Why one can maintain that there is a probability loophole in the CHSH

TL;DR

This paper argues that the standard CHSH inequality form is not universally valid and that local hidden variables can violate it with nonzero probability, challenging common assumptions in quantum foundations.

Contribution

It demonstrates that the traditional CHSH inequality does not hold universally and introduces the possibility of violations due to local hidden parameters.

Findings

CHSH inequality form is not always valid

Local hidden variables can violate CHSH

Violations are not eliminated by basic principles

Abstract

In the paper it is demonstrated that the particular form of CHSH, S=E{A(1)[B(1)-B(2)]-A(2)[B(1)+B(2)]} with, S maximally 2 and minimally -2,for A and B functions in {-1,1}, is not generally valid. The nonzero probability that local hidden extra parameters violate the CHSH, is not eliminated with basic principles derived from the CHSH.