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

TL;DR

This paper introduces a hidden variable model for the spin singlet that reproduces quantum probabilities by violating measurement independence, illustrating how non-local influences, free will limitations, or conspiratorial assumptions can explain quantum correlations.

Contribution

It demonstrates that violations of measurement independence can be modeled through local classical resources, unifying non-locality, free will limitations, and conspiracy explanations.

Findings

The model reproduces quantum probabilities for spin singlet.

Violations of measurement independence can be explained locally.

Conspiratorial and free will limitations are realizable with classical resources.

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 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. It is demonstrated that the last two cases admit a realization through existing local classical resources.