Quantum entanglement is defined "as a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently instead, a quantum state may be given for the system as a whole.
For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. Because of the nature of quantum measurement, however, this behavior gives rise to effects that can appear paradoxical. For example any measurement of a property of a particle can be seen as acting on that particle (e.g. by collapsing a number of superimposed states); and in the case of entangled particles, such action must also act on the entangled system as a whole. It thus appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances."
Einstein referred to this as "spooky action at a distance" because it assumed that objects or particle can interact instantaneously, regardless of distance separating them which according to his perception of reality this was not possible.
To demonstrate this he co-authored a paper with Podolsky–Rosen which came to be called the EPR Paradox whose intent was to show that Quantum Mechanics could not be a complete theory of nature because it does not agree with his perception of reality. 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.
But this may not be the case for two reasons. The first is based on the core principals of Einstein’s theories while the second involves the physical properties of the wave function that quantum mechanics used to define the probability of a particle’s state.
However understanding why is only possible if one redefines Einstein’s four dimensional space-time universe to one consisting of four *spatial* dimensions.
(The reason will become obvious later.)
Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space identical to those of our three-dimensional space. 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 energy 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 that of constant motion 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.
One of the more common ways to visualize how gravity can be cause by a curvature in space-time is by comparing its effects to the effects a curved surface of a rubber diaphragm has on a marble. The marble follows a circular pattern around the deformity in the surface of the diaphragm. Similarly planets revolve around the sun because they follow a curved path in the deformed "surface" of space-time.
The same example can be used to visualize how a curvature in a "surface" of three dimensional space can be responsible for gravitational accelerations however in this case it would caused by a deformation in that "surface" with respect to a fourth *spatial* instead of a time dimension.
As was mentioned earlier one of the advantage to redefining Einstein space-time concepts in terms of four *spatial* dimensions instead of four dimensional space-time is that it not only allows one to understand gravitational energy but also the energy of constant relative motion in terms of the geometric properties of space.
Briefly the article “Defining energy?" showed one can define constant momentum or the energy of relative motion in terms of a constant displacement of a "flat surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension.
One way of visualizing would be to use the earlier example of the rubber diaphragm. However instead of its "surface" being curved it would be flat with respect to its soundings and the energy associated with its relative motion would be defined by its separation with respect to a four *spatial* dimension form the "surface" with which it’s velocity is being measured from.
In other words one can define the energy of an object or particle in constant relative motion in terms of a displacement a "flat surface" of a three-dimensional space manifold with respect to a time or four *spatial* dimension because as was shown above they would be equivalent .
However Einstein’s Theory of Relativity tells us the length of an object or particle contracts; approaching zero as it nears the speed of light. Additionally he told us that at the speed of light it becomes zero when observed from all other reference frames because at that speed its length in the direction of motion becomes zero.
But his theory also tells us from the perspective of the photon moving at the speed of light, the physical distance or space between observers and their observations must also be zero because from the photons perspective the observers are moving at the velocity of light with respect to them.
In other words according to the core principals of Einstein Theory of Relativity two entangle photons will interact instantaneously, regardless of the distance separating them from the perspective of external observers measuring their properties because from a photon perspective the distance between those measurements is zero.
There can be no other interpretation if one accepts the validity of Einstein theories.
However as mentioned earlier one can also understand the "reality" behind quantum entanglement by deriving the probability functions quantum mechanics associates with Schrödinger wave equation in terms of Einstein theories when they are redefined, as was done earlier in terms of four "spatial* dimensions.
This is because it is possible, as was done in the article “The *reality* of quantum probabilities” Mar 31, 2011 to define the physicality of the probability function quantum mechanics associates the wave function of a particle as being the result of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Very briefly that article showed that one can derive the quantum mechanical properties energy/mass by extrapolating the laws of classical resonance to a matter wave in a continuous non-quantized field of energy/mass moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(Louis de Broglie was the first to predict the existence of a continuous form of energy/mass when he theorized all particles have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)
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 be meet in one consisting of a continuous non-quantized field of energy/mass and four *spatial* dimensions.
The existence of four *spatial* dimensions would give a matter 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 continuous non-quantized field of energy/mass 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 it.
These resonant systems are responsible for the quantum mechanical properties energy/mass.
However assuming energy is result of a displacement in four *spatial* dimension also allows one to define the physicality of the probability distribution associated with the wave function of individual particles by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.
As was shown earlier redefining Einstein space-time in terms of four *spatial* dimension tells us that the energy of a photon moving at the speed of light is distributed throughout the universe in a two-dimensional plane that is perpendicular to its velocity vector therefore as the article “The *reality* of quantum probabilities” Mar 31, 2011 showed the probability’s associated with a quantum particle’s wave function would be distributed throughout the entire two-dimensional "surface’ of the three-dimensional space manifold it is occupying with respect to a fourth *spatial* dimension.
The effect of this would be analogous to what happens when one vibrates a rod on a continuous rubber diaphragm. The oscillations caused by the vibrations would be felt over its entire surface while their magnitudes would be greatest at the point of contact and decreases as one move away from it.
However, this means if one extrapolates the mechanics of the rubber diaphragm to a "surface" of a three-dimensional space manifold one must assume the physical oscillations in the surface of three-dimensional space that associated with the wave function must exist everywhere in three-dimensional space. This also means there would be a non-zero probability they could be found anywhere in our three-dimensional environment.
As mentioned earlier the article “The *reality* of quantum probabilities” Mar 31, 2011 showed a quantum mechanical system 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 Classical Wave Mechanics tells us that 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 quantum system 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,
However this means each individual particle in a quantum system has its own wave and probably function and therefore the total probability of a quantum system being in a given configuration when observed would be equal to the sum of the individual probability functions of each particle in that system.
