Putting Bell's inequalities into context by putting context into Bell's inequalities

TL;DR

This paper explores how non-Kolmogorovian epistemic uncertainty within Dempster-Schafer theory affects Bell inequalities, introducing a contextual framework that aligns local classical models with quantum predictions.

Contribution

It develops a contextual approach incorporating measurement device states into probabilistic models, challenging traditional Bell inequality assumptions.

Findings

Contextual probabilities violate Bell inequalities

A local classical model reproduces quantum predictions

Measurement device states are integral to the probabilistic framework

Abstract

Within the Dempster-Schafer theory of evidence a non-Kolmogorovian kind of epistemic uncertainty arises, which is encoded using multi-valued maps. We analyse the possible implications such non-Kolmogorovian epistemic uncertainty may have for Bell-type inequalities relating to the Einstein-Podolsky-Rosen-Bohm (EPRB) thought experiment. Our analysis leads to a notion of contextuality concerning complexes of physical measurement conditions. The use of multi-valued maps reveals an implicit link between this contextuality and counterfactual outcomes, and results in a formulation wherein the states of measurement devices are explicitly taken into account as part of the probabilistic event space. This reflects a conception of measurement that was advocated by Bell some time ago. It results in context-conditioned measure-theoretic probabilities, which do not obey Bell-type inequalities, but which are nonetheless perfectly compatible with local classical physical models. We give an example of a local classical model that reproduces the quantum mechanical predictions and that fits within the contextual framework.