Probability and logical structure of statistical theories
type: Item
instance of: scholarly article
title: Probability and logical structure of statistical theories
zbMATH Open document ID: 0661.03050
DOI: 10.1007/BF00671311
author: Michael J. W. Hall
published in: International Journal of Theoretical Physics
publication date: 1988-01-01T00:00:00Z
review text: A characterization of statistical theories is given which incorporates both classical and quantum mechanics. It is shown that each statistical theory induces an associated logic and joint probability structure, and simple conditions are given for the structure to be of a classical or quantum type. This provides an alternative for the quantum logic approach to axiomatic quantum mechanics. The Bell inequalities may be derived for those statistical theories that have a classical structure and satisfy a locality condition weaker than factorizability. The relation of these inequalities to the issue of hidden variable theories for quantum mechanics is discussed and clarified.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 4079417
zbMATH Keywords: statistical theory
zbMATH Keywords: associated logic
zbMATH Keywords: joint probability structure
zbMATH Keywords: Bell inequalities
zbMATH Keywords: hidden variable theories
MaRDI profile type: Publication
cites work: On the Problem of Hidden Variables in Quantum Mechanics
cites work: Q3952094
cites work: The logic of quantum mechanics
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cites work: Q3881378
cites work: States, effects, and operations. Fundamental notions of quantum theory. Lectures in mathematical physics at the University of Texas at Austin. Ed. by A. Böhm, J. D. Dollard and W. H. Wootters
full work available at URL: https://doi.org/10.1007/bf00671311
OpenAlex ID: W2057515684
description: scientific article; zbMATH DE number 4079417