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

Journal Article · Sun Mar 15 04:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4915292· OSTI ID:22403121

Hofer-Szabó, Gábor ^[1]; Vecsernyés, Péter ^[2]

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1. Research Center for the Humanities, Budapest (Hungary)
2. Wigner Research Centre for Physics, Budapest (Hungary)

The aim of this paper is to implement Bell’s notion of local causality into a framework, called local physical theory. This framework, based on the axioms of algebraic field theory, is broad enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will arise as the classical case of our definition. 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 to be locally causal. Finally, comparing 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.

• OSTI ID: 22403121
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 56; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRAIC FIELD THEORY
BELL THEOREM
CAUSALITY
PROBABILISTIC ESTIMATION
QUANTUM MECHANICS