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                                                    Philosophy of Science

                                                    Article contents

                                                    Quantum Logic, Conditional Probability, and Interference

                                                    Published online by Cambridge University Press:  01 April 2022

                                                    Jeffrey Bub
                                                    Jeffrey Bub*
                                                    Affiliation:
                                                    Department of Philosophy, University of Western Ontario
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                                                    Abstract

                                                    Friedman and Putnam have argued (Friedman and Putnam 1978) that the quantum logical interpretation of quantum mechanics gives us an explanation of interference that the Copenhagen interpretation cannot supply without invoking an additional ad hoc principle, the projection postulate. I show that it is possible to define a notion of equivalence of experimental arrangements relative to a pure state φ, or (correspondingly) equivalence of Boolean subalgebras in the partial Boolean algebra of projection operators of a system, which plays a role in the Copenhagen explanation of interference analogous to the role played by the material equivalence, given φ, of certain propositions in the Friedman-Putnam quantum logical analysis. I also show that the quantum logical interpretation and the Copenhagen interpretation are equally capable of avoiding the paradoxical conclusion of the Einstein-Podolsky-Rosen argument (Einstein, Podolsky, and Rosen 1935). Thus, neither interference phenomena nor the correlations between separated systems provide a test case for distinguishing between the relative acceptability of the Copenhagen interpretation and the quantum logical interpretation as explanations of quantum effects.

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                                                    Research Article
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                                                    Philosophy of Science , Volume 49 , Issue 3 , September 1982 , pp. 402 - 421
                                                    Copyright
                                                    Copyright © Philosophy of Science Association 1982

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                                                    References

                                                    Bub, J. (1977), “Von Neumann's Projection Postulate as a Probability Conditionalization Rule in Quantum Mechanics”, Journal of Philosophical Logic 6: 381–390.CrossRefGoogle Scholar
                                                    Bub, J. (1979), “The Measurement Problem of Quantum Mechanics”, Problems in the Foundations of Physics, Francia, G. Toraldo di (ed.). Amsterdam: North-Holland.Google Scholar
                                                    Einstein, A., Podolsky, B., and Rosen, N. (1935), “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”, Physical Review 47: 777.CrossRefGoogle Scholar
                                                    Fine, A. (1973), “The Two Problems of Quantum Measurement”, Proceedings of the Fourth International Congress for Logic, Methodology and Philosophy of Science, Suppes, P. (ed.). Amsterdam: North Holland.Google Scholar
                                                    Friedman, M. and Putnam, H. (1978), “Quantum Logic, Conditional Probability, and Interference”, Dialectica 32: 305–315.CrossRefGoogle Scholar
                                                    Jauch, J. M. and Piron, C. (1969), “On the Structure of Quantal Proposition Systems”, Helvetia Physica Acta 42: 842.Google Scholar
                                                    Kochen, S. and Specker, E. P. (1967), “The Problem of Hidden Variables in Quantum Mechanics”, Journal of Mathematics and Mechanics 17: 59.Google Scholar
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                                                    This article has been cited by the following publications. This list is generated based on data provided by Crossref.
                                                    Teller, Paul 1983. The Projection Postulate as a Fortuitous Approximation. Philosophy of Science, Vol. 50, Issue. 3, p. 413.
                                                    McGrath, James H. 1986. Quantum Disjunctive Facts. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1986, Issue. 1, p. 76.
                                                    Bub, Jeffrey 1989. On Bohr's response to EPR: A quantum logical analysis. Foundations of Physics, Vol. 19, Issue. 7, p. 793.
                                                    BUB, JEFFREY 1989. The Philosophy of Quantum Mechanics. The British Journal for the Philosophy of Science, Vol. 40, Issue. 2, p. 191.
                                                    Bub, Jeffrey 1990. On Bohr's response to EPR: II. Foundations of Physics, Vol. 20, Issue. 8, p. 929.
                                                    Bub, Jeffrey 1991. The problem of properties in quantum mechanics. Topoi, Vol. 10, Issue. 1, p. 27.
                                                    Pavičić, M. 1992. Bibliography on quantum logics and related structures. International Journal of Theoretical Physics, Vol. 31, Issue. 3, p. 373.
                                                    van Rijsbergen, C. J. 2004. The Geometry of Information Retrieval.
                                                    Epperson, Michael 2020. RELATIONAL REALISM AND THE ONTOGENETIC UNIVERSE. Angelaki, Vol. 25, Issue. 3, p. 108.
                                                    Zhong, Shengyang 2021. Quantum states: an analysis via the orthogonality relation. Synthese, Vol. 199, Issue. 5-6, p. 15015.
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