  The Bell theorem stands as an insuperable roadblock in the path to a very
desired intuitive solution of the EPR 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 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 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. Indeed, this assumption can neither be properly implemented within
the standard framework of quantum mechanics. Namely, the proof of the theorem
assumes that there exists a preferred absolute 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
and, hence, to define jointly their response functions over the space of
hypothetical hidden configurations for all their possible alternative settings.
We notice, however, that only the relative orientation between the two
measurement devices in every single realization of the experiment is a properly
defined physical degree of freedom, while their global rigid orientation is a
spurious gauge degree of freedom. Hence, the preferred frame of reference
required by the proof of the Bell theorem does not necessarily exist. Following
this observation, we build an explicitly local model of hidden variables that
reproduces the predictions of quantum mechanics for the Bell states.
