Bell’s Theorem for Space-Like Separation

Brandon Fogel

Warren K. Leffler

Igor Vasil'evich Volovich

Bell's theorem states that some quantum correlations can not be represented by classical correlations of separated random variables. It has been interpreted as incompatibility of the requirement of locality with quantum mechanics. We point out that in fact the space part of the wave function was neglected in the proof of Bell's theorem. However this space part is crucial for considerations of property of locality of quantum system. Actually the space part leads to an extra factor in quantum correlations and as a result the ordinary proof of Bell's theorem fails in this case. We present a criterium of locality in a realist theory of hidden variables. It is argued that predictions of quantum mechanics for Gaussian wave functions can be consistent with Bell's inequalities and hence Einstein's local realism is restored in this case.

Damian Canals‐Frau

Gordon Watson

Rebooting Einstein's ideas about local-causality, an engineer brings local-causality to quantum theory via operators and variables in 3-space. Taking realism to be the view that external reality exists and has definite properties, his core principle is common-sense local realism (CLR): the union of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively). Endorsing Einstein-separability — system X is independent of what is done with system Y that is spatially separated from X — Bell's famous mission is advanced. That is, by means of parameters λ, a more complete specification of EPRB's physics is successful. A consequent locally-causal refutation of Bell's theorem allows EPRB correlations to be explained in a classical way, in line with Einstein's ideas, without reference to Hilbert space, quantum states, etc. Conclusion: Bell's theorem is based on a mathematical error; an error in reduction is inconsistent with Bell's opening assumptions.