The Clauser-Horne-Shimony-Holt inequality in the context of a broad random variable

TL;DR

This paper rigorously analyzes the CHSH inequality within probability theory, revealing potential for a broader inequality that does not conflict with quantum mechanics or Bell's inequality, supported by computational simulations.

Contribution

It introduces a new perspective on the CHSH inequality by avoiding prior assumptions, leading to the possibility of a larger inequality compatible with quantum mechanics.

Findings

Potential for a greater inequality than CHSH that is not violated by quantum mechanics

Computational simulations support the existence of such inequalities

No conflict with Bell's inequality or hidden variables

Abstract

In this work we aim to analyze the Clauser-Horne-Shimony-Holt CHSH inequality strictly in the context of probability theory. In the course of assembling inequality we have to take care not to produce assumptions a priori, that is, physically or intuitively accepted suppositions. Of course, this does not mean that after these considerations, we put the adequate physical conditions suitable and generally accepted in these contexts. This allows us to clearly visualize the possibility of finding a greater inequality than that of CHSH in which it is included. This inequality does not contradict the CHSH inequality. This result is suported by using a robust computational simulation, showing the possibility for obtaining an inequality for quantum mechanics that is not violated and allows random hidden variables without any conflict with Bell's inequality.