Einstein and Bell, von Mises and Kolmogorov: reality and locality, frequency and probability

TL;DR

This paper analyzes the frequency interpretation of quantum experiments, suggesting that violations of Bell's inequalities may result from collective dependence rather than nonlocality, challenging traditional probabilistic assumptions.

Contribution

It introduces a frequency-based perspective on quantum correlations, proposing that collective dependence explains Bell inequality violations without invoking nonlocality.

Findings

Frequencies of hidden variables may fluctuate across experiments.

Violations of Bell's inequalities can arise from collective dependence.

Dependence of collectives differs from event dependence, affecting interpretations.

Abstract

We perform frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes. In fact, frequencies for hidden variables for quantum particles and measurement devices may fluctuate from run to run of an experiment. These fluctuations of frequencies for micro-parameters need not contradict to the stabilization of frequencies for physical observables. If, nevertheless, micro-parameters are also statistically stable, then violations of Bell's inequality and its generalizations may be a consequence of dependence of collectives corresponding to two different measurement devices. Such a dependence implies the violation of the factorization rule for the simultaneous probability distribution. Formally this rule coincides with the well known BCHS locality condition (or outcome independence condition). However, the frequency approach implies totally different interpretation of dependence. It is not dependence of events, but it is dependence of collectives. Such a dependence may be induced by the same preparation procedure.