The Bell's theorem revisited: a subtle, though crucial, assumption has gone unnoticed, and it might not be justified!

David H Oaknin (1)

1 Rafael Advanced Defense Systems Ltd.

The Bell's theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the Einstein-Podolsky-Rosen paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem states through an experimentally testable inequality that the predictions of quantum mechanics for the Bell's polarization states of two entangled particles cannot be reproduced by any statistical model of hidden variables that shares certain intuitive features. In this paper we show, however, that the proof of the Bell's inequality involves a subtle, though crucial, assumption that is not required by fundamental physical principles and, moreover, it might not be fulfilled in the experimental setup that tests the inequality. In fact, this assumption can neither be properly implemented within the framework of quantum mechanics. Namely, the proof of the Bell's theorem assumes that there exists an absolute preferred frame of reference, supposedly provided by the lab, which enables to compare the orientation of the polarization measurement devices for successive realizations of the experiment. The need for this assumption can be readily checked by noticing that the theorem does not hold when the orientation of one of the detectors is taken as a reference frame to define the relative orientation of the second detector, in spite that this frame is an absolutely legitimate choice according to Galileo's principle of relativity. We further notice that the absolute frame of reference required by the proof of the Bell's theorem cannot exist in models in which the hidden configuration of the pair of entangled particles has a randomly set preferred direction that spontaneously breaks the global rotational symmetry. In fact, following this observation we build an explicit local model of hidden variables that reproduces the predictions of quantum mechanics for the Bell's states.

Mots clés: Quantum mechanics; EPR paradox; Bell's inequality; CHSH inequality; Bell's states; hidden variables; statistical model; locality; rotational symmetry; gauge symmetries; spontaneous symmetry breaking

Domaines: Physique [physics]; Physique mathématique [math-ph]; Relativité Générale et Cosmologie Quantique [gr-qc]

David H Oaknin. The Bell's theorem revisited: a subtle, though crucial, assumption has gone unnoticed, and it might not be justified!: Bell vs. Galileo: the proof of the inequality clashes with the principle of relativity. 2019. ⟨hal-01862953v2⟩