On the meaning of locality: the overlapping assumptions

TL;DR

This paper critically examines the assumptions underlying locality in Bell's theorem, revealing nuanced distinctions and proposing that any fundamental theory consistent with quantum mechanics must reject outcome independence.

Contribution

It clarifies the relationships among various locality assumptions and introduces a new perspective on non-contextuality and outcome independence in quantum theories.

Findings

Separability is equivalent to local causality and leads to factorizability.

Relativistic causality is not necessarily equivalent to parameter independence.

Quantum mechanics implies the rejection of outcome independence in fundamental theories.

Abstract

We examine the locality assumption of Bell's theorem in three steps of EPRB experiment. Depending on the context, locality is embodied in the conditions of separability, local causality, factorizability, relativistic causality, and non-contextuality. We show that separability, characterized by the constraint of zero covariance, is equivalent to local causality which leads to factorizability through the measurement process. Factorizability is the conjunction of parameter independence and outcome independence. It is commonly believed that relativistic causality is equivalent to parameter independence, which is satisfied by quantum mechanics. According to our approach, however, this is unjustified due to the second step analysis of EPRB experiment, including the measurement on the first particle. We define non-contextuality based on preparation procedure and measurement process. Preparation-based non-contextuality is an independent assumption, but non-locality within the framework of a separable model can be interpreted as measurement-based contextuality. Finally, we show that any fundamental theory consistent with quantum mechanics, should refute outcome independence in its framework of description.