Abstract
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.
Similar content being viewed by others
References
E. Prugovečki,Stochastic Quantum Mechanics and Quantum Spacetime (D. Reidel, Dordrecht, 1984).
P. A. Schilpp, ed.,Albert Einstein: Philosopher-Scientist (Harper and Row, New York, 1959).
D. Gromes,Z. Phys. 236, 276 (1970).
G. C. Hegerfeldt,Phys. Rev. D 10, 3320 (1974).
B. K. Skagerstam,Int. J. Theor. Phys. 15, 213 (1976).
J. F. Perez and I. F. Wilde,Phys. Rev. D 16, 315 (1977).
G. N. Fleming,Phys. Rev. B 139, 963 (1965).
G. C. Hegerfeldt and S. N. M. Ruijsenaars,Phys. Rev. D 22, 377 (1980).
S. N. M. Ruijsenaars,Ann. Phys. (N.Y.) 137, 33 (1981).
E. Prugovečki,Quantum Mechanics in Hilbert Space (Academic Press, New York, 1981), 2nd edn.
A. S. Wightman,Rev. Mod. Phys. 34, 845 (1962).
W. Heisenberg,Phys. Today 29(3, 32 (1976).
A. Einstein,Ann. Phys. 17, 891 (1905).
R. Hofstadter,Rev. Mod. Phys. 28, 214 (1956).
D. P. Barberet al., Phys. Rev. Lett. 43, 1915 (1979).
F. E. Close,An Introduction to Quarks and Partons (Academic Press, New York, 1979).
J. C. Pati, A. Salam, and J. Strathdee,Phys. Lett. B 59, 265 (1975).
H. Harari,Phys. Lett. B 86, 83 (1979).
H. Feigl and M. Brodbeck,Readings in the Philosophy of Science (Appleton-Century-Crofts, New York, 1953).
A. R. Marlow, ed.,Mathematical Foundations of Quantum Mechanics (Academic Press, New York, 1978).
A. O. Barut and R. Raczka,Theory of Group Representations and Applications (PWN, Warsaw, 1977).
D. I. Blokhintsev,Space and Time in the Microworld (D. Reidel, Dordrecht, 1973).
S. T. Ali and E. Prugovečki, “Harmonic analysis and systems of covariance for phase space representations of the Poincaré group,” preprint.
E. Prugovečki,Phys. Rev. D 18, 3655 (1978).
S. T. Ali, “Harmonic analysis on phase space. I. Reproducing kernel Hilbert spaces, POV measures, and systems of covariance," Concordia University preprint.
M. Born,Rev. Mod. Phys. 21, 463 (1949).
F. Rohrlich, inFoundations of Radiation Theory and Quantum Electrodynamics, A. O. Barut, ed. (Plenum Press, New York, 1980).
T. L. Fine,Theories of Probability: An Examination of Foundations (Academic Press, New York, 1973).
A. Pap,An Introduction to the Philosophy of Science (Free Press of Glencoe, New York, 1962).
M. Bunge,Causality (World Publishing, Cleveland and New York, 1970).
A. S. Eddington,Relativity Theory of Protons and Electrons (Cambridge University Press, London, 1936).
G. O. Okikiolu,Aspects of the theory of Bounded Integral operators in Lp-spaces (Academic Press, New York, 1971).
A. Erdélyi, ed.,Tables of Integral Transforms, Vol. 1 (McGraw-Hill, New York, 1954).
T. G. Blaneyet al., Nature 251, 46 (1974).
Author information
Authors and Affiliations
Additional information
Supported by an NSERC Fellowship.
Suported in part by NSERC research grant No. A5206.
Rights and permissions
About this article
Cite this article
Greenwood, D.P., Prugovečki, E. Stochastic microcausality in relativistic quantum mechanics. Found Phys 14, 883–906 (1984). https://doi.org/10.1007/BF00737555
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00737555