A possible statistics loophole in Bell's theorem

TL;DR

This paper questions the robustness of Bell's theorem by highlighting potential issues in experimental verification due to unknown hidden-variable distributions, prompting a re-evaluation of its implications.

Contribution

It reveals that while the theoretical proof remains unaffected, experimental tests of Bell's theorem may be compromised by hidden-variable distribution uncertainties.

Findings

Theoretical proof of Bell's theorem is unaffected by counterfactual reasoning.

Experimental verification may be unknowably affected by hidden-variable distribution ignorance.

Lays groundwork for rethinking Bell's theorem and its experimental implications.

Abstract

Bell's theorem proves the incompatibility between quantum mechanics and local realistic hidden-variable theories. In this paper we show that, contrary to a common belief, the theoretical proof of Bell's theorem is not affected by counterfactual reasoning. Then, we demonstrate that the experimental verification of this theorem may be affected in an unknowable way by our ignorance about the probability distribution of the hidden variables. Our study is based on the standard theory of random variables, and lays the groundwork for a critical rethinking of Bell's theorem and its consequences.