Philosophy of Science 65 (1):50-75 (1998)
Abstract |
Conventional wisdom 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. 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 correspondence principle (or the motivation behind it, at least) are then briefly examined.
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Reprint years | 1998 |
DOI | 10.1086/392626 |
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References found in this work BETA
The Undivided Universe: An Ontological Interpretation of Quantum Theory.David Bohm - 1993 - Routledge.
Unified Dynamics for Microscopic and Macroscopic Systems.GianCarlo Ghirardi, Alberto Rimini & Tullio Weber - 1986 - Physical Review D 34 (D):470–491.
Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony.James T. Cushing - 1994 - University of Chicago Press.
The Undivided Universe: An Ontological Interpretation of Quantum Theory.David Bohm & Basil J. Hiley - 1993 - Routledge.
On the Problem of Hidden Variables in Quantum Mechanics.J. S. Bell - 2004 - In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. pp. 1--13.
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Citations of this work BETA
Non-Integrability and Mixing in Quantum Systems: On the Way to Quantum Chaos.Mario Castagnino & Olimpia Lombardi - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):482-513.
Non-Integrability and Mixing in Quantum Systems: On the Way to Quantum Chaos.Mario Castagnino & Olimpia Lombardi - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):482-513.
View all 7 citations / Add more citations
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