Possible Experience: from Boole to Bell

TL;DR

This paper revisits classical logical inequalities and demonstrates a local realistic counterexample to Bell inequalities, proposing a new interpretation of the Born rule as a pre-measure of probability.

Contribution

It connects Boole's and Vorob'ev's inequalities with quantum Bell inequalities, providing a local realistic example that challenges common interpretations.

Findings

A local realistic counterexample violating Bell inequalities.

A reinterpretation of the Born rule as a pre-measure of probability.

Connection between classical logical inequalities and quantum nonlocality.

Abstract

Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier inequalities presented by Boole and the findings of Vorob'ev as related to these inequalities. These findings together with a space-time generalization of Boole's elements of logic lead us to a completely transparent Einstein local counterexample from everyday life that violates certain variations of the Bell inequalities. We show that the counterexample suggests an interpretation of the Born rule as a pre-measure of probability that can be transformed into a Kolmogorov probability measure by certain Einstein local space-time characterizations of the involved random variables.