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

Understand

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 detectors settings and vice versa (Measurement Independence).
• It otherwise satisfies the hypotheses of Setting Independence, Outcome Independence -- made in the derivation of Bell inequality -- and that of compliance with Malus's Law -- made in the derivation of 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 detectors 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.