International Journal of Theoretical Physics

, Volume 27, Issue 11, pp 1285–1312 | Cite as

Probability and logical structure of statistical theories

  • Michael J. W. Hall


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.


Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic Locality Condition 
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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Michael J. W. Hall
    • 1
  1. 1.Department of Theoretical Physics, Research School of Physical SciencesAustralian National UniversityCanberraAustralia

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