There can be no doubt the probabilistic interpretation of Schrödinger’s wave function predicts with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it.

However, defining our world in this manner presents a problem because that equation defines all its possible configurations that it can have before one makes an observation.  In quantum mechanical jargon when an "observation" is made the wave function which initially is in a superposition of all possible eigenstates collapses and appears to reduce to a single eigenstate due to interaction with the external world.

But the question then become what happened to all of the other possibilities.  Because according to quantum mechanical interpretation of the wave equation they are just a real as the one which we observe.

Many physicists have attempted to provide an explanation as what happens to these other possibilities because quantum mechanics would not be valid without them.

One of the most bazaar, in my option is the many-worlds interpretation because it that asserts the objective reality of the wave function and denies the actuality of its collapse.  Briefly it implies that all possible alternate histories and futures are real, each representing an actual "world" (or "universe") and that when an observation is made. In layman’s terms, the hypothesis states there is a very large; perhaps infinite number of parallel universes, and everything that could possibly have happened in our past, but did not, has occurred in the past of some other universe or universes.

However, we may be able to find a much simpler and less bazaar explanation of what actually happens to the wave function when an observation is made if we interrupt it terms of the physicality which can associated it with instead of its abstract mathematical properties. One

thing that I am pretty sure we can all agree on is that an energy associated with transverse wave define by it consist of alternating spatial displacements that extend outward from is source.

We also know that Einstein define gravitational energy in terms a positive curvature or distortion in the geometry of a universe consisting of space-time however, if we are to be consistent with Einstein definition of gravity, we must define traverse properties of the wave function in terms of the physicality of a transverse wave in the geometry of the universe. Yet one can only define the transverse properties of a wave with respect to the spatial not time properties of our universe. Therefore, to integrate it with Einstein’s theories one must be able to derive the energy associated with it in terms of the spatial properties of a transverse wave in the geometry of our universe.

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

However doing so would allow one to derive the probabilistic interpretation of Schrödinger’s wave equation and quantum properties of a particle in terms of the laws of classical wave mechanics.

For example, the article “Why is energy/mass quantized?” Oct 4, 2007 showed one can derive the quantization of a wave on a "surface" of a three-dimensional space manifold with respect to fourth spatial dimension by extrapolating our understanding of a resonant structure and perception of a wave in a three-dimensional environment.

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

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

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

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

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

In our three-dimensional environment the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical properties of a photon or an electromagnetic field.

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

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

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

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

Additionally, 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 allows for the integration of one of most perplexing aspects of quantum mechanics; that of how and why a particles position when observed is based on probabilities.

The physics of wave mechanics tell 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 simultaneously distributed over the entire universe.  However, the relativistic properties of space time tell us the distance perceived by objects or particles in relative motion is dependent on their velocity which become zero at the speed of light.  Therefore, from the perspective of an energy wave moving at the speed of light, the distance between all points in the universe along its velocity vector is zero.  In other words, because its energy is moving at the speed of light it would distributed or simultaneous exists at every point in the universe along its velocity vector.  There can be no other conclusion if one accepts the validity of Einstein’s theories.)

As mentioned earlier the article “Why is energy/mass quantized?” shown a 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, 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 quantum mechanical jargon when an "observation" is made of the energy represented by the wave function which as mentioned earlier would be distributed throughout the entire universe collapses and is reduce to the single eigenstate due to interaction with the external world.

This shows how one can physically connect the probabilities associated quantum mechanics to our observable environment by redefining them in terms of the relativistic properties of Einstein’s space-time universe in terms of four *spatial* dimensions.

In other words by changing our interoperation of Schrödinger’s wave function from a mathematical one to the physicality of a transverse wave in either four *spatial* dimensions or four dimensional space-time will allow us to ingrate the world of quantum mechanics into the space-time-universe defined by Einstein because as was shown above its probabilistic mathematical interpretation can be predicted by using them.  Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

It should be remembered 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 terms of the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

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What gives Quantum computers their power is the fact they use the qubit that exists in superposition which allows it to encode information in four states instead of two states as standard computers do. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today’s most powerful semiconductor driven supercomputers.

