to form a physical image of electrical forces if one converts or transposes Einstein’s space-time universe to one of only four *spatial* dimensions.

Einstein gave us the ability to do this when he used the velocity of light and the equation E=mc^2 to define geometric properties of forces in space-time environment because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a universe consisting of only four *spatial* dimensions.   Additionally because the velocity of light is constant it is possible to 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 time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

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

This allows one to form a physical image of electrical force as was done in the article “What is electromagnetism? Sept, 27 2007 in terms of the differential force caused by the “peaks” and “toughs” of a energy wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed it is possible to derive the electrical properties of electromagnetism by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a wave moving on a “surface” of three-dimensional space manifold with respect to a fourth *spatial* dimension.

A wave on the two-dimensional surface of water 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 will be 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.

Similarly a 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.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by a 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.

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

This 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.

This shows how one can define a physician image for the causality electromagnetic forces in terms of the existence of four spatial dimensions.

Einstein was unable to accomplish this in terms of four-dimensional space-time because as mentioned earlier time is only observe to move in one direction forwards and therefore could not support the bi-directional component of electromagnetic forces.

However this also shows that Einstein was right, as was mentioned above in the  American Institute of Physics article that electromagnetism and gravity can both be explained as aspects of some broader mathematical structure because as was shown above using only valid mathematical rules one can transform his space-time equations to four *spatial* dimensions thereby allowing one to form a clear physical image explaining the causality electromagnetic forces.

It should be remember that Einstein’s genius allows us to choose whether to create physical images of an unseen “reality” in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in choose terms of energy/mass and the constant velocity of light.

Later Jeff

Copyright 2018 Jeffrey O’Callaghan

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