J.S. Bell's Concept of Local Causality

TL;DR

This paper clarifies Bell's original concept of local causality, explaining its mathematical formulation, and discusses its implications for quantum theory, local realism, and the derivation of Bell inequalities.

Contribution

It provides a detailed, pedagogical exposition of Bell's concept of local causality, including its mathematical formulation and relation to the EPR argument.

Findings

Bell's local causality can be formalized mathematically.

Bell's formulation leads to testable inequalities.

The paper clarifies Bell's interpretation versus common misconceptions.

Abstract

John Stewart Bell's famous 1964 theorem is widely regarded as one of the most important developments in the foundations of physics. It has even been described as "the most profound discovery of science." Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many textbooks and commentators report that Bell's theorem refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen in 1935) of supplementing ordinary quantum theory with additional ("hidden") variables that might restore determinism and/or some notion of an observer-independent reality. On this view, Bell's theorem supports the orthodox Copenhagen interpretation. Bell's own view of his theorem, however, was quite different. He instead took the theorem as establishing an "essential conflict" between the now well-tested empirical predictions of quantum theory and relativistic \emph{local causality}. The goal of the present paper is, in general, to make Bell's own views more widely known and, in particular, to explain in detail Bell's little-known mathematical formulation of the concept of relativistic local causality on which his theorem rests. We thus collect and organize many of Bell's crucial statements on these topics, which are scattered throughout his writings, into a self-contained, pedagogical discussion including elaborations of the concepts "beable", "completeness", and "causality" which figure in the formulation. We also show how local causality (as formulated by Bell) can be used to derive an empirically testable Bell-type inequality, and how it can be used to recapitulate the EPR argument.