What are the bearers of hidden states? On an important ambiguity in the formulation of Bell's theorem

TL;DR

This paper examines the assumptions behind Bell's theorem, focusing on the ambiguous role of hidden states and proposing a new approach to relate local causality with other assumptions in quantum mechanics.

Contribution

It clarifies the ambiguity in the formulation of Bell's theorem by analyzing different views on hidden states and proposing a novel method to connect local causality with key assumptions.

Findings

Straightforward attempts to relate hidden states to Bell's conclusion fail

Refined approaches also face difficulties in establishing the connection

A new method combining previous intuitions offers a promising direction

Abstract

One of the conclusions that Bell drew from his famous inequality was that any hidden variable theory that satisfies Local Causality is incompatible with the predictions of Quantum Mechanics for Bell's Experiment. However, Local Causality does not appear in the derivation of Bell's inequality. Instead, two other assumptions are used, namely Factorizability and Settings Independence. Therefore, in order to establish the mentioned Bell's conclusion, we need to relate these two assumptions to Local Causality. The prospects for doing so turn out to depend on the assumed location of the hidden states that appear in Bell's inequality. In this paper, I consider the following two views on such states: (1) that they are states of the two-particle system at the moment of preparation, and (2) that they are states of thick slices of the past light cones of measurements. I argue that straightforward attempts to establish Bell's conclusion fail in both approaches. Then, I consider three refined attempts, which I also criticise, and I propose a new way of establishing Bell's conclusion that combines intuitions underlying several previous approaches.