Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-11T01:05:51.910Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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

REFERENCES

Bub, J. (1979), “The Measurement Problem of Quantum Mechanics”, Proceedings of the International School of Physics “Enrico Fermi”, G. Toraldo di Francia. Amsterdam: North Holland: 71–121.Google Scholar
Finkelstein, D. (1970), “Matter, Space, and Logic”, in Boston Studies in the Philosophy of Science V, Cohen, R. S. and Wartofsky, M., (eds.) Dordrecht: Reidel: 199–215.Google Scholar
Friedman, M. and Glymour, C. (1972), “If Quanta had Logic”, Journal of Philosophical Logic 1 :16–28.CrossRefGoogle Scholar
Friedman, M. and Putnam, H. (1978), “Quantum Logic, Conditional Probability, and Interference”, Dialectica 32, 3–4: 305–315.CrossRefGoogle Scholar
Gudder, S. and Boyce, S. (1970), “A Comparison of the Mackey and Segal Models for Quantum Mechanics”, International Journal of Theoretical Physics 3, 1: 7–21.CrossRefGoogle Scholar
Hardegree, G. (1979), “The Conditional in Abstract and Concrete Quantum Logic”, in The Logico-Algebraic Approach to Quantum Mechanics II, Hooker, C., (ed.) Dordrecht: Reidel: 49–108.CrossRefGoogle Scholar
Hardegree, G. (forthcoming), “Material Implication in Orthomodular (and Boolean) Lattices”, Notre Dame Journal of Formal Logic.Google Scholar
Hellman, G. (1980), “Quantum Logic and Meaning”, Philosophy of Science Association Proceedings 1980 Vol. II, Asquith, P.D. and Giere, R.N., (eds.) East Lansing, MI: PSA.Google Scholar
Jauch, J.M. (1968), Foundations of Quantum Mechanics. Reading, Mass.: Addison-Wesley.Google Scholar
Kochen, S. (unpublished), “The Interpretation of Quantum Mechanics”.Google Scholar
Kochen, S. and Specker, E.P. (1967), “The Problem of Hidden Variables in Quantum Mechanics”, Journal of Mathematics and Mechanics, 17, 1: 59–87.Google Scholar
Piron, C. (1976), Foundations of Quantum Physics. New York: Benjamin.Google Scholar
Putnam, H. (1975), “The Logic of Quantum Mechanics”, in Philosophical Papers, I Cambridge: Cambridge University Press: 215–271.Google Scholar
Quine, W. V. (1953), “Two Dogmas of Empiricism”, in From a Logical Point of View. Cambridge: Harvard University Press.Google Scholar
Quine, W. V. (1960), Word and Object. Cambridge: M.I.T.Google Scholar
Schilpp, P.A. (ed.) (1963), The Philosophy of Rudolf Carnap. La Salle, IL: Open Court.Google Scholar

A correction has been issued for this article:

Corrections