Is Bell's theorem relevant to quantum mechanics? On locality and non-commuting observables

TL;DR

This paper argues that Bell's theorem is not relevant to quantum mechanics involving non-commuting observables and introduces models that explain EPR correlations without invoking non-locality.

Contribution

It clarifies the limitations of Bell's theorem for non-commuting observables and proposes models that reproduce EPR correlations without requiring non-locality.

Findings

Bell's theorem does not apply to non-commuting observables in quantum mechanics.

Models based on conservation laws and equivalence classes can explain EPR correlations without non-locality.

Bell's inequalities are not violated by quantum phenomena involving incompatible observables.

Abstract

Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum-mechanics, and conclude that Bell's theorem is not expected to be relevant to quantum phenomena described by non-commuting observables, irrespective of the issue of locality. Then, we try to disentangle the locality issue from the existence of joint distributions by introducing two models accounting for the EPR correlations but denying the existence of joint distributions. We will see that these models do not need to resort explicitly to non-locality: the first model relies on conservation laws for ensembles, and the second model on an equivalence class by which different configurations lead to the same physical predictions.