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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Birkhoff, G., and von Neumann, J. (1936). “The Logic of Quantum Mechanics,”Annals of Mathematics,37, 823.
d'Espagnat, B. (1979). “Quantum Theory and Reality,”Scientific American,Nov. p. 128.
Dixmier, J. (1957).Les Algèbres d'Operateur dans L'Espace, Hilbertien, Paris, Gautheir-Villars.
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.
Foulis, D. J. (1960). “Baer*-Semigroups”,Proceedings of the American Mathematical Society,11, 648.
Gudder, S. P. (1971). “Representations of Groups as Automorphism of Orthomodular Lattices and Posets,”Canadian Journal of Mathematics,23, 659.
Jauch, J. M. (1968).Foundations of Quantum Mechanics. Addison-Wesley, Reading. Massachusetts.
Jauch, J. M. (1974). “Quantum Probability Calculus,”Synthese,29, 131.
Koppe, H., and Zapp, H. C. (1983). To be published.
Levi-Leblond, J. M. (1976).American Journal of Physics,44, 271.
Lüders, G. (1951). “Über die Zustandsänderungen durch den Messprozess”,Annalen der Physik,8, 322.
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.
Mittelstaedt, P. (1976b).Philosophical Problems of Modern Physics, Chap. III. D. Reidel, Dordrecht, Holland.
Mittelstaedt, P. (1976/80).Der Zeitbegriff in der Physik, Bibliographisches Institut, Mannheim.
Mittelstaedt, P. (1978).Quantum Logic. D. Reidel, Dordrecht, Holland.
Mittelstaedt, P., and Stachow, E. W. (1978). The Principle of Excluded Middle in Quantum Logic,”Journal of Philosophical Logic,7, 181.
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.
Pfarr, J. (1983). “An Operational Approach to the Lorentz-Transformation,”International Journal of Theoretical Physics (to be published).
Piron, C. (1976).Foundations of Quantum Physics. W. A. Benjamin, New York.
Schlieder, S. (1968). “Einige Bemerkungen zur Zustandsänderung...,”Communications in Mathematical Physics,7, 305.
Schlieder, S. (1971). “Zum kausalen Verhalten eines relativistischen quantenmechanischen Systems,” in P. Dürr (Ed.)Quanten und Felder, Vieweg Verlag, Braunschweig.
Stachow, E. W. (1978a). “Quantum Logical Calculi and Lattice Structures,”Journal of Philosophical Logic,7, 347.
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.
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.
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.
Stachow, E. W. (1981a). “Logical Foundations of Quantum Mechanics,”International Journal of Theoretical Physics,19, 251.
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.
Streater, R. F., and Wightman, A. W. (1964).PCT, Spin and Statistics and All That, W. A. Benjamin, New York.
Vigier, J.-P. (1981). Private Communication.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mittelstaedt, P. Relativistic quantum logic. Int J Theor Phys 22, 293–314 (1983). https://doi.org/10.1007/BF02082895
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02082895