International Journal of Theoretical Physics

, Volume 22, Issue 4, pp 293–314 | Cite as

Relativistic quantum logic

  • Peter Mittelstaedt
Article

Abstract

On the basis of the well-known quantum logic and quantum probability a formal language of relativistic quantum physics is developed. This language incorporates quantum logical as well as relativistic restrictions. It is shown that relativity imposes serious restrictions on the validity regions of propositions in space-time. By an additional postulate this relativistic quantum logic can be made consistent. The results of this paper are derived exclusively within the formal quantum language; they are, however, in accordance with well-known facts of relativistic quantum physics in Hilbert space.

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References

  1. Birkhoff, G., and von Neumann, J. (1936). “The Logic of Quantum Mechanics,”Annals of Mathematics,37, 823.Google Scholar
  2. d'Espagnat, B. (1979). “Quantum Theory and Reality,”Scientific American,Nov. p. 128.Google Scholar
  3. Dixmier, J. (1957).Les Algèbres d'Operateur dans L'Espace, Hilbertien, Paris, Gautheir-Villars.Google Scholar
  4. Finkelstein, D. (1969). “Matter, Space and Logic,” in R. S. Cohen and M. W. Wortofsky (Eds.), Boston Studies in the Philosophy of Science, Vol. V. D. Reidel, Dordrecht, Holland.Google Scholar
  5. Foulis, D. J. (1960). “Baer*-Semigroups”,Proceedings of the American Mathematical Society,11, 648.Google Scholar
  6. Gudder, S. P. (1971). “Representations of Groups as Automorphism of Orthomodular Lattices and Posets,”Canadian Journal of Mathematics,23, 659.Google Scholar
  7. Jauch, J. M. (1968).Foundations of Quantum Mechanics. Addison-Wesley, Reading. Massachusetts.Google Scholar
  8. Jauch, J. M. (1974). “Quantum Probability Calculus,”Synthese,29, 131.Google Scholar
  9. Koppe, H., and Zapp, H. C. (1983). To be published.Google Scholar
  10. Levi-Leblond, J. M. (1976).American Journal of Physics,44, 271.Google Scholar
  11. Lüders, G. (1951). “Über die Zustandsänderungen durch den Messprozess”,Annalen der Physik,8, 322.Google Scholar
  12. Mittelstaedt, P. (1976a). “On the Applicability of the Probability Concept in Quantum Mechanics,” in: Harper and Hooker (Eds.),Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. III, p. 155. D. Reidel, Dordrecht: Holland.Google Scholar
  13. Mittelstaedt, P. (1976b).Philosophical Problems of Modern Physics, Chap. III. D. Reidel, Dordrecht, Holland.Google Scholar
  14. Mittelstaedt, P. (1976/80).Der Zeitbegriff in der Physik, Bibliographisches Institut, Mannheim.Google Scholar
  15. Mittelstaedt, P. (1978).Quantum Logic. D. Reidel, Dordrecht, Holland.Google Scholar
  16. Mittelstaedt, P., and Stachow, E. W. (1978). The Principle of Excluded Middle in Quantum Logic,”Journal of Philosophical Logic,7, 181.Google Scholar
  17. Ochs, W. (1981). “Some Comments on the Concept of State in Quantum Mechanics,” inSymposium on Logic, Probability and Measurement in Quantum Mechanics, Erkenntnis,16. D. Reidel, Dordrecht: Holland.Google Scholar
  18. Pfarr, J. (1983). “An Operational Approach to the Lorentz-Transformation,”International Journal of Theoretical Physics (to be published).Google Scholar
  19. Piron, C. (1976).Foundations of Quantum Physics. W. A. Benjamin, New York.Google Scholar
  20. Schlieder, S. (1968). “Einige Bemerkungen zur Zustandsänderung...,”Communications in Mathematical Physics,7, 305.Google Scholar
  21. Schlieder, S. (1971). “Zum kausalen Verhalten eines relativistischen quantenmechanischen Systems,” in P. Dürr (Ed.)Quanten und Felder, Vieweg Verlag, Braunschweig.Google Scholar
  22. Stachow, E. W. (1978a). “Quantum Logical Calculi and Lattice Structures,”Journal of Philosophical Logic,7, 347.Google Scholar
  23. Stachow, E. W. (1978b). “An Operational Approach to Quantum Probabilities,” in C. A. Hooker, (Ed.)Physical Theory as Logico-Operational Structure, p. 285. D. Reidel, Dordrecht, Holland.Google Scholar
  24. Stachow, E. W. (1979). “Operational Quantum Probabilities,” Abstracts of the 6th International Congress of Logic, Methodology and Philosophy of Science, 1979, Bönecke Druck, Clausthal, Germany.Google Scholar
  25. Stachow, E. W. (1980). “A Model Theoretic Semantics for Quantum Logic,” in P. D. Asquith and R. N. Giere (Eds.),Proceedings of the PSA 1980, East Lansing, Michigan, 1980, p. 272.Google Scholar
  26. Stachow, E. W. (1981a). “Logical Foundations of Quantum Mechanics,”International Journal of Theoretical Physics,19, 251.Google Scholar
  27. Stachow, E. W. (1981b). “Der quantenmechanische Wahrscheinlichkeitskalkül,” in J. Nitsch. J. Pfarr, and E. W. Stachow (Eds.),Grundlagenprobleme der modernen Physik, p. 271. Bibliographisches Institut, Mannheim.Google Scholar
  28. Streater, R. F., and Wightman, A. W. (1964).PCT, Spin and Statistics and All That, W. A. Benjamin, New York.Google Scholar
  29. Vigier, J.-P. (1981). Private Communication.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Peter Mittelstaedt
    • 1
  1. 1.Institut für Theoretische Physik der Universität zu KölnKölnGermany

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