However, another property of quantum mechanics that makes them possible is known as entanglement because to make a practical quantum computer, scientists have to devise ways of making measurements indirectly to preserve the integrity of the qubit.  One way of doing this is to use quantum entangled superpositioned bits resulting in each one having four values.

Entanglement is important because it allows one to remotely view the properties of the individual components of the qubit.  For example, it you apply an outside force to two atoms, it can cause them to become entangled, and the second atom can take on the properties of the first atom. So, if left alone, an atom will spin in all directions. However, the instant it is disturbed it chooses one spin, or one value; and at the same time, the second entangled atom will choose an opposite spin, or value. This allows scientists to know the value of the state of an individual components of in a qubit by observing its entangled companion without actually looking at or disturbing the qubit

The fact that entanglement exists has been experimental proven beyond a shadow of a doubt.  However, one must be careful not to make hasty assumptions as to why because knowing more about the physical properties of the operating environment of a device can greatly streamline the design process of everything from transistors in modern computers to the Qubit in a quantum computer.

In 1935, Einstein co-authored a paper with Podolsky–Rosen 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 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.

This meant that science has to accept that either the reality of our physical world or the concept of separability does not exist.

Many would prefer to assume the separability defined by Newtonian physics does not exist instead of the reality of our particle world because without that "reality" Einstein and many others believe science would have little meaning.

However, measurements Allen Aspect made on polarized photons that showed that Bells inequity was violated appeared to verify the concepts of quantum mechanics assumes the act of measuring the state of a pair of entangled particles instantly affects the other no matter how far they are apart. In other words, the Newtonian concept separability does not apply to quantum environment. 

However, one must be careful not to extrapolate the unique properties of a photon like the fact that they are the only particle that moves at the speed of light to other particles that make up the qubit.

We believe Einstein, Podolsky, and Rosen were aware of this special property of a photon because they 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 us a reasons why they would entangled which were different from those given by quantum mechanics.

Einstein told us that the observe distance between the measurement of end points of objects or particles in relative motion would be shorter in direct relationship to their speed from the perspective of those objects or particles. 

In other words, the faster particles are moving relative to the observers the shorter the distance between the end points of those observations will be from their perspective.   At the speed of light he tells us the distance between the end points of any and all measurements will be zero from the perspective of any particle moving at the speed of light.

However, he also told us that due to the relativistic properties space and time there is no special reference frame by which one can measure distance.  Therefore, one would be justified in measuring the distance between the end points of the observation from the perspective of the photons as well as from the laboratory environment where they are being observed by humans.

Yet as was just mentioned he also tells us since photons are moving at the speed of light the distance between the end point of the measurements made between all human observers in the universe no matter where they are must be is zero.  However, because all of the confirmation entanglement involves the properties of photons, we must look at the world from their perspective and not form those of human observers.

In other words, Einstein specified "two free particles" not just photons because he knew the reason they would be entangled is because the distance between the end points of all measurements made by humans from perspective of all photons would be zero therefore they would be entangled. Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

As was mentioned earlier the fact that entanglement exists has been experimental proven beyond a shadow of a doubt with respect to a photon.  However, as is show above Einstein Theory of Relativity provides an alternating explanation as to why with respect to photons, which is just a valid as the one provided by quantum mechanics. Since it is one of the foundational concepts of quantum computing knowing which one of them is is responsible will give engineers a better understanding its strengths and limitations and will hopefully allow them to design systems that will take better advantage of them.

Latter Jeff

Copyright Jeffrey O’Callaghan 2019

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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

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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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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

<font face="Arial">New Page 1</font>Please visit our Facebook group The Road to unification of Quantum and Relativistic theories if you would like to comment or contribute to our project e Road to unification part  2007 thru 2010  Ebook

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