  The strong experimental evidence for the violation of Bell's inequalities is
widely interpreted as the ultimate proof of the impossibility to describe
Bell's polarization states of two entangled particles in terms of a local and
realistic statistical model of hidden variables in which the observers are free
to choose the settings of their measurements. In this paper we note, however,
that Bell's theorem relies crucially on a fourth implicit theoretical
assumption, in addition to the explicit hypotheses of locality, physical
realism and 'free will'. Namely, we note that the proof of Bell's inequalities
for generic models of hidden variables implicitly assumes that there exists an
absolute reference frame of angular coordinates, with respect to which we can
define the polarization properties of the hidden configurations of the pair of
particles. This implicit additional assumption, however, is not required by any
fundamental physical principle and, indeed, it may be incorrect if the hidden
configuration of the pair of entangled particles breaks the rotational symmetry
along an otherwise arbitrary direction. We explicitly show that by giving up to
this additional implicit assumption it is possible to build a local and
realistic model of hidden variables for Bell's polarization states, which
complies with the demands of 'free-will' and fully reproduces the quantum
mechanical predictions. The model presented here offers a new insight into the
notion of quantum entanglement and the role of measurements in the dynamics of
quantum systems. It may help also to develop new tools for performing numerical
simulations of quantum systems.
