Abstract
An interpretation of quantum mechanics that rejects hidden variables has to say something about the way measurement can be understood as a transformation on states of individual systems, and that leads to the core of the interpretive problems posed by Luders' projection rule: What, if any, is its physical content? In this paper I explore one suggestion which is implicit in usual interpretations of the rule and show that this view does not stand on solid ground. In the process, important aspects of the role played by the projection postulate in the conceptual structure of quantum mechanics will be clarified. It will be shown in particular that serious objections can be raised against the (often implicit) view that identifies the physical relation of compatibility preserved by Luders' rule with the relation of simultaneous measurability.
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References
Bell, J.: 1982, ‘On the Impossible Wave Pilot’, Foundation of Physics 12.
Bub, J.: 1974, The Interpretation of Quantum Mechanics, D. Reidel, Dordrecht.
Bub, J.: 1979, ‘The Measurement Problem in Quantum Mechanics’, in di Francia (ed.), Problems in the Foundations of Physics, Addison Wesley, Reading, Massachusetts.
Friedman, M. and H. Putnam: 1978, ‘Quantum Logic, Conditional Probability and Interference’, Dialectica 32, 3–4.
Furry, W. H.: 1965, ‘Some Aspects of the Quantum Theory of Measurement’, Theor. Physics Institute, University of Colorado, Summer 1965.
Hardegree, G.: 1976, ‘The Conditional in Quantum Logic’, in P. Suppes (ed.), Logic and Probability in Quantum Mechanics, D. Reidel, Dordrecht.
Hardegree, G.: 1977, ‘Relative Compatibility in Conventional Quantum Mechanics’, Foundations of Physics 7/8, 495–510.
Hellman, G.: 1981, ‘Quantum Logic and the Projection Postulate’, Philosophy of Science 48, 469–86.
Herbut, F.: 1969, ‘Derivation of the Change of State in Measurement from the Concept of Minimal Measurement’, Annals of Physics 55, 271–300
Herbut, F.: 1974, International Journal of Theoretical Physics II, 193–204.
Jauch, J. M.: 1968, Foundations of Quantum Mechanics, Addison Wesley, Reading, Massachusetts.
Jordan, T.: 1969, Linear Operators for Quantum Mechanics, printed by T. Jordan.
Luders, G.: 1951, ‘Uber die Zustansanderung durch den Messprozess’, Ann. d. Phys. 8, 322–28.
Martinez, S.: 1987, ‘The Projection Postulate in the Conceptual Structure of Quantum Mechanics’, Ph.D dissertation, Indiana University.
Martinez, S.: forthcoming, ‘Luders’ Rule as a Description of Individual State Transformations’, forthcoming in Philosophy of Science.
Margenau, H. and J. L. Park: 1968, ‘Simultaneous Measurability in Quantum Theory’, International Journal of Theoretical Physics 1, 211–83.
Margenau, H. and J. L. Park: 1973, ‘The Physics and the Semantics of Quantum Measurement’, Foundations of Physics 3, 19–28.
Muynck, M., P. Janssen, and A. Santman: 1979, ‘Simultaneous Measurement and Joint Probability Distributions in Quantum Mechanics’, Foundations of Physics, 9, 712–22.
Stairs, A.: 1982, ‘Discussion: Quantum Logic and Luders' Rule’, Philosophy of Science 49, 422–36.
Stein, H. and A. Shimony: 1971, ‘Limitations on Measurements’, in B. d'Espagnat (ed.), Foundations of Quantum Mechanics, Academic Press, New York, pp. 55–76.
Teller, P.: 1983, ‘The Projection Postulate as a Fortuitous Approximation’, Philosophy of Science 50, 413–31.
Von Neumann, J.: 1955, Mathematical Foundations of Quantum Mechanics (trans. by R. T. Beyer), Princeton, New Jersey.
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This paper consists for the most part in material drawn from my dissertation (Martinez 1987) directed by Linda Wessels and Geoffrey Hellman.
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Martinez, S. A search for the physical content of Luders' rule. Synthese 82, 97–125 (1990). https://doi.org/10.1007/BF00413671
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DOI: https://doi.org/10.1007/BF00413671