Bell's inequality: Physics meets Probability

TL;DR

This paper explores the interpretation of Bell's inequality violations, suggesting they indicate incompatibility of certain random variables rather than solely nonlocality or the death of reality, challenging traditional conclusions.

Contribution

It offers a novel perspective that Bell's inequality violation signifies the incompatibility of random variables, emphasizing the interpretative ambiguity beyond nonlocality or realism.

Findings

Bell's inequality violation implies incompatibility of random variables

Multiple interpretations exist for Bell's inequality violations

Bell's inequality cannot definitively determine the quantum-classical relationship

Abstract

We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation of Bell's type inequalities is a well known sufficient condition of incompatibility of random variables -- impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell's inequality -- a few pairs of random variables (two dimensional vector variables) involved in the EPR-Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus one can choose between: a) completeness of quantum mechanics; b) nonlocality; c) `` death of reality''; d) non-Kolmogorovness. In any event, violation of Bell's inequality has a variety of possible interpretations. Hence, it could not be used to derive the unique conclusion on the relation between quantum and classical models.