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Lüders's Rule as a Description of Individual State Transformations

Published online by Cambridge University Press:  01 April 2022

Sergio Martinez
Sergio Martinez*
Affiliation:
Instituto de Investigaciones Filosoficas Universidad National Autonoma de Mexico
*
‡Send reprint requests to Instituto de Investigaciones Filosoficas, Universidad Nacional Autonoma de Mexico, Circ. Mario de la Cueva, 04510 Coyoacan, MEXICO, D.F.
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Abstract

Usual derivations of Lüders's projection rule show that Lüders's rule is the rule required by quantum statistics to calculate the final state after an ideal (minimally disturbing) measurement. These derivations are at best inconclusive, however, when it comes to interpreting Lüders's rule as a description of individual state transformations. In this paper, I show a natural way of deriving Lüders's rule from well-motivated and explicit physical assumptions referring to individual systems. This requires, however, the introduction of a concept of individual state which is not standard.

Type
Research Article
Information
Philosophy of Science , Volume 58 , Issue 3 , September 1991 , pp. 359 - 376
Copyright
Copyright © 1991 The Philosophy of Science Association

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Footnotes

†

I would like to thank Linda Wessels and Geoffrey Hellman who directed the research on which this paper is based. I also would like to thank an anonymous referee of this Journal for valuable comments.

References

Beltrametti, E. G. and Cassinelli, G. (1981), The Logic of Quantum Mechanics. Reading, MA: Addison-Wesley.Google Scholar
Bub, J. (1979), “The Measurement Problem of Quantum Mechanics”, in T. di Francia (ed.), Physics. Reading, MA: Addison-Wesley, pp. 71–124.Google Scholar
Friedman, M. and Putnam, H. (1978), “Quantum Logic, Conditional Probability, and Interference”, Dialectica 32: 305–315.CrossRefGoogle Scholar
Hardegree, G. M. (1980), “Micro-States in the Interpretation of Quantum Theory”, in P. D. Asquith and R. N. Giere, (eds.), PSA 1980, vol. 1. East Lansing: Philosophy of Science Association, pp. 43–54.Google Scholar
Herbut, F. (1969), “Derivation of the Change of State in Measurement from the Concept of Minimal Measurement”, Annals of Physics 55: 271–300.CrossRefGoogle Scholar
Kochen, S. (1979), “The Interpretation of Quantum Mechanics”, Department of Mathematics, Princeton University. Unpublished manuscript.Google Scholar
Lüders, G. (1951), “Über die Zustansänderung durch den Messprozess”, Annalen der Physik 8: 322–328.Google Scholar
Maeda, F. and Maeda, S. (1970), Theory of Symmetric Lattices. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Martinez, S. (1988), “Minimal Disturbance in Quantum Logic”, in A. Fine and J. Leplin (eds.), PSA 1988, vol. 1. East Lansing: Philosophy of Science Association, pp. 83–88.Google Scholar
Martinez, S. (1990), “A Search for the Physical Content of Lüders's Rule”, Synthese 82: 97–125.CrossRefGoogle Scholar
Mielnik, B. (1968), “Geometry of Quantum States”, Communications in Mathematical Physics 9: 55–80.CrossRefGoogle Scholar
Piron, C. (1976), Foundations of Quantum Physics. Reading, MA: Benjamin.Google Scholar
Stairs, A. (1982), “Discussion: Quantum Logic and the Lüders Rule”, Philosophy of Science 49: 422–436.CrossRefGoogle Scholar
van Fraassen, B. C. and Hooker, C. A. (1976), “A Semantic Analysis of Niels Bohr's Philosophy of Quantum Theory”, in W. L. Harper and C. A. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Vol. 3, Foundations and Philosophy of Statistical Theories in the Physical Sciences. Dordrecht: Reidel, pp. 221–241.CrossRefGoogle Scholar
von Neumann, J. ([1932] 1955), Mathematical Foundations of Quantum Mechanics. Translated by R. T. Beyer. Originally published as Mathematische Grundlagen der Quantenmechanik. (Berlin: Springer-Verlag.) Princeton: Princeton University Press.Google Scholar