Presently, there is disconnect between our understanding of one of the most mysterious facets of Quantum Mechanics quantum, that of quantum entanglement and the classical one of separation.

Entanglement occurs when two Particles are linked together no matter their separation from one another. Quantum mechanics assumes even though these entangled particles are not physically connected, they still are able to share information with each other instantaneously seemingly breaking one of the most hard-and-fast rules of classical physics and Einstein theories: that no information can be transmitted faster than the speed of light.

Even though it may be hard for some to accept the instantaneous sharing of information over what appears to be long distances has been proven time and time again over the years.

For example, when researchers create two entangled particles, separate them and independently measure their properties, they find that the outcome of one measurement influences the observed properties of the other particle.

This was made possible in 1964, when John Bell showed there is a theoretical limit beyond which correlations can only be explained by quantum entanglement, not classical physics.

However, we must be careful not to jump to conclusions because Einstein gave us the definitive answer as to how and why particles are entangled in terms of the physical properties of space-time even though he was so upset to what he called this  “spooky action at a distance.” that in 1935 he along with Podolsky Rosen proposed the following thought experiment which came to be called the EPR Paradox.

In 1935, Einstein co-authored a paper with Podolsky–Rosen highlighted a problem that they felt showed that Quantum Mechanics could not be a complete theory of nature.  This thought experiment came to be called the EPR Paradox. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature.

The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known.  Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the 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.

As was mentioned earlier, in response to Einstein’s argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles.  If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle’s limited influence.

In other words, he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are “spacelike” separated.

When Bell published his theorem in1964 the technology to verify or reject it did not exist. However, in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

Since then there have been many experiments using the properties of paired of photons and other particles that verify without any doubt that two photons and others particles that are spatially separated can be entangled.

In quantum mechanics it is assumed that the act of measuring the state of one of a pair of entangled particles instantly affects the other no matter how far they are apart.

However, Einstein in his Special Theory of Relativity gives us a classical explanation in terms his theory for the entanglement of two particles.

For example, with regards to the polarized photons mentioned earlier that Allen Aspect used to verify the quantum mechanical interpretation of entanglement his theory tells us that because photons must always be moving at the speed of light they can never be separated with respect to an external observer no matter how far apart he or she perceives them to be.

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

However, his theory tells the distance between the two photons A and B would be defined by their relative speed with respect to an observer.

Specifically, he told us that it would be defined by

Yet, this tell us that the separation between two photons moving at the speed of light from their perspective would be zero no matter how far apart they might be from the perspective of an observer in a laboratory because according to the concepts of relativity one can view the photons as being stationary and the observers as moving at the velocity of light.

Therefore, according to Einstein’s theory all photons which are traveling at the speed of light are entangled with all other paired photons no matter how far apart or “spacelike” separated they may appear to be to ALL observers.

In other words, the inequities in the measurements made on ALL REPEAT ALL pairs of photons should be violated in a world containing the physical reality of Einstein’s theories because they will influence each other no matter how far they may be separated when viewed from a reference frame other than a photon’s, such as a laboratory.

Up until now we only have addressed the entanglement of photons that are moving at the speed of light.  However, the same the relativistic properties of motion can be applied to explain the entanglement of other particles that are not moving at that speed.

This is because quantum mechanics defines the composition of matter in terms of its wave particle duality.  More specifically, as was shown in the previously article  “Quantum mechanics in a nutshell…Don’t look: waves. Look: particles“ Dec. 1, 2015 it assumes that before an observation is made matter is propagated though space in terms of its wave properties and only after being observed does it present its particle properties.

In other words, in Quantum Mechanics matter has an extended volume while moving through space which is directly related to the wavelength associated with its particle properties.

This means the wavelengths of two particles in motion will overlap and be entangled if the separation between the end points of an observation as measured from their perspective is less that the wavelength of those particles.

However, as mentioned earlier Einstein tells us that we must use this theory to derive the separation of two moving particles from their perspective and not from the prospective of observers in a laboratory.

Therefore, even though particles may appear to be separated from the view point of a laboratory observer they may not be separated from the view point of the particles that are moving with respect to those observers because of an overlap of their wave properties..

In other words, one does not have to break one of the most hard-and-fast rules of classical physics and Einstein theories: that no information can be transmitted faster than the speed of light because one can use his classical theories to explain how and why particles that appear to be separated can communicate instantaneously.

The illusion is not that entanglement of two spatial separated particles from the perspective of the observers in Allen Aspect experiment mentioned earlier does not exist.  The illusion is that entanglement is not the result of the quantum mechanical properties of matter but instead is the result of the physical reality of Einstein’s Theory of Relativity because it tells us that the separation of particles must be measured from their perspective and not from the perspective of an observer in a laboratory.

Copyright Jeffrey O’Callaghan 2020

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