Abstract
A propositional calculus for quantum mechanical systems is presented which formalizes “sequential” connectives “and then” and “or then” for yes-no experiments in the framework of complex Hilbert space. Properties of these connectives are compared with some well-known lattice-theoretical results in quantum logic. Probabilities and objectivization versus the Copenhagen interpretation are discussed in connection with Young's two-slit experiment.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beltrametti, E. G., and Cassinelli, G., (1977). “On state transformations induced by yes-no experiments, in the context of quantum logic,”Journal of Philosophical Logic,6, 369.
Bub, J. (1977). “Von Neumann's Projection Postulate as a probability conditionalization rule in quantum mechanics,”Journal of Philosophical Logic,6, 381.
Hardegree, G. M. (1976). “The conditional in quantum logic,”Logic and Probability in Quantum Mechanics, P. Suppes, ed., p. 55, Reidel, Dordrecht.
Hübner, K. (1964). “Über den Begriff der Quantenlogik,”Sprache im technischen Zeitalter, 925.
Jammer, M. (1974).The Philosophy of Quantum Mechanics. Wiley, New York.
Jauch, J. M. (1968).Foundations of Quantum Mechanics. Addison-Wesley, Reading, Massachusetts.
Lüders, G. (1951). “Über die Zustandsänderung durch den Messprozess,”Annalen der Physik,8, 322.
Mittelstaedt, P. (1959). “Untersuchungen zur Quantenlogik,”Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse, 322.
Mittelstaedt, P. (1970). “Quantenlogische Interpretation orthokomplementärer quasimodularer Verbände,”Zeitschrift für Naturforschung,25A, 1773.
Mittelstaedt, P. (1972). “On the interpretation of the lattice of subspaces of the Hilbert space as a propositional calculus,”Zeitschrift für Naturforschung,27A, 1358.
Mittelstaedt, P. (1976). “On the applicability of the probability concept to quantum theory,”Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. III, Harper and Hooker, eds., p. 155, Reidel, Dordrecht.
Mittelstaedt, P. (1978).Quantum Logic. Reidel, Dordrecht.
Mittelstaedt, P. (1979). “Quantum Logic,”Problems in the Foundations of Physics, p. 264, LXXII Corso, Bologna (Contains a summary of the work on quantum logic by the “Cologne School”),
v. Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, transl. by R. T. Beyer. Princeton U.P., Princeton, New Jersey.
Piron, C. (1964). “Axiomatique quantique,”Helvetica Physica Acta,37, 439.
Piron, C. (1976).Foundations of Quantum Physics. Addison-Wesley, Reading, Massachusetts.
Stachow, E. -W. (1976). “Completeness of quantum logic,”Journal of Philosophical Logic,5 237.
Sz.-Nagy, B. (1967).Spektraldarstellung linearer Transformationen des Hilbertschen Raumes. Springer, Berlin.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rehder, W. Quantum logic of sequential events and their objectivistic probabilities. Int J Theor Phys 19, 221–237 (1980). https://doi.org/10.1007/BF00670678
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00670678