Foundations of Physics

, Volume 14, Issue 9, pp 883–906 | Cite as

Stochastic microcausality in relativistic quantum mechanics

  • D. P. Greenwood
  • E. Prugovečki


A recently formulated concept of stochastic localizability is shown to be consistent with a concept of stochastic microcausality, which avoids the conclusions of Hegerfeldt's no-go theorem as to the inconsistency of sharp localizability of quantum particles and Einstein causality. The proposed localizability on quantum space-time is shown to lead to strict asymptotic causality. For finite time evolutions, upper bounds on propagation to the exterior of stochastic light cones are derived which show that the resulting probabilities are too small to be actually observable in a realistic context.


Time Evolution Quantum Mechanic Relativistic Quantum Finite Time Light Cone 
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  1. 1.
    E. Prugovečki,Stochastic Quantum Mechanics and Quantum Spacetime (D. Reidel, Dordrecht, 1984).Google Scholar
  2. 2.
    P. A. Schilpp, ed.,Albert Einstein: Philosopher-Scientist (Harper and Row, New York, 1959).Google Scholar
  3. 3.
    D. Gromes,Z. Phys. 236, 276 (1970).Google Scholar
  4. 4.
    G. C. Hegerfeldt,Phys. Rev. D 10, 3320 (1974).Google Scholar
  5. 5.
    B. K. Skagerstam,Int. J. Theor. Phys. 15, 213 (1976).Google Scholar
  6. 6.
    J. F. Perez and I. F. Wilde,Phys. Rev. D 16, 315 (1977).Google Scholar
  7. 7.
    G. N. Fleming,Phys. Rev. B 139, 963 (1965).Google Scholar
  8. 8.
    G. C. Hegerfeldt and S. N. M. Ruijsenaars,Phys. Rev. D 22, 377 (1980).Google Scholar
  9. 9.
    S. N. M. Ruijsenaars,Ann. Phys. (N.Y.) 137, 33 (1981).Google Scholar
  10. 10.
    E. Prugovečki,Quantum Mechanics in Hilbert Space (Academic Press, New York, 1981), 2nd edn.Google Scholar
  11. 11.
    A. S. Wightman,Rev. Mod. Phys. 34, 845 (1962).Google Scholar
  12. 12.
    W. Heisenberg,Phys. Today 29(3, 32 (1976).Google Scholar
  13. 13.
    A. Einstein,Ann. Phys. 17, 891 (1905).Google Scholar
  14. 14.
    R. Hofstadter,Rev. Mod. Phys. 28, 214 (1956).Google Scholar
  15. 15.
    D. P. Barberet al., Phys. Rev. Lett. 43, 1915 (1979).Google Scholar
  16. 16.
    F. E. Close,An Introduction to Quarks and Partons (Academic Press, New York, 1979).Google Scholar
  17. 17.
    J. C. Pati, A. Salam, and J. Strathdee,Phys. Lett. B 59, 265 (1975).Google Scholar
  18. 18.
    H. Harari,Phys. Lett. B 86, 83 (1979).Google Scholar
  19. 19.
    H. Feigl and M. Brodbeck,Readings in the Philosophy of Science (Appleton-Century-Crofts, New York, 1953).Google Scholar
  20. 20.
    A. R. Marlow, ed.,Mathematical Foundations of Quantum Mechanics (Academic Press, New York, 1978).Google Scholar
  21. 21.
    A. O. Barut and R. Raczka,Theory of Group Representations and Applications (PWN, Warsaw, 1977).Google Scholar
  22. 22.
    D. I. Blokhintsev,Space and Time in the Microworld (D. Reidel, Dordrecht, 1973).Google Scholar
  23. 23.
    S. T. Ali and E. Prugovečki, “Harmonic analysis and systems of covariance for phase space representations of the Poincaré group,” preprint.Google Scholar
  24. 24.
    E. Prugovečki,Phys. Rev. D 18, 3655 (1978).Google Scholar
  25. 25.
    S. T. Ali, “Harmonic analysis on phase space. I. Reproducing kernel Hilbert spaces, POV measures, and systems of covariance," Concordia University preprint.Google Scholar
  26. 26.
    M. Born,Rev. Mod. Phys. 21, 463 (1949).Google Scholar
  27. 27.
    F. Rohrlich, inFoundations of Radiation Theory and Quantum Electrodynamics, A. O. Barut, ed. (Plenum Press, New York, 1980).Google Scholar
  28. 28.
    T. L. Fine,Theories of Probability: An Examination of Foundations (Academic Press, New York, 1973).Google Scholar
  29. 29.
    A. Pap,An Introduction to the Philosophy of Science (Free Press of Glencoe, New York, 1962).Google Scholar
  30. 30.
    M. Bunge,Causality (World Publishing, Cleveland and New York, 1970).Google Scholar
  31. 31.
    A. S. Eddington,Relativity Theory of Protons and Electrons (Cambridge University Press, London, 1936).Google Scholar
  32. 32.
    G. O. Okikiolu,Aspects of the theory of Bounded Integral operators in Lp-spaces (Academic Press, New York, 1971).Google Scholar
  33. 33.
    A. Erdélyi, ed.,Tables of Integral Transforms, Vol. 1 (McGraw-Hill, New York, 1954).Google Scholar
  34. 34.
    T. G. Blaneyet al., Nature 251, 46 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • D. P. Greenwood
    • 1
  • E. Prugovečki
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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