A remark on the role of indeterminism and non-locality in the violation of Bell's inequality

TL;DR

This paper introduces a macroscopic model to explore how non-locality and indeterminism influence Bell's inequality violations, revealing that non-locality consistently increases violations, while indeterminism's effect varies with initial conditions.

Contribution

It presents a new macroscopic model that allows independent variation of non-locality and indeterminism, showing their distinct impacts on Bell's inequality violations.

Findings

Increasing non-locality enhances Bell inequality violation.

Indeterminism can either increase or decrease violation depending on initial state.

The model aligns with previous findings on non-locality but offers new insights on indeterminism.

Abstract

Some years ago Aerts et al. presented a macroscopic model in which the amount of non-locality and indeterminism could be continuously varied, and used it to show that by increasing non-locality one increases, as expected, the degree of violation of Bell's inequality (BI), whereas, more surprisingly, by increasing indeterminism one decreases the degree of the violation of BI. In this note we propose a different macroscopic model in which the amount of non-locality and indeterminism can also be parameterized, and therefore varied, and we find that, in accordance with the model of Aerts et al., an increase of non-locality produces a stronger violation of BI. However, differently from their model, we also find that, depending on the initial state in which the system is prepared, an increase of indeterminism can either strengthen or weaken the degree of violation of BI.