What is a passive symmetry, and what is an active symmetry? I think I know: A passive symmetry is a symmetry that emerges because there are choices (like coordinate system, units system, gauge choice) in the representation of the data. An active symmetry is a symmetry that is observed to be there (like energy conservation). The passive symmetries are true by definition or by construction. THe active symmetries are subject to empirical test. Today Soledad Villar and I spent time talking about a truly formal definition in terms of commutative diagrams.
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