Quantum entanglement: a classical explanation

Quantum entanglement is the name that describes the way that particles can share information and interact with each other regardless of how far apart they are.

For example an electron in certain atoms will spontaneously decay after being excited by emitting pairs of polarized photons such that one is aligned horizontally the other vertically.  According to quantum mechanics these photons are entangled and act of observing one instantly affects the other no matter how far they are apart.
This instantaneous communication between the entangled photons is at the heart of quantum entanglement.  This is the “spooky action at a distance” Einstein believed was theoretically implausible because according to Relativistic Theories information cannot be propagated instantaneously but only at the speed of light.

To demonstrate this 1935, Einstein co-authored a paper with Podolsky and Rosen which was intended 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 system A.  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.

Many believed this provided experimental verification of the concept of Quantum entanglement.  Additionally it meant that science has to accept that either the reality of our physical world or the concept of separability does not exist.

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 that 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 that the distance between two photons or any particle moving at the speed of light with respect to all observes would be zero no matter how far apart any observer might perceive them.to be 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.  This would be true even if the photons were moving in oppose directions because of the fact that their velocity is squared

Therefore according to Einstein’s theory all photons which are traveling at the speed of light are entangled with all other photon no matter how far apart or “spacelike” separated they may appear to be to all observer 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 will influence each other even when they are “spacelike” separated when viewed from the reference frame other than a photon which is 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 the relativity properties of motion.

One method for determining if this is the reason why Allen Aspect observed that 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 mechanism 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 than 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.

Later Jeff

Copyright 2015 Jeffrey O’Callaghan

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