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Bell's inequality



   

A photon  is the minimum quantity of light that can exist at a given frequency. Light as a wave has a polarization or an angle at which the wave oscillates. A polarizer 

is a material that will let light pass completely if the polarization of the light is aligned with the polarizer and will block it completely if the they are orthogonal. At other angles () it lets some fraction () of the energy of the light through. Polarizing sun glasses are effective in part because sunlight that is reflected off the surface of an object at a sharp angle is hightly polarized. In classical physics the quantity of radiation that passes a polarizer is determined by the angle. If we have a single photon this will not work. Either the photon gets completely through or it does not get through at all. There is no way the photon can spilt into two parts one of which makes it and another that does not. Thus in the angle of the polarizer determines the probability that the photon will traverse the polarizer. Further if the photon does traverse the polarizer its polarization will be exactly aligned with the polarizer.

Now consider a particle that decays into two photons. Conservation laws require that the polarizations of the two particles be exactly correlated. Quantum mechanics requires that the particles do not have a polarization value until they are observed.

This seems very strange. Something that cannot exist in either particle is exactly aligned between them. It gets stranger. Before either particle is observed we have no idea what the polarization is. If one particle traverses a polarizer and we then detect it the probability that the second particle will traverse its polarizer can be computed by assuming that both particles polarization are exactly correlated with the polarizer that the first particle traversed. For some combinations of polarizer angles, this correlation is so high that such results cannot be modeled unless the angle of the first polarizer affects the probability that the second particle will be detected. Experiments to test this such as that illustrated in Figure gif on page gif have been performed. The time between when the polarizers change and when this has an effect is determined by the distance from a polarizer to the closest detector. In theory such an experiment could be spread over a billion light years and a polarizer setting a billions years away could affect a detection in an arbitrarily short time. That is what predicts. Bell[3] and Eberhard[12,13] proved this. Bell showed that correlated results that are space-like 

separated most obey a mathematical relationship known as Bell's inequality  . Quantum mechanics predicts this inequality is violated. Two events are space-like separated if they are far enough apart in distance and close enough together in time that light cannot travel between them.

Does nature act this way? We do not know because none of the experiments to date are conclusive. Most physicists believe these predictions of in part because they have a very strange property associated with the claim that probabilities are irreducible. One of the polarizers must influence one of the detections but we cannot tell which one. As a result the predictions are the same in any relativistic frame of reference. However no mathematical model can reproduce these predictions without operating in a preferred frame of reference in a way that violates relativity. Many physicists believe that something special is happening hear that cannot be modeled by classical mathematics and that does not involve nonlocal effects. Perhaps they are right and perhaps they are rationalizing.

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