No probability loophole in the CHSH

TL;DR

This paper critically examines Geurdes's probabilistic counterexample to Bell's theorem, revealing a flaw that results in a non-local hidden variable model, thus reaffirming the CHSH inequality's robustness.

Contribution

The paper identifies a fundamental flaw in Geurdes's construction, demonstrating it cannot produce a local hidden variable model violating CHSH.

Findings

Geurdes's method generates non-local models.

The claimed probability of violation is invalid.

The CHSH inequality remains unviolated by local models.

Abstract

Geurdes (2014, Results in Physics) outlines a probabilistic construction of a counterexample to Bell's theorem. He gives a procedure to repeatedly sample from a specially constructed "pool" of local hidden variable models (depending on a table of numerically calculated parameters) and select from the results one LHV model, determining a random value S of the usual CHSH combination of four (theoretical) correlation values. He claims Prob(|S| > 2) > 0. We expose a fatal flaw in the analysis: the procedure generates a non-local hidden variable model. To disprove this claim, Geurdes should program his procedure and generate random LHV's till he finds one violating the CHSH inequality.