The contextuality loophole is fatal for Bell inequalities: Reply to a comment by I. Schmelzer

TL;DR

This paper clarifies that the so-called 'contextuality loophole' in Bell's theorem is a misunderstanding, emphasizing the importance of correctly modeling measurement settings and the limitations of hidden variable models.

Contribution

It refutes claims of a 'contextuality loophole' by clarifying the proper interpretation of contextuality in Bell inequalities.

Findings

Bell inequalities can be invalidated by proper inclusion of measurement context

Hidden variable models face limitations when describing incompatible experiments

Misinterpretations of contextuality lead to incorrect conclusions about Bell's theorem

Abstract

Ilya Schmelzer wrote recently: {\it Nieuwenhuizen argued that there exists some "contextuality loophole" in Bell's theorem. This claim in unjustified}. It is made clear that this arose from attaching a meaning to the title and the content of the paper different from the one intended by Nieuwenhuizen. "Contextual loophole" means only that if the supplementary parameters describing measuring instruments are correctly introduced, Bell and Bell-type inequalities may not be proven. It is also stressed that a hidden variable model suffers from a "contextuality loophole" if it tries to describe different sets of incompatible experiments using a unique probability space and a unique joint probability distribution.