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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

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