Symmetries and the explanation of conservation laws in the light of the inverse problem in Lagrangian mechanics

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2):325-345 (2008)
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Abstract

Many have thought that symmetries of a Lagrangian explain the standard laws of energy, momentum, and angular momentum conservation in a rather straightforward way. In this paper, I argue that the explanation of conservation laws via symmetries of Lagrangians involves complications that have not been adequately noted in the philosophical literature and some of the physics literature on the subject. In fact, such complications show that the principles that are commonly appealed to to drive explanations of conservation laws are not generally correct without caveats. I hope here to give a clearer picture of the relationship between symmetries and conservation laws in Lagrangian mechanics via an examination of the bearing that results in the inverse problem in the calculus of variations have on this topic.

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Sheldon Smith
University of California, Los Angeles

Citations of this work

Classical Mechanics Is Lagrangian; It Is Not Hamiltonian.Erik Curiel - 2014 - British Journal for the Philosophy of Science 65 (2):269-321.
A Primer on Energy Conditions.Erik Curiel - 2017 - In Dennis Lehmkuhl, Gregor Schiemann & Erhard Scholz (eds.), Towards a Theory of Spacetime Theories. Birkhäuser. pp. 43-104.
Symmetries as by-products of conserved quantities.Diego Romero-Maltrana - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):358-368.

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References found in this work

Laws and meta-laws of nature: Conservation laws and symmetries.Marc Lange - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):457-481.
Laws and Meta-Laws of Nature.Marc Lange - 2007 - The Harvard Review of Philosophy 15 (1):21-36.
Armstrong, Cartwright, and Earman on Laws and Symmetry.Bas C. Van Fraassen - 1993 - Philosophy and Phenomenological Research 53 (2):431 - 444.
Armstrong, Cartwright, and Earman on laws and symmetry.Review author[S.]: Bas C. van Fraassen - 1993 - Philosophy and Phenomenological Research 53 (2):431-444.

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