An inconsistency in the CHSH inequality

TL;DR

This paper argues that the assumptions behind the CHSH inequality are incompatible with experimental physics, challenging the conclusion that quantum mechanics irreconcilably conflicts with local realism, and discusses the possibility of an experimental proof.

Contribution

It reveals a fundamental inconsistency in the assumptions used to derive the CHSH inequality, questioning its experimental validity as a test of local realism.

Findings

Mathematical assumptions of CHSH are incompatible with experimental physics

Current experiments cannot definitively dismiss local hidden variable theories

An experimental proof of CHSH inequality is theoretically possible but practically challenging

Abstract

Violation of the CHSH inequality supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. We show that the mathematical assumptions underlying the proof of the CHSH inequality are, in fact, incompatible with the physics of the experiments testing such inequality. This implies that we cannot dismiss local realistic hidden variable theories on the basis of currently available experimental data yet. However, we also show that an experimental proof of CHSH inequality is, in principle, possible, but it is unclear how to implement, in practice, such an experiment.