I'm wondering what's the real difference between symmetry and invariance in Physics? I believe that sometimes the two words are given the same meaning and some other times they are used in a different way.
To me a symmetry is more of a physical property: if you rotate the experiment-table and you get the same results, the system is symmetric with respect to rotations.
While invariance is a mathematical concept, like a gauge transformation.
Is it right to think about it this way? Any insights?
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