Local realist (but contextual) derivation of the EPR-Bohm correlations

TL;DR

This paper presents a local, realist, and contextual frequency-based model that reproduces EPR-Bohm correlations without contradicting Bell's theorem, emphasizing the role of observable incompatibility.

Contribution

It introduces a frequency probabilistic model that derives EPR-Bohm correlations without assuming a joint probability distribution, challenging traditional interpretations.

Findings

Reproduces EPR-Bohm correlations using frequency approach

Shows local and realist model consistent with quantum results

Highlights the role of observable incompatibility in quantum correlations

Abstract

The probabilistic structure of quantum mechanics is investigated in the frequency framework. Such an approach can be interpreted as a contextual approach to quantum probabilities. By using rather complicated frequency calculations we reproduce the EPR-Bohm correlation function which is typically derived by using the calculus of probabilities in a Hilbert space. Our frequency probabilistic model of the EPR-Bohm experiment is a realist model -- physical observables are considered as objective properties of physical systems. It is also local -- a measurement over one part of a composite system does not disturb another part of this system. Nevertheless, our result does not contradict to the well known Bell's ``NO-GO'' theorem. J. Bell used the conventional (Kolmogorov) measure-theoretical approach. We use the frequency approach. In the latter approach there are no reasons to assume that the simultaneous probability distribution exists: corresponding frequencies may fluctuate and not approach any definite limit (which Bell would like to use as the probability). The frequency probabilistic derivation demonstrated that incompatibility of observables under consideration plays the crucial role in producing of the EPR-Bohm correlations.