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The Projection Postulate as a Fortuitous Approximation

Published online by Cambridge University Press:  01 April 2022

Paul Teller*
Affiliation:
Department of Philosophy, University of Illinois, Chicago

Abstract

If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal “measurement process” in nature. This fact suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics.

Type
Research Article
Copyright
Copyright © Philosophy of Science Association 1983

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Footnotes

Much of this research was supported by NSF grant #SES-8108175. My thinking has been guided at a great many points by the work of Geoffrey Hellman, Michael Friedman, Jeffrey Bub, Allen Stairs, and Arthur Fine. Two anonymous referees insisted on more careful treatment at a number of crucial junctures, thereby greatly strengthening the paper.

References

Bub, J. (1982), “Quantum Logic, Conditional Probability, and Interference”, Philosophy of Science 49: 402421.10.1086/289068CrossRefGoogle Scholar
Fine, A. (1969), “On the General Quantum Theory of Measurement”, Proceedings of the Cambridge Philosophical Society 65: 111122.10.1017/S0305004100044145CrossRefGoogle Scholar
Friedman, M. and Putnam, H. (1978), “Quantum Logic, Conditional Probability and Interference”, Dialectica 32: 305315.10.1111/j.1746-8361.1978.tb01319.xCrossRefGoogle Scholar
Hellman, G. (1981), “Quantum Logic and the Projection Postulate”, Philosophy of Science 48: 469486.10.1086/289011CrossRefGoogle Scholar
Herbert, F. (1974), “Minimal Disturbance Measurement as a Specification in von Neumann's Quantal Theory of Measurement”, International Journal of Theoretical Physics 11: 193204.10.1007/BF01809569CrossRefGoogle Scholar
Lüders, G. (1951), “Über die Zustandsäderung durch den Messprozess”, Annalen der Physik 8: 322328.Google Scholar
Margenau, H. (1936), “Quantum Mechanical Description”, Physical Review 49: 240242.10.1103/PhysRev.49.240CrossRefGoogle Scholar
Margenau, H. (1958), “Philsophical Problems Concerning the Meaning of Measurement in Physics”, Philosophy of Science 25: 2333.10.1086/287574CrossRefGoogle Scholar
Stairs, A. (1982), “Quantum Logic and the Lüders Rule”, Philosophy of Science 49: 422436.10.1086/289069CrossRefGoogle Scholar
Teller, P. (1976), “Conditionalization, Observation and Change of Preference”, in Harper, W. and Hooker, C., eds: Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Dordrecht: D. Reidel.Google Scholar
von Neumann, J. (1955), Mathematical Foundations of Quantum Mechanics. Princeton, N.J.: Princeton University Press.Google Scholar