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Intimate Connections: Symmetries and Conservation Laws in Quantum versus Classical Mechanics

Published online by Cambridge University Press:  01 January 2022

Pablo Ruiz de Olano
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Abstract

In this article, I use a number of remarks made by Eugene Wigner to defend the claim that the nature of the connection between symmetries and conservation laws is different in quantum and in classical mechanics. In particular, I provide a list of three differences that obtain between the Hilbert space formulation of quantum mechanics and the Lagrangian formulation of classical mechanics. I also show that these differences are due to the fact that conservation laws are not the only consequence that symmetries have in quantum mechanics and to the fact that, in classical mechanics, the connection between symmetries and conservation laws does not always obtain.

Type
Physical Sciences
Information
Philosophy of Science , Volume 84 , Issue 5 , December 2017 , pp. 1275 - 1288
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

A version of this article was presented at the Universities of Cambridge and Oxford in the winter of 2015. I would like to thank Jeremy Butterfield and Chris Timpson for organizing these talks and the audience at these two events for their comments and suggestions. I would also like to thank Katherine Brading, Harvey Brown, Anjan Chakravartty, Don Howard, and Nicholas Teh for their feedback on previous versions of this article.

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