A Appropriate Probability Model for the Bell Experiment

TL;DR

This paper introduces an explicit probability model for Bell experiments that aligns with quantum mechanics and experiments, satisfies Bell inequalities, and challenges the traditional assumptions of realism and locality.

Contribution

It proposes a new probability model for Bell experiments that avoids violations of Bell inequalities by not assuming realism and incorporating only observable settings.

Findings

The model aligns with quantum mechanics and experimental results.

It satisfies Bell inequalities, contradicting the common interpretation of violations.

Extension with hidden variables results in a non-separable, non-local, or non-deterministic model.

Abstract

The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This contradiction led many to question the underlying assumptions, viz. so-called realism and locality. The probability model underlying the Bell inequality is generally left implicit. We propose an explicit probability model for the CHSH version of the Bell experiment. This model has only two simultaneously observable detector settings per measurement, and therefore does not assume realism. The quantum expectation now becomes a conditional expectation, given the two detector settings. This probability model is in full agreement with both quantum mechanics and experiments. As a result, the model satisfies the Bell inequality; there are no so-called violations. We extend this model to include a hidden variable. This extended model is not Bell-separable. This non-separability implies that the model is non-deterministic or non-local (or both).