A simple model for the spin singlet: mathematical equivalence of non-locality, slave will and conspiracy

Abstract

A hidden-variable model reproducing the quantum mechanical probabilities for a spin singlet is presented. The model violates only the hypothesis of independence of the distribution for the hidden variables from the detector settings and vice versa (measurement independence). It otherwise satisfies the hypotheses of setting independence, outcome independence—made in the derivation of the Bell inequality—and that of compliance with Malus's law—made in the derivation of the Leggett inequality. It is shown that the violation of the measurement independence hypothesis may be explained alternatively by assuming a non-local influence of the detector settings on the hidden variables, or by taking the hidden variable to influence the choice of settings (limitation of free will), or finally by purporting a conspiracy. It is demonstrated that the last two cases admit a realization through existing local classical resources.