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The Projection Postulate: A New Perspective

Published online by Cambridge University Press:  01 April 2022

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

Previous work has shown that the problem of measurement in quantum mechanics is not correctly seen as one of understanding some allegedly univocal process of measurement in nature which corresponds to the projection postulate. The present paper introduces a new perspective by showing that how we are to understand the nature of the change of quantum mechanical state on measurement depends very sensitively on the interpretation of the state function, and by showing how attention to this dependence can greatly sharpen the problems and relations between them. In particular, the problems take a form resembling their traditional formulation only on an inexact value interpretation, according to which the state function attributes inexact values of quantities to systems. On other interpretations we can apply (with various drawbacks) the subensemble idea, according to which a discontinuous change of quantum mechanical description results on measurement simply because we need a new state function to describe a new object.

Type
Research Article
Information
Philosophy of Science , Volume 51 , Issue 3 , September 1984 , pp. 369 - 395
Copyright
Copyright © Philosophy of Science Association 1984

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Footnotes

†

Arthur Fine, Geoffrey Hellman, and two referees provided helpful comments on this work. The research was supported by a National Science Foundation grant #SES-8203560.

References

Ballentine, L. E. (1970), “The Statistical Interpretation of Quantum Mechanics”, Reviews of Modern Physics 42: 358–87.CrossRefGoogle Scholar
Belinfante, F. J. (1975), Measurements and Time Reversal in Objective Quantum Theory. Oxford: Pergamon Press.Google Scholar
Bell, J. S. (1966), “On the Problem of Hidden Variables in Quantum Mechanics”, Reviews of Modern Physics 38: 447–52.CrossRefGoogle Scholar
Blokhintsev, D. T. (1964), Principles of Quantum Mechanics. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Bub, J. (1968), “The Daneri-Loinger-Prosperi Quantum Theory of Measurement”, Nuovo Cimento 57B: 503–20.CrossRefGoogle Scholar
Bub, J. (1975), “Popper's Propensity Interpretation of Probability and Quantum Mechanics”, in G. Maxwell and R. Anderson (eds.). Minnesota Studies in the Philosophy of Science. Vol. VI. Minneapolis: University of Minnesota Press.Google Scholar
Bub, J. (1976), “Randomness and Locality in Quantum Mechanics”, in P. Suppes (ed.). Logic and Probability in Quantum Mechanics. Dordrecht: D. Reidel.Google Scholar
Bub, J. (1979), “On the Quantum Theory of Measurement”, in G. Toraldo di Francia (ed.). Problems in the Foundations of Physics. Amsterdam: North Holland.Google Scholar
Clauser, J., and Shimoney, A. (1978), “Bell's Theorem: Experimental Tests and Implications”, Reports on Progress in Physics 41: 1882–1927.CrossRefGoogle Scholar
d'Espagnat, B. (1976), Conceptual Foundations of Quantum Mechanics. London: W. A. Benjamin, Inc.Google Scholar
Einstein, A. (1950), “Physics and Reality”, in Out of My Later Years. New York: Philosophical Library.Google Scholar
Feyerabend, P. K. (1962), “Problems in Microphysics”, in R. G. Colodney (ed.). Frontiers of Science and Philosophy. Pittsburgh: University of Pittsburgh Press.Google Scholar
Feyerabend, P. K. (1968–69), “On a Recent Critique of Complementarity”, Philosophy of Science 35: 309–31; 36: 82–105.CrossRefGoogle Scholar
Fine, A. (1973), “Probability and the Interpretation of Quantum Mechanics”, British Journal for the Philosophy of Science 24: 1–37.CrossRefGoogle Scholar
Fine, A. (1974), “On the Completeness of Quantum Theory”, Synthese 27: 257–89.Google Scholar
Fine, A. (1982a), “Hidden Variables, Joint Probability, and the Bell Inequalities”, Physical Review Letters 48: 291–95.CrossRefGoogle Scholar
Fine, A. (1982b), “Joint Distributions, Quantum Correlations, and Commuting Observables”, Journal of Mathematical Physics 23: 1306–10.CrossRefGoogle Scholar
Fine, A., and Teller, P. (1979), “Algebraic Constraints on Hidden Variables”, Foundations of Physics 8: 629–36.Google Scholar
Friedman, M., and Putnam, H. (1978), “Quantum Logic, Conditional Probability, and Interference”, Dialectica 32: 305–15.CrossRefGoogle Scholar