As mentioned earlier Allen Aspect verified that Bell inequities were violated by the quantum mechanical measurements made on pairs of polarized photons that were space like separated or in different local realities.
Yet, as just mentioned the wave or probability function of a quantum system is a summation of the probably function of all of the particles it contains. Therefore, two particles which originated in the same quantum system and were moving in opposite directions would have identical wave or probability functions even if they were not physically connect.
The measurements Allen Aspect made on the polarized photon verified that Bells inequity was violated because a correlation was found 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 they must be entangled or physical connected even though they were in different local realities. In other words the Newtonian concept separability does not apply to quantum environment.
However, this may not be true.
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. Yet if it is true as mentioned earlier that each entangled particle has an identical wave or probably function as it moves through space the measurement of the state of one particle would be reflected in the measurement of the other. This is because the probability of them being in a specific state would be determined at the point of origin or where they were entangled and that common probably would be “carried” by each particle until a measurement was made. Therefore when making a measurement on one particle in a close system containing two entangled particles the rules of quantum mechanics tell us that the inequities found in Bell’s Theorem should be violated not because they are physically connected in space but because they are connected through their common probability function.
In other words the reason why Bell’s inequity is violated in a quantum system is not because the particles are physically entangled or connected in space at the time of measurement but because their individual wave or probability functions were "entangled" or identical at the time of their separation and remained that way until a measurement was made on them.
But to say the correlation of the quantum characteristics of two particles are identical because they are entangle or are physically connected is like saying the correlation between the color characteristics of the hair of identical twins is because they have been physically connect throughout their entire life.
This shows that Quantum Mechanics is a "complete theory of nature" contrary to what Einstein believed because based on the core principals of relativity one can define a mechanism responsible for the correlation of the quantum characteristics of particles that exist in non-local environments by extrapolating the "reality" of a environment governed by the physical laws laid down by him or the rules governing quantum mechanics.
Copyright Jeffrey O’Callaghan 2014
Is it possible to define a “reality” behind the quantum world in terms of the classical laws of physics and the space-time environment defined by Einstein?
In other words can one use our everyday experiences to understand the irrationality behind many of the assumptions made by quantum mechanics and integrate them into the space-time environment in which we all live
For example the paradoxical wave–particle behavior of energy/mass, one of the fundamental concepts defining Quantum mechanics defies the “reality” of the four dimensional world we live in because of its inability to describe/define how quantum-scale objects can simultaneously exist as waves and particles. Many have tried to explain it 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.
However, it is possible to explain the wave–particle duality of the quantum world in terms of the “reality” of classical concepts and four dimensional space-time by redefining Einstein’s space-time environment to its equivalent four spatial dimension counterpart because it will allow one to directly apply classical concepts of Newtonian space to the wave properties quantum mechanics associates with particles.
(The reasons will become obvious latter.)
Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space. 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 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 and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.
This, as mentioned earlier will allow us to understand the reasons behind the paradoxical wave–particle duality of light when it is partially reflected by two surfaces, as outlined on pages 17 thru 23 of Richard P Feynman book “QED The Strange Theory of Light and Matter” in terms of the laws of classical physics.
On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface. Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.
In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.
These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.
However, wave theory also predicts the energy variations should be continuous.
In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.
Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass. This indicates that their energy is not transmitted by a wave but by a particle.
However this observational paradox can be resolved if particles are, as mentioned earlier are viewed in terms four *spatial* dimension instead of four dimensions space-time because it shows their behavior can be described in terms of a resonant “structure” generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
For example in the article “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of energy/mass and a photon by extrapolating the laws of classical of resonance in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally it showed that all energy must be propagated in these resonant systems.
Briefly it showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
Therefore if one extrapolates the laws of classical wave mechanics to a fourth *spatial* dimension these oscillations in a “surface” of a three-dimensional space manifold would generate a resonant system or “structure” in space.
Classical mechanics tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency.
Similarly the incremental or discrete energies associated with individual photons in Richard Feynman’s experiment could be explained by assuming that they are a result of the fundamental or a harmonic of the fundamental frequency resonant properties of four *spatial* dimensions.
This shows how one can derive the quantum mechanical properties of energy/mass and a photon by extrapolating the laws of classical wave mechanics to a matter wave on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.
However, one can also describe the physicality of a particle in terms of the wave properties of its resonant structure.
In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.
The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?“
This provides the ability to understand how and why a photon can have the properties of both a wave and a particle because it clearly defines their interdependence in terms of the laws of Classical wave mechanics
However it also defines the physical reality of particle-wave duality in terms of the classical of the properties of a matter wave moving on the “surface” of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was show earlier they are equivalent
For example, the wave like interference of photons he observed would be due to the wave properties of the resonant “system” defined in the article “Why is energy/mass quantized?“.
If the distance between the two glass surfaces in Richard Feynman’s experiment is equal to half of the wavelength of the resonant “system” associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.
If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.
However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy would be propagated in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying.
Yet this also defines the reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because Classical wave mechanics tells us that when two waves of the same frequency interact their frequency will or does not change. Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.
This indicates that viewing the quantum mechanical world of wave–particle duality in terms of the geometric properties of a resonant “system” generated by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to derive its “reality” by extrapolating the laws of classical mechanics in three-dimensional environment to a fourth *spatial* dimension.
It should be remember Einstein’s genius allows us to chose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the physical relationship of particles and waves
Copyright Jeffrey O’Callaghan 2014