Laws and meta-laws of nature: Conservation laws and symmetries

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):457-481 (2007)
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Abstract

Symmetry principles are commonly said to explain conservation laws—and were so employed even by Lagrange and Hamilton, long before Noether's theorem. But within a Hamiltonian framework, the conservation laws likewise entail the symmetries. Why, then, are symmetries explanatorily prior to conservation laws? I explain how the relation between ordinary (i.e., first-order) laws and the facts they govern (a relation involving counterfactuals) may be reproduced one level higher: as a relation between symmetries and the ordinary laws they govern. In that event, symmetries are meta-laws; they are not mere byproducts of the dynamical and force laws. Symmetries then explain conservation laws whereas conservation laws lack the modal status to explain symmetries. I elaborate the variety of natural necessity that meta-laws would possess. Proposed metaphysical accounts of natural law should aim to accommodate the distinction between meta-laws and mere byproducts of the laws just as they must accommodate the distinction between laws and accidents.

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Marc Lange
University of North Carolina, Chapel Hill

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References found in this work

The world as one of a kind: Natural necessity and laws of nature.John Bigelow, Brian Ellis & Caroline Lierse - 1992 - British Journal for the Philosophy of Science 43 (3):371-388.
Symmetry in intertheory relations.M. L. G. Redhead - 1975 - Synthese 32 (1-2):77 - 112.
Laws and their stability.Marc Lange - 2005 - Synthese 144 (3):415Ð432.
Symmetries and Noether's theorems.Katherine Bracing & Harvey R. Brown - 2003 - In Katherine A. Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press. pp. 89.

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