The Bell's theorem revisited: a subtle, though crucial, assumption has gone unnoticed, and it might not be justified!
Résumé
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 theorem involves a subtle, though crucial, assumption that is not required by fundamental physical principles and, hence, it is not necessarily fulfilled in the experimental setup that tests the inequality. In fact, this assumption can neither be properly implemented within the standard framework of quantum mechanics. Namely, the proof of the Bell's theorem assumes that there exists a preferred absolute frame of reference, supposedly provided by the lab, which would enable to compare the orientation of the polarization measurement devices for successive realizations of the experiment and, hence, to define jointly their response functions over the space of hypothetical hidden configurations for all their possible alternative settings. The need for this assumption can be readily checked by noticing that the proof of the theorem does not necessarily hold when the orientation of one of the detectors is taken as a reference to define the relative orientation of the second detector, in spite that this is an absolutely legitimate choice according to Galileo's principle of relativity. We solve this puzzle by noticing that only the relative orientation between the two measurement devices in every single realization of the experiment is a properly defined physical degree of fredom, while their global rigid orientation is an spurious unphysical gauge degree of freedom. Therefore, the preferred absolute frame of reference required by the proof of the Bell's theorem does not necessarly exist. In particular, an absolute frame of reference cannot exist in models in which the gauge symmetry of the experimental setup under global rigid rotations of the two detectors is spontaneously broken by the hidden configurations of the pair of entangled particles and a non-zero geometric phase appears under some cyclic gauge symmetry transformations. Following this observation we build an explicitly local model of hidden variables that reproduces the predictions of quantum mechanics for the Bell's states.
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