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 wholeâ€.
Einstein referred to this as “spooky action at a distance” because it assumed that particles can interact instantaneously, regardless of distance separating them which according to his perception of reality this was not possible.
However if one accepts the reality of the space-time universe defined by Einstein one would realize that according the core principals of his theories there is nothing spooky about action at distance relative to an observers velocity.Â
Even so he was so convince that he co-authored a paper with Podolskyâ€“Rosen whose intent was to show that if Quantum Mechanics was a valid theory it could not be complete because it does not agree with most people’s 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 SchrÃ¶dinger 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 on the other.
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 entanglement does not exist because they are mutually excessive.
However Einstein himself predicted the entanglement of particles that are moving at the velocity of light no matter how far apart they are in his Special Theory of Relativity because he showed us thatÂ the separability or the distance between two points is dependent on the velocity of the observer with respect to what is being observed.
For example his theory tells the distance between the two objects 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
However this tell us the distance or length between observations measured between two photons or any particle moving at the speed of light from the perspective a photon would be zero no matter how far those observation might from the perspective of the observers making them because according to the concepts of relativity one could view the photons as being stationary and the observers as moving at the velocity of light.Â This is true even if they are moving in opposite directions.
Therefore according to Einstein’s theory all photons which are traveling at the speed of light are physical entangled with all other photons that originated within a common system no matter how far apart or “spacelike” separated they may appear to be to all observers who are not traveling at the speed of light.
In other words inequities in the measurements made on pairs of photons should be violated in a world containing the physical reality of Einstein’s theory and separability because they are not “spacelike” separated when viewed from all reference frames which is not traveling at the speed of light.
This tells us that the hidden variable that would allow Quantum Mechanics to become a complete theory of nature is Einstein Theory of Relativity or the Relativistic properties of motion.
Additionally if quantum entanglement did not occur for photons that were space like separated then the physical reality of Einstein space-time universe as defined by his theory of Relativity must be discarded
One method for determining if this is the reason why Allen Aspect observed polarized photons violated Bells inequities would be to see if they are also violated by particles that were traveling slower that the speed of light because they would according to the Theory of Relativity could be “spacelike” separated.
In others words if it was observed that particles which were not traveling at the speed of light did not violate Bell’s inequity then it would support Einstein perception of reality and provide a physical verification for the causality in terms of the existence of space-time for one of the most puzzling aspects of quantum mechanics; that of quantum entanglement.
However if it is found that bell’s inequity is violated by particles moving slower than the speed of light then Einstein’s perception of reality would be invalidated because it demands that things which are “spacelike” separated can only have a limited influence one each other.
Yet one must be careful when performing the calculations because the distance separating the particles would not be determined by the distance between the end points as viewed by the experimenter but by relativistic distance as viewed from the particles,
Copyright Jeffrey O’Callaghan 2016