Laws and meta-laws of nature: Conservation laws and symmetries |
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| Institution: | 1. Department of Physics, Durham University, South Road, Durham DH1 3LE, UK;2. Department of Philosophy, Durham University, 50 Old Elvet, Durham DH1 3HN, UK;1. Department of Humanities and Philosophy, University of Florence, Italy;2. Unit for HPS, University of Sydney, Australia |
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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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