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Foundations of Physics

, Volume 6, Issue 5, pp 511–525 | Cite as

Hidden variables and locality

  • Jeffrey Bub
Article

Abstract

Bell's problem of the possibility of a local hidden variable theory of quantum phenomena is considered in the context of the general problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space, and Bell's result is presented as a generalization of Maczynski's theorem for maximal magnitudes. The proof of this generalization is shown to depend on the impossibility of recovering the quantum statistics for sequential probabilities in a classical representation without introducing a randomization process for the hidden variables. Hidden variable theories that exclude such a randomization process are termed “strict,” and it is shown that the class of local hidden variable theories is included in the class of strict theories. A counterargument by Freedman and Wigner is evaluated with reference to Clauser's extension of a hidden variable model proposed by Bell.

Keywords

Statistical State Quantum Statistic Mechanical System Randomization Process General Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. Kochen and E. P. Specker,J. Math. Mech. 17, 59 (1967).Google Scholar
  2. 2.
    M. J. Maczynski,Rep. Math. Phys. 2, 135 (1971).Google Scholar
  3. 3.
    J. S. Bell, “Introduction to the Hidden Variable Question,” inFoundations of Quantum Mechanics, B. d'Espagnat, ed. (Academic Press, New York, 1967).Google Scholar
  4. 4.
    D. Bohm,Phys. Rev. 85, 166 (1952).Google Scholar
  5. 5.
    D. Bohm and J. Bub,Rev. Mod. Phys. 38, 453 (1966).Google Scholar
  6. 6.
    J. S. Bell,Rev. Mod. Phys. 38, 447 (1966).Google Scholar
  7. 7.
    J. S. Bell,Physics (N.Y.), 195 (1964).Google Scholar
  8. 8.
    S. Freedman and E. Wigner,Found. Phys. 3, 457 (1973).Google Scholar
  9. 9.
    J. Bub,Found. Phys. 3, 29 (1973).Google Scholar
  10. 10.
    J. Bub,The Interpretation of Quantum Mechanics (D. Reidel, Dordrecht, 1974).Google Scholar
  11. 11.
    J. F. Clauser,Am. J. Phys. 39, 1095 (1971).Google Scholar
  12. 12.
    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt,Phys. Rev. Lett. 23, 880 (1969).Google Scholar
  13. 13.
    S. J. Freedman and J. F. Clauser,Phys. Rev. Lett. 28, 938 (1972).Google Scholar
  14. 14.
    R. A. Holt, “Atomic Cascade Experiments,” Doct. Diss., Harvard University (1973), unpublished.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Jeffrey Bub
    • 1
    • 2
  1. 1.Tel-Aviv UniversityRamat-AvivIsrael
  2. 2.University of Western OntarioLondonCanada

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