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

Diederik Aerts was the first in the eighties to develop a concrete example of a macroscopic “classical” entity violating Bell's inequalities (BI). In more recent years, he also developed a macroscopic model in which the amount of non-locality and indeterminism can be continuously varied, and used it to show that by increasing non-locality one increases the degree of violation of BI, whereas by increasing indeterminism one decreases the degree of violation of BI. In this article we introduce and analyze a different macroscopic model in which the amount of non-locality and indeterminism can also be parameterized, and therefore varied, and find that, in accordance with the model of Aerts, an increase of non-locality does produce a stronger violation of BI. However, differently from his 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.