Foundations of Physics

, Volume 16, Issue 4, pp 391–405

Quantum mechanics without probability amplitudes

  • William K. Wootters
Part III. Invited Papers Dedicated To John Archibald Wheeler

Abstract

First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    John A. Wheeler, “Genesis and Observership,” inFoundational Problems in the Special Sciences, R. E. Butts and J. Hintikka, eds. (Reidel, Dordrecht, Holland, 1987); “Frontiers of Time,” inProblems in the Foundations of Physics (Proceedings of the International School of Physics “Enrico Fermi”: course 72) (Italian Physical Society, 1979); “Beyond the Black Hole,” inSome Strangeness in the Proportion, Harry Woolf, ed. (Addison-Wesley, Reading, Massachusetts, 1980);Am. J. Phys. 51, 398 (1983).Google Scholar
  2. 2.
    W. Gale, C. Guth, and G. T. Trammell,Phys. Rev. 165, 1434 (1968); W. Band and J. L. Park,Found. Phys. 1, 133 (1970); J. L. Park and W. Band,Found. Phys. 1, 211 (1971); W. Band and J. L. Park,Found. Phys. 1, 339 (1971);Am. J. Phys. 47, 188 (1979); I. D. Ivanovic,J. Math. Phys. 24, 1199 (1983).Google Scholar
  3. 3.
    I. D. Ivanovic,J. Phys. A: Mat. Gen. 14, 3241 (1981).Google Scholar
  4. 4.
    John S. Bell,Physics 1, 195 (1964); John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt,Phys. Rev. Lett. 23, 880 (1969); Stuart J. Freedman and John F. Clauser,Phys. Rev. Lett. 28, 938 (1972); P. J. Bussey,Phys. Lett. A 90, 9 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • William K. Wootters
    • 1
  1. 1.Department of Physics and AstronomyWilliams CollegeWilliamstown

Personalised recommendations