Analysis of Wigner's Set Theoretical Proof for Bell-type inequalities

TL;DR

This paper critically examines Wigner's set theoretical proof of Bell inequalities, revealing that its assumptions are unjustified and do not directly challenge Einstein's local realism, thus questioning the proof's implications for quantum nonlocality.

Contribution

The paper clarifies the assumptions in Wigner's proof, showing they are unrelated to local realism and do not invalidate Einstein's perspective.

Findings

Wigner's assumption is not related to local realism

His conclusions do not apply to EPR experiments

Contradictions with experimental results are not relevant to local realism

Abstract

We present a detailed analysis of the set theoretical proof of Wigner for Bell type inequalities with the following result. Wigner introduced a crucial assumption that is not related to Einstein's local realism, but instead, without justification, to the existence of certain joint probability measures for possible and actual measurement outcomes of Einstein-Podolsky-Rosen (EPR) experiments. His conclusions about Einstein's local realism are, therefore, not applicable to EPR experiments and the contradiction of the experimental outcomes to Wigner's results has no bearing on the validity of Einstein's local realism.