On the concept of Bell's local causality in local classical and quantum theory

TL;DR

This paper rigorously defines Bell's local causality within a comprehensive framework, analyzing its relation to local primitive causality, classicality, and Bell inequalities in classical and quantum theories.

Contribution

It introduces a precise formulation of local causality using local physical theories and explores its implications for classical and quantum models.

Findings

Bell inequalities require classicality or commuting common causes.

Local causality is distinct from local primitive causality.

The framework clarifies the conditions under which Bell inequalities can be derived.

Abstract

The aim of this paper is to give a sharp definition of Bell's notion of local causality. To this end, first we unfold a framework, called local physical theory, integrating probabilistic and spatiotemporal concepts. Formulating local causality within this framework and classifying local physical theories by whether they obey local primitive causality --- a property rendering the dynamics of the theory causal, we then investigate what is needed for a local physical theory, with or without local primitive causality, to be locally causal. Finally, comparing Bell's local causality with the Common Cause Principles and relating both to the Bell inequalities we find a nice parallelism: Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.