Complete account of randomness in the EPR-Bohm-Bell experiment

TL;DR

This paper demonstrates that the apparent violations of Bell's inequality arise from an improper probabilistic model and presents a fully consistent classical probability framework that aligns with experimental data.

Contribution

It introduces a complete probabilistic model for the EPR-Bohm-Bell experiment that accounts for setting selection probabilities, resolving paradoxes caused by incomplete descriptions.

Findings

The conventional Bell model neglects setting selection probabilities.

Proper inclusion of setting probabilities removes contradictions.

The new model aligns with experimental results and classical probability theory.

Abstract

We show that paradoxical consequences of violations of Bell's inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a combination of statistical data collected for different settings of polarization beam splitters (PBSs). In fact, such data consists of some conditional probabilities which only partially define a probability space. Ignoring this conditioning leads to apparent contradictions in the classical probabilistic model (due to Kolmogorov). We show how to make a completely consistent probabilistic model by taking into account the probabilities of selecting the settings of the PBSs. Our model matches both the experimental data and is consistent with classical probability theory.