I (naively) have thought symmetries are also about representational invariance. Something about swapping the axis shouldn’t change any measurable outcome, implying certain kinds of symmetry.
It sounds like your naive view was better than mine if you already had that idea, as that’s basically Nate’s point. I see the general ‘definition’ of symmetry in math or physics as “if I change X in Y way, it doesn’t ‘really’ change”. In physics symmetries usually mean there’s a conservation law. Specifically that’s only true for continuous ones, but you can still get important stuff out of the discrete ones like the CPT theorem or fermions vs bosons for exchange symmetry
Neat idea—and that makes sense!
I (naively) have thought symmetries are also about representational invariance. Something about swapping the axis shouldn’t change any measurable outcome, implying certain kinds of symmetry.
It sounds like your naive view was better than mine if you already had that idea, as that’s basically Nate’s point. I see the general ‘definition’ of symmetry in math or physics as “if I change X in Y way, it doesn’t ‘really’ change”. In physics symmetries usually mean there’s a conservation law. Specifically that’s only true for continuous ones, but you can still get important stuff out of the discrete ones like the CPT theorem or fermions vs bosons for exchange symmetry