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Nonseparability and Quantum Chaos

Published online by Cambridge University Press:  01 April 2022

Frederick M. Kronz
Frederick M. Kronz*
Affiliation:
Department of Philosophy, The University of Texas at Austin
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Abstract

Conventional wisdom currently has it that chaotic behavior is either strongly suppressed or absent in quantum models. Indeed, some researchers have concluded that these considerations serve to undermine the correspondence principle, thereby raising serious doubts about the adequacy of quantum mechanics as a fundamental physical theory. Thus, the quantum chaos question is a prime subject for philosophical analysis. The most significant reasons given for the absence or suppression of chaotic behavior in quantum models are the linearity of Schrödinger's equation and the unitarity of the time-evolution described by that equation. Both are shown in this essay to be irrelevant by demonstrating that the crucial feature for chaos is the nonseparability of the Hamiltonian. That demonstration indicates that quantum chaos is likely to be exhibited in models of open quantum systems. A measure for probing such models for chaotic behavior is developed, and then used to show that quantum mechanics has chaotic models for systems having a continuous energy spectrum. The prospects of this result for vindicating the essence of the correspondence principle are then briefly examined.

Type
Research Article
Information
Philosophy of Science , Volume 65 , Issue 1 , March 1998 , pp. 50 - 75
Copyright
Copyright © Philosophy of Science Association 1998

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Footnotes

†

Send requests for reprints to the author, Department of Philosophy, The University of Texas at Austin, Austin, TX 78712–1180.

‡

This essay was completed with support from the National Science Foundation, grant number SBR-9602122. I would also like to thank Harald Atmanspacher, Robert Bishop, Jeremy Butterfield, and some anonymous referees for their insightful comments and constructive criticisms on earlier versions of this essay.

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