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Quantum Logic and the Projection Postulate

Published online by Cambridge University Press:  01 April 2022

Geoffrey Hellman
Geoffrey Hellman*
Affiliation:
Department of Philosophy, Indiana University
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Abstract

This paper explores the status of the von Neumann-Lüders state transition rule (the “projection postulate”) within “real-logic” quantum logic. The entire discussion proceeds from a reading of the Lüders rule according to which, although idealized in applying only to “minimally disturbing” measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effect that QL has an explanatory advantage over Copenhagen and other interpretations which relativize truth-value assignments to experimental arrangements. Two versions of QL, the lattice-theoretic (LT) and partial-Boolean-algebra (PBA), are considered. It turns out that the projection postulate is intimately connected with the choice of conditional connective for QL. The effect of the projection postulate is obtained with the Sasaki conditional. However, this choice is found to require extra assumptions, on both the LT and PBA versions, which are either just as ad hoc as the projection postulate itself or indefensible from within the real-logic QL framework.

Type
Research Article
Information
Philosophy of Science , Volume 48 , Issue 3 , September 1981 , pp. 469 - 486
Copyright
Copyright © 1981 by the Philosophy of Science Association

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Footnotes

†

This material is based in part upon work supported by the National Science Foundation under Grant No. SES-7924874. I am grateful to Linda Wessels, Gary Hardegree and the Quantum Mechanics Study Group at Indiana University for helpful discussion and to a referee for valuable comments on an earlier draft of this paper.

References

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