The EPR "paradox"

The error that Barnard warned us about is still being made, even by some physicists. In the EPR experiment, as modified by Bohm, an atom A at rest and of spin 0 decays into two particles of spin 1/2, which by the law of conservation of momentum, must fly out in opposite directions. By the law of conservation of angular momentum, the spins of the two particles must add up to zero. Suppose that we measure the spins of both particles in the z-direction. In quantum mechanics, this means that the operators S(1) and S(2) describing the two spins must be completely anti-correlated in the state of the system after the decay. Clearly, this anti-correlation is "caused" by the fact that the particles have a common origin, the decaying atom A. Theory predicts and experiments confirm that we get 1/2 for S(1) and -1/2 for S(2), or vice versa. We never find the same value (1/2,1/2) or (-1/2,-1/2) for the pair of values in the same sample. However, we still see people claiming that the finding of spin 1/2 for S(1) "causes" S(2) to jump to the opposite value, -1/2, and vice versa. They claim that quantum mechanics requires non-local instantaneous influences. But we, knowing that the particles are correlated because of a common cause, just smile.

The jump in the probability distribution of S(2), assigned by an observer Alice = (1) on her measurement of S(1), is called the collapse of the wave packet. It is exactly that given by Bayes's rule for conditioning a distribution on receipt of knowledge. Bayes's rule says that if E and F are events, with probabilities P(E) and P(F), then the probability of E, given that F has been observed, is the conditional probability P(E|F), given by

P(E|F) = P(E and F)/P(F)

(enough maths: Ed.)

The quantum variables S(1) and S(2) commute and can be described by a purely classical probability. If you agree that in the classical description the observation of say S(1) = 1/2 does not cause S(2) to jump to the value S(2) = -1/2, then for consistency, you must adopt the same view in quantum probability. The only evidence of a causal influence at a distance would be the following. Alice measures S(1) and finds say 1/2; she then knows that S(2) is -1/2. Now Alice rotates S(1) using apparatus space-like to Bob = (2), so that S(1) is now -1/2. If then Bob finds that this rotation has influenced S(2), so that it is say, now equal to +1/2, then we would have detected instantaneous influence at a distance. QM predicts no change in S(2) under these circumstances, and no experiment has ever reported any such result. See my detailed article.

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