Steeger, Jer and Feintzeig, Benjamin H. (2021) Is the Classical Limit "Singular"? [Preprint]

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Abstract

We argue against claims that the classical ℏ→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 ℏ→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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Steeger, Jer jsteeger@uw.edu 0000-0003-2771-4145 Feintzeig, Benjamin H. bfeintze@uw.edu
Additional Information:	Final version submitted to Studies in History and Philosophy of Science.
Keywords:	classical limit, singular limits, inter-theory reduction, C*-algebras, strict deformation quantization
Subjects:	Specific Sciences > Physics > Quantum Mechanics General Issues > Reductionism/Holism Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Jer Steeger
Date Deposited:	25 May 2021 01:35
Last Modified:	17 Sep 2022 00:49
Item ID:	19097
Subjects:	Specific Sciences > Physics > Quantum Mechanics General Issues > Reductionism/Holism Specific Sciences > Physics > Symmetries/Invariances
Date:	24 May 2021
URI:	https://philsci-archive.pitt.edu/id/eprint/19097

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