A Dempster-Schafer approach to Bell's inequalities

TL;DR

This paper introduces a novel approach using Dempster-Schafer evidence theory to model EPRB experiments, challenging traditional Bell inequality results by incorporating a different type of epistemic uncertainty.

Contribution

It replaces Kolmogorov probability with Dempster-Schafer theory, providing a new framework that aligns with classical determinism and locality while violating Bell inequalities.

Findings

Dempster-Schafer theory models epistemic uncertainty absent in Kolmogorov theory.

Conditional relative frequencies are compatible with classical determinism.

Bell-type inequalities are not satisfied under this new modeling approach.

Abstract

We present an alternative approach to modeling Einstein-Podolsky-Rosen-Bohm (EPRB)-type experiments. The basis for our approach will be to replace the conventional Kolmogorov theory of probability, with the more general Dempster-Schafer theory of evidence. This leads to the identification of a distinct type of epistemic uncertainty, which is not present in Kolmogorov theory, but which is relevant in modeling experiments with operationally incompatible observables. Our treatment naturally yields conditional relative frequencies, which are perfectly compatible with classical determinism and locality, but which do not satisfy Bell-type inequalities.