An explicit statistical model for the Bell experiment

Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing quantum phenomena in terms of locally defined elements of reality. In a series of recent papers, we have noticed, however, that this conclusion inadvertently, yet crucially, relies on the assumed existence of an absolute frame of reference, with respect to which it would be possible to describe independently of each other the hypothetical elements of reality and the measurement devices that test them. Otherwise, a non-zero geometric phase may appear in the description of the former with respect to a closed sequence of settings of the latter, leading to the violation of the inequality. Following this observation, we discuss an explicit statistical model, which fully reproduces the predictions of Quantum Mechanics for the Bell experiment.