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Are symmetry principles laws of nature, or meta-laws of nature? The intuition is that laws of nature are contingent. That is, it could be different in different logically possible worlds. Does this hold true for symmetry principles? Could there be some symmetric principles that had to hold in all possible worlds?

Are symmetry principles laws of nature, or meta-laws of nature? The intuition is that laws of nature are contingent. That is, it could be different in different logically possible worlds. Does this hold true for symmetry principles? Could there be some symmetric principles that had to hold in all possible worlds?

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My view (which I defended in my recent book, "Laws and Lawmakers" from Oxford University Press) is that symmetry principles in physics are widely regarded as meta-laws. For instance, the principle that all first-order laws must be invariant under arbitrary displacement in time or space explains why all first-order laws have this feature (and, in a Hamiltonian framework, ultimately explains why various physical quantities are conserved). The symmetry principles function as constraints upon what first-order laws there could have been. Had there been an additional force, for instance, then the laws governing its operation would have obeyed these symmetry principles, since these symmetry principles are meta-laws. Eugene Wigner and others have suggested that the relation of symmetry principles to the first-order laws they govern is like the relation of those first-order laws to the particular events they govern.

I see no reason why symmetry principles would differ from first-order laws by holding in all possible worlds. It is easy to construct a set of first-order laws that violates any of the classical symmetry principles (e.g., that treats some spatiotemporal locations differently from others). So the symmetry principles seem to be contingent, just as the first-order laws are. However, the symmetry principles could still be more robust under counterfactual antecedents than the first-order laws are. As I said, had there been an additional force law, then it would still have accorded with the classical symmetry principles.