Gibbins, T. (1983), “Quantum Logic and Ensembles”, in R. Swinburne (ed.). Space, Time, and Causality. Dordrecht: D. Reidel.Google Scholar
Giere, R. N. (1976), “A Laplacean Formal Semantics for Single-Case Propensities”, Journal of Philosophical Logic 5: 321–53.Google Scholar
Groenewald, H. J. (1957), “Objective and Subject Aspects of Statistics in Quantum Description”, in S. Körner (ed.). Observation and Interpretation. London: Butterworth Publications.Google Scholar
Groenewald, H. J. (1971), “Quantal Observation in Statistical Interpretation”, in T. Bastin (ed.). Quantum Theory and Beyond. Cambridge: Cambridge University Press.Google Scholar
Halpin, J. (forthcoming), “Stalnaker's Conditional and Bell's Problem”.Google Scholar
Heisenberg, W. (1955), “The Development of the Interpretation of the Quantum Theory”, in W. Pauli (ed.). Niels Bohr and the Development of Physics. Oxford: Pergamon Press.Google Scholar
Heisenberg, W. (1958), Physics and Philosophy. London: G. Allen & Unwin.Google Scholar
Hooker, C. (1972), “The Nature of Quantum Mechanical Reality”, in R. G. Colodney (ed.). Paradigms and Paradoxes. Pittsburgh: University of Pittsburgh Press.Google Scholar
Joseph, G. (forthcoming), “Quantum Ensembles and Quantum Probabilities”.Google Scholar
Kemble, E. C. (1951), “Reality, Measurement and the State of the System in Quantum Mechanics”, Philosophy of Science 18: 273–99.CrossRefGoogle Scholar
Kemble, E. C. (1973), The Fundamental Principles of Quantum Mechanics. New York: McGraw-Hill.Google Scholar
Kochen, S., and Specker, E. P. (1967), “The Problem of Hidden Variables in Quantum Mechanics”, Journal of Mathematics and Mechanics 17: 59–87.Google Scholar
Margenau, H. (1936), “Quantum Mechanical Description”, Physical Review 49: 240–42.CrossRefGoogle Scholar
Margenau, H. (1958), “Philosophical Problems Concerning the Meaning of Measurement in Physics”, Philosophy of Science 25: 23–33.CrossRefGoogle Scholar
Margenau, H. (1963a), “Measurement in Quantum Mechanics”, Annals of Physics 23: 469–85.CrossRefGoogle Scholar
Margenau, H. (1963b), “Measurements in Quantum States”, Philosophy of Science 30: 1–16, 138–57.CrossRefGoogle Scholar
Margenau, H., and Hill, R. (1961), “Correlations Between Measurements in Quantum Theory”, Progress of Theoretical Physics 26: 722–38.CrossRefGoogle Scholar
Margenau, H., and Park, J. L. (1967), “Objectivity in Quantum Mechanics”, in M. Bunge (ed.). Delaware Seminar in the Foundations of Physics. Vol. I. New York: Springer.Google Scholar
Popper, K. R. (1982), Quantum Theory and the Schism in Physics. Totowa: Rowman and Littlefield.Google Scholar
Putnam, H. (1968), “Is Logic Empirical?”, in R. Cohen and M. Wartofsky (eds.). Boston Studies in the Philosophy of Science 5, pp. 216–41. Dordrecht: D. Reidel.Google Scholar
Sklar, L. (1970), “Is Probability a Dispositional Property?”, Journal of Philosophy 67: 355–66.CrossRefGoogle Scholar
Sklar, L. (1974), “Review of D. H. Mellor's The Matter of Chance”, Journal of Philosophy 71: 418–23.Google Scholar
Stairs, A. (1983), “On the Logic of Pairs of Quantum Systems”, Synthese: (forthcoming).Google Scholar
Stapp, H. (1971), “S-Matrix Interpretation of Quantum Theory”, Physical Review D 3: 1303–20.CrossRefGoogle Scholar
Stapp, H. (1972), “The Copenhagen Interpretation”, American Journal of Physics 40: 1098–1116.CrossRefGoogle Scholar
Teller, P. (1979), “Quantum Mechanics and the Nature of Continuous Physical Quantities”, Journal of Philosophy 76: 345–61.CrossRefGoogle Scholar
Teller, P. (1981), “The Projection Postulate and Bohr's Interpretation of Quantum Mechanics”, in P. Asquith and R. Giere (eds.). Proceedings of the 1980 Philosophy of Science Association Meetings. Vol. 2. East Lansing: Philosophy of Science Association.Google Scholar
Teller, P. (1983), “The Projection Postulate as a Fortuitous Approximation”, Philosophy of Science 50: 413–31.CrossRefGoogle Scholar
van Fraassen, B. (1974a), “The Einstein-Podolsky-Rosen Paradox”, Synthese 29: 291–310.CrossRefGoogle Scholar
van Fraassen, B. (1974b), “The Labyrinth of Quantum Logics”, in R. Cohen and M. Wartofsky (eds.). Boston Studies in the Philosophy of Science 13, pp. 224–53. Dordrecht: D. Reidel.Google Scholar
van Fraassen, B. (1979), “Foundations of Probability: A Modal Frequency Interpretation”, Problems in the Foundations of Physics. 72 Corso. Bologna: Soc. Italiana di Fisica.Google Scholar