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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.

Type
Research Article
Information
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