Bell's theorem and the issue of determinism and indeterminism

TL;DR

This paper analyzes how deterministic quantum theories like Bohmian mechanics relate to Bell's theorem, arguing that determinism does not necessarily violate the independence assumption crucial for Bell's inequalities.

Contribution

It clarifies that determinism alone does not undermine the independence assumption in Bell's theorem, emphasizing the role of entanglement and effective wave functions.

Findings

Determinism does not inherently violate measurement independence.

Entanglement can coexist with deterministic theories without contradicting Bell's assumptions.

Effective wave functions support the independence premise in Bohmian mechanics.

Abstract

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell's theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell's theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave function can go together with effective wave functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave functions are sufficient for the mentioned independence premise to hold.