The Role of Symmetry in the Interpretation of Physical Theories
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The symmetries of a physical theory are often associated with two things: conservation laws (via e.g. Noether's and Schur's theorems) and representational redundancies ("gauge symmetry"). But how can a physical theory's symmetries give rise to interesting (in the sense of non-trivial) conservation laws, if symmetries are transformations that correspond to no genuine physical difference? In this article, I argue for a disambiguation in the notion of symmetry. The central distinction is between what I call "analytic" and "synthetic" symmetries, so called because of an analogy with analytic and synthetic propositions. "Analytic" symmetries are the turning of idle wheels in a theory's formalism, and correspond to no physical change; "synthetic" symmetries cover all the rest. I argue that analytic symmetries are distinguished because they act as fixed points or constraints in any interpretation of a theory, and as such are akin to Poincaré's conventions or Reichenbach's 'axioms of co-ordination', or 'relativized constitutive a priori principles'.