Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-20T22:42:57.133Z Has data issue: false hasContentIssue false
  • English
  • Français

Micro-States in the Interpretation of Quantum Theory

Published online by Cambridge University Press:  28 February 2022

Gary M. Hardegree
Gary M. Hardegree*
Affiliation:
University of Massachusetts, Amherst
Get access Rights & Permissions [Opens in a new window]

Extract

In the present work, I discuss the interpretation of quantum mechanics (QM) from the viewpoint of quantum logic (QL). I regard the objects of QL to be the possible (accidental) properties that can be ascribed to a quantum system SYS. The basic idea is that, at any given moment t, SYS actualizes some properties, but not others. The micro-state of SYS at time t is identified with the set of all properties that SYS actualizes at time t.

One thing an interpretation of QM is supposed to do, I believe, is delineate the admissible quantum micro-states. Since the characterization of quantum micro-states is intimately related to the characterization of quantum logical consistency, the interpretation of QM is intimately tied to the interpretation of QL.

Two kinds of interpretations are discussed. Strict interpretations are based on the assumption that the properties of a system are individuated by the projection operators on the associated Hilbert space.

Type
Part II. Quantum Logic and the Interpretation of Quantum Mechanics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1980 , Issue 1: Volume One: Contributed Papers 1980 , 1980 , pp. 42 - 54
Copyright
Copyright © 1980 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.)

References

Abbott, J.C. (1967). “Semi-Boolean Algebra.” Mathematicki Vesnik 4: 177–198.Google Scholar
Birkhoff, G. and von Neumann, J. (1936). “The Logic of Quantum Mechanics.” Annals of Mathematics 37: 823–13.CrossRefGoogle Scholar
Fine, A. (1974). “On the Completeness of Quantum Mechanics.” Synthese 29: 257–89.CrossRefGoogle Scholar
Gleason, A.M. (1957). “Measures on the Closed Subspaces of Hilbert Space.” Journal of Mathematics and Mechanics 6: 885–93.Google Scholar
Hardegree, G.M. (1979). “Reichenbach and the Interpretation of Quantum Mechanics.” In Hans Reichenbach: Logical Empiricist. Edited by Salmon, W.C. Dordrecht: D. Reidel. Pages 513–566.CrossRefGoogle Scholar
Hardegree, G.M. and Frazer, P.J. (1980). “Charting the Laybrinth of Quantum Logics.” In Proceedings of a Workshop on Quantum Logic. Edited by Beltrametti, E. New York: Plenum Press. In press.Google Scholar
Jauch, J.M. (1968). Foundations of Quantum Mechanics. Reading, MA: Addison-Wesley.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
Kochen, S. and Specker, E.P. (1980). The Interpretation of Quantum Mechanics.” Unpublished manuscript.Google Scholar
Piron, C. (1976). Foundations of Quantum Physics. Reading, MA: W.A. Benjamin.Google Scholar
Reichenbach, H. (1944). Philosophic Foundations of Quantum Mechanics. Los Angeles and Berkeley: University of California Press.Google Scholar
van Fraassen, B.C. (1973). “Semantic Analysis of Quantum Logic.” In Contemporary Research in the Foundations and Philosophy of Quantum Theory. (The University of Western Ontario Series in the Philosophy of Science, vol. 2). Edited by Hooker, C.A. Dordrecht: D. Reidel. Pages 80–113.Google Scholar
von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin: Springer. (Translated by R.T. Beyer as The Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press, 1955).Google Scholar
Wigner, E. (1931). Gruppentheorie und ihre Anwendung. Vieweg: Braunschweig. (Translated by J.J. Griffen as Group Theory. New York: Academic Press, 1959).Google Scholar