A Stronger Bell Argument for (Some Kind of) Parameter Dependence

TL;DR

This paper strengthens Bell's theorem by deriving inequalities that exclude a broader class of non-local theories, emphasizing the necessity of parameter dependence over outcome dependence to explain quantum non-locality.

Contribution

It introduces a stronger Bell argument that rules out non-local theories beyond outcome dependence, clarifying the role of parameter dependence in quantum non-locality.

Findings

Outcome dependence alone is insufficient to explain Bell violations.

Certain non-local theories with parameter dependence are excluded by the new inequalities.

Quantum theory exhibits at least one form of parameter dependence in measurement outcomes.

Abstract

It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a new derivation of the inequalities from non-trivial non-local theories and formulates a stronger Bell argument excluding also these non-local theories. Taking into account all possible theories, the conclusion of this stronger argument provably is the strongest possible consequence from the violation of Bell inequalities on a qualitative probabilistic level (given usual background assumptions). Among the forbidden theories is a subset of outcome dependent theories showing that outcome dependence is not sufficient for explaining a violation of Bell inequalities. Non-local theories which can violate Bell inequalities (among them quantum theory) are rather characterised by the fact that at least one of the measurement outcomes in some sense (which is made precise) probabilistically depends both on its local as well as on its distant measurement setting ('parameter'). When Bell inequalities are found to be violated, the true choice is not 'outcome dependence or parameter dependence' but between two kinds of parameter dependences, one of them being what is usually called 'parameter dependence'. Against the received view established by Jarrett and Shimony that on a probabilistic level quantum non-locality amounts to outcome dependence, this result confirms and makes precise Maudlin's claim that some kind of parameter dependence is required.