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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 interact or share information with each other instantaneously.

Many believe this means the universe does not live by the law’s classical laws of separation or those derived by Einstein which stated that no information can be transmitted faster than the speed of light.

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.

Quantum mechanics assumes that entanglement occurs when two particles or molecules share on a quantum level one or more properties such as spin, polarization, or momentum. This  connection persists even if you move one of the entangled objects far away from the other. Therefore, when an observer interacts with one the other is instantly affected.

There is irrefutable experimental evidence the act of measuring the state of one of a pair of particles can instantaneously effect another even though they are physically separated from each other.

However, before we come to the conclusion it is a result of their quantum mechanical properties, we should first examine the experimental setup and any variables that may allow us to come to a different conclusion.

In quantum physics, it is assumed entangled particles remain connected so that actions performed on one immediately affect the other, even when separated by great distances. The rules of  Quantum physics also state that an unobserved photon exists in all possible states simultaneously but, when observed or measured, exhibits only one state.

One of the experiments that many assume verifies that entanglement is a quantum phenomenon uses (This description was obtained from the Live Science web site) a laser beam fired through a certain type of crystal which causes individual photons to be split into pairs of entangled photons. The photons can be separated by a large distance, hundreds of miles or even more. 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 (or information) 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. Scientists have successfully demonstrated quantum entanglement with photos, electrons, molecules of various sizes, and even very small diamonds.

However, Einstein told us there are no preferred reference frames by which one can measure distance.

Therefore he tells the distance between the observational points in a laboratory, can also be defined from the perspective of the photons in the above experiment.

Yet, this tell us (Please see attached graphic) that the separation between the observation points in a laboratory from the perspective of two photons moving at the speed of light would be ZERO no matter how far apart they might be from the perspective of an observer in that laboratory. This is because, as was just mentioned 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 no matter how far they may appear to be from the perspective of an observer who is looking at them.

In other words, entanglement of photons can be explained and predicted terms of the relativistic properties of space-time as defined by Einstein as well as by quantum mechanics.

One way of determining if this is correct would be to determine if particles which were NOT moving at the speed of light experience entanglement over the same distances as photon which are.

This is because, the degree of relativistic shortening of the distance between the end points of the observations of two particle is dependent on their velocity with respect to the laboratory were they are being observed.

Therefore, all photons no matter how far apart they are from the perspective of a lab will be entangled because Einstein tells due to the fact that they are moving at the speed of light that distance will be Zero from their perspective.

However, he also tells us that for particles moving slower than the speed of light the distance between will be greater than zero and how much more would depend on their the relative speed with respect to it. In other words, the slower with respect to the lab they are moving the less that distance will be shortened.

Therefore, if it was found that only photons experience entanglement when the observation points were separated by large distances it would support the idea that it is caused by the relativistic properties of space defined by Einstein.

However, one must remember the wave particle duality of existence as defined by Quantum mechanics tell us that before a particle is observed it has an extended length equal due to its wavelength. Therefore, all particles will be entangled if the reduction in length between the endpoints of the observations when adjusted with respect to their relative velocity is less their wave length as defined by quantum mechanics.

A more conclusive argument could be made for the idea that entanglement is a result of the relativistic properties of space if it was found that entanglement ceased when the relativistic distance between the end points of observation when viewed from the perspective of particle moving slower than the speed of light was greater than its wavelength as defined by quantum mechanics.

Some have suggested that “There are inertial frames for every speed less than light – speaking informally – but there is no inertial frame for light speed itself. Any attempt to generate one actually generates a degenerate frame which can cover only an infinitesimal fraction of space-time.” However the argument that there are “There are inertial frames for every speed less than light”

because they would create an infinitesimal fraction of space-time is invalid, because Special Relativity WITHOUT EXCEPTION defines an inertial frame reference as one which is not undergoing acceleration.  Therefore, even though using a photon as a reference frame may create infinitesimal 2 dimensional  fraction of space-time the conceptual foundations formulas for length contractions of reference frames in relative motion define by Einstein tells us that one can exist. One reason that all of the mass which is contained in it is not undergoing acceleration.Therefore, the  fact that it may define a degenerate frame would be irrelevant to the conclusion draw above because as that post showed it is the distance between the end points of the observation when viewed from a photon that determines whether or not it will be entangled.

Copyright Jeffrey O’Callaghan 2020

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