Skip to main content
SpringerLink
Log in

Quantum mechanics and the concept of joint probability

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The concepts of joint probability as implied by the Copenhagen and realist interpretations of quantum mechanics are examined in relation to (a) the rules for manipulation of probabilistic quantities, and (b) the role of the Bell inequalities in assessing the completeness of standard quantum theory. Proponents of completeness of the Copenhagen interpretation are required to accept a modification of the classical laws of probability to provide a mechanism for complementarity. A new formulation of the locality postulate is given, not involving factorizability or conditional probabilities, which clarifies the role of locality in the derivation of the Bell inequalities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Fine,Phys. Rev. Lett. 48, 291 (1982).

    Google Scholar 

  2. R. Cox,The Algebra of Probable Inference (John Hopkins, University Press, Baltimore, 1961).

    Google Scholar 

  3. For example: A. N. Kolmogorov,Foundations of Probability (Chelsea, New York, 1950); H. Jeffreys,Theory of Probability (Clarendon Press, Oxford, 1961), 3rd edn.; B. de Finetti,Theory of Probability (Wiley, New York, 1974), Vol. 1, pp. 99 and 136.

  4. I. Pitowsky,J. Math. Phys. 27, 1556 (1986).

    Google Scholar 

  5. W. de Muynck,Phys. Lett. 114A, 65 (1986).

    Google Scholar 

  6. A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).

    Google Scholar 

  7. N. Bohr,Phys. Rev. 48, 696 (1935).

    Google Scholar 

  8. A. M. Gleason,J. Math. Mech. 6, 885 (1957).

    Google Scholar 

  9. G. Birkhoff and J. von Neumann,Ann. Math. 37, 823 (1936).

    Google Scholar 

  10. J. M. Jauch and C. Piron,Helv. Phys. Acta 36, 827 (1963).

    Google Scholar 

  11. L. E. Ballentine,Am. J. Phys. 54, 883 (1986).

    Google Scholar 

  12. D. Bohm,Phys. Rev. 85, 166 and 180 (1952).

    Google Scholar 

  13. J. F. Clauser and M. A. Horne,Phys. Rev. D 10, 526 (1974).

    Google Scholar 

  14. A. Fine, inLogic and Probability in Quantum Mechanics, P. Suppes, ed. (Reidel, Dordrecht, 1976), p. 249.

    Google Scholar 

  15. J. S. Bell,Physics 1, 195 (1964).

    Google Scholar 

  16. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt,Phys. Rev. Lett. 23, 880 (1969).

    Google Scholar 

  17. A. Aspect and P. Grangier, inFoundations of Quantum Mechanics in the Light of New Technology, S. Kamefuchiet al., eds. (Physical Society of Japan, Tokyo, 1984).

    Google Scholar 

  18. E.g., M. Ferrero and E. Santos,Phys. Lett. 116A, 356 (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Physics, Research School of Physical Sciences, Australian National University, 2600, Canberra, A.C.T., Australia

    Michael J. W. Hall

Authors
  1. Michael J. W. Hall
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hall, M.J.W. Quantum mechanics and the concept of joint probability. Found Phys 19, 189–207 (1989). https://doi.org/10.1007/BF00734525

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00734525

Keywords

Search

Navigation