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The Bell inequality is thought to be a common constraint shared by all modelsof local hidden variables that aim to describe the entangled states of twoqubits. Since the inequality is violated by the quantum mechanical descriptionof these states, it purportedly allows distinguishing in an experimentallytestable way the predictions of quantum mechanics from those of models of localhidden variables and, ultimately, ruling the latter out. In this paper, weshow, however, that the models of local hidden variables constrained by theBell inequality all share a subtle, though crucial, feature that is notrequired by fundamental physical principles and, hence, it might not befulfilled in the actual experimental setup that tests the inequality. Indeed,the disputed feature neither can be properly implemented within the standardframework of quantum mechanics and it is even at odds with the fundamentalprinciple of relativity. Namely, the proof of the inequality requires theexistence of a preferred absolute frame of reference (supposedly provided bythe lab) with respect to which the hidden properties of the entangled particlesand the orientations of each one of the measurement devices that test them canbe independently defined through a long sequence of realizations of theexperiment. We notice, however, that while the relative orientation between thetwo measurement devices is a properly defined physical magnitude in everysingle realization of the experiment, their global rigid orientation withrespect to a lab frame is a spurious gauge degree of freedom. Following thisobservation, we were able to explicitly build a model of local hidden variablesthat does not share the disputed feature and, hence, it is able to reproducethe predictions of quantum mechanics for the entangled states of two qubits.

Are models of local hidden variables for the singlet polarization state necessarily constrained by the Bell inequality?