Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-04T02:21:32.901Z Has data issue: false hasContentIssue false
  • English
  • Français

The Trouble with Superselection Accounts of Measurement

Published online by Cambridge University Press:  01 April 2022

Mariam Thalos
Mariam Thalos*
Affiliation:
Department of Philosophy, State University of New York at Buffalo
*
†Send requests for reprints to the author, Department of Philosophy, State University of New York at Buffalo, 607 Baldy Hall, Buffalo, NY 14620-1010; e-mail: thalos@acsu.buffalo.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

A superselection rule advanced in the course of a quantum-mechanical treatment of some phenomenon is an assertion to the effect that the superposition principle of quantum mechanics is to be restricted in the application at hand. Superselection accounts of measurement all have in common a decision to represent the indicator states of detectors by eigenspaces of superselection operators named in a superselection rule, on the grounds that the states in question are states of a so-called classical quantity and therefore not subject to quantum interference effects. By this strategy superselectionists of measurement expect to dispense with use of projection postulates in treatments of measurement. I shall argue that superselection accounts of measurement are self-contradictory, and that treatments of infinite systems, if they can avoid the contradiction, are not true superselection accounts.

Type
Research Article
Information
Philosophy of Science , Volume 65 , Issue 3 , September 1998 , pp. 518 - 544
Copyright
Copyright © Philosophy of Science Association 1998

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.)

Footnotes

‡

For helpful discussions and critical remarks on early drafts, I would like to thank Arthur Fine and Michael Friedman, as well as two anonymous referees for this journal. For first-rate editorial direction, I would like to thank Jeremy Butterfield. And for what remains dark or unintelligible at this late stage, in spite of all the help I have received, I have only myself to thank.

References

[1] Araki, Huzihiro. On superselection rules. Proc. 2nd Int. Symp. Foundations of Quantum Mechanics, pp. 348–354, 1986.Google Scholar
[2] Enrico, G. Beltrametti and Gianni Cassinelli. The Logic of Quantum Mechanics. Addison-Wesley Publishing Company, Reading, MA, 1981.Google Scholar
[3] Bohm, A. and Gadella, M. Dirac Kets, Gamow Vectors and Gel'fand Triplets. Springer-Verlag, New York, 1989.10.1007/3-540-51916-5CrossRefGoogle Scholar
[4] Bohm, Arno. Quantum Mechanics: Foundations and Applications. Springer-Verlag, New York, 1986.10.1007/978-3-662-01168-3CrossRefGoogle Scholar
[5] Brown, Harvey R. The insolubility proof of the quantum measurement problem. Foundations of Physics, 16(9): 847–870, 1986.10.1007/BF00765334CrossRefGoogle Scholar
[6] Bub, J. How to solve the measurement problem of quantum mechanics. Foundations of Physics, 18(7): 701–722, 1988.Google Scholar
[7] Bub, J. Measurement and “beables” in quantum mechanics. Foundations of Physics, 21(1): 25–42, 1988.Google Scholar
[8] Bub, J. From micro to macro: A solution to the measurement problem of quantum mechanics. PSA 1988, 2: 134–144, 1989.Google Scholar
[9] Bub, J. On states and probabilities in quantum mechanics. Supplemento ai Rendiconti del Circolo Matematico di Palermo, II(25): 109–132, 1991.Google Scholar
[10] Daneri, A., Loinger, A., and Prosperi, G. M. Quantum theory of measurement and ergodicity conditions. Nuclear Physics, 33,: 297–319, 1962.CrossRefGoogle Scholar
[11] Duhem, Pierre. Le mixte et la combinaison chimique: Essai sur l'evolution d'une idee. Fayard, Paris, 1902.Google Scholar
[12] Fine, Arthur. Insolubility of the quantum measurement problem. The Physical Review D, 2(12): 2783–2787, 1970.Google Scholar
[13] Hughes, R. I. G. The Structure and Interpretation of Quantum Mechanics. Harvard University Press, Cambridge, 1989.10.1063/1.2811188CrossRefGoogle Scholar
[14] Jordan, Thomas F. Linear Operators for Quantum Mechanics. Thomas Jordan, Duluth, MN, 1969.CrossRefGoogle Scholar
[15] Legett, A. J. Schrodinger's cat and her laboratory cousins. Contemporary Physics, 25(6): 583–598, 1984.Google Scholar
[16] Machida, Shigeru and Namiki, Mikio. Proposal of experimental test of “environment-induced superselection rule” in quantum measurement theory. Proc. 2nd Int. Symp. Foundations of Quantum Mechanics, pp. 355–359, 1986.Google Scholar
[17] Needham, Paul. Macroscopic objects: An exercise in Duhemian ontology. Philosophy of Science, 63: 205–224, 1996.10.1086/289909CrossRefGoogle Scholar
[18] Shimony, Abner. Approximate measurement in quantum mechanics. ii. Physical Review D, 9,: 2321–2323, 1974.10.1103/PhysRevD.9.2321CrossRefGoogle Scholar
[19] Stein, Howard. On a theorem of Fine and Shimony.Google Scholar
[20] van Fraassen, Bas C. Quantum Mechanics: An Empiricist View. Clarendon Press, Oxford, 1991.10.1093/0198239807.001.0001CrossRefGoogle Scholar
[21] Wan, K. K. and Harrison, F. E. Superconducting rings, superselection rules and quantum measurement problems. Physics Letters A, 174: 1–8, 1993.CrossRefGoogle Scholar
[22] Wan, Kay-Kong. Superselection rules, quantum measurement, and the Schrodinger's cat. Canadian Journal of Physics, 58: 976–982, 1980.10.1139/p80-135CrossRefGoogle Scholar
[23] Weyl, Hermann. The Theory of Groups and Quantum Mechanics. Dover, New York, 1950.Google Scholar
[24] Wigner, E. The problem of measurement. American Journal of Physics, 31: 6–15, 1963.CrossRefGoogle Scholar