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Is the classical limit “singular”? |
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| Authors: | Jeremy Steeger Benjamin H Feintzeig |
| Institution: | Department of Philosophy, University of Washington, USA;Research Assistant Professor of Philosophy, California Institute of Technology, Caltech M/C 20-7, 1200 East California Blvd, Pasadena, CA, 91125, USA;Department of Philosophy, Swarthmore College, Swarthmore, PA, 19081, USA;San Francisco State University, Physics and Astronomy Department, 1600 Holloway Avenue, San Francisco, CA, 94132, USA;Department of Philosophy, Yale University, New Haven, CT, 06511, USA |
| Abstract: | We argue against claims that the classical ? → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ? → 0 limit. We then use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics. |
| Keywords: | Inter-theory reduction Strict deformation quantization C1-algebras Eliminative reduction Explanation Category theory |
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