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What Are the Symmetries of the Real World?
Gauge symmetry is one of the more complicated type of symmetries. It's a basic principle that a theorem that's true here is also true over there. And same for a physical law, right? I mean, if gravity is like this over here, it should also be like this over there. All the laws of physics should be unchanged if the symmetry we have in mind is a very simple one like translation.