>>12618338I agree that the historical development might be helpful:
Electromagnetism was first developed by Maxwell. I have no idea how he came up with it, but I know for sure it wasn't gauge symmetry. But it doesn't matter for us here how he got it, he did it somehow and people in the 19th century were happy that they had a theory of the electromagnetic field.
Fast forward some years later: Some autist with background in group theory stared long enough at Maxwell's theory and realized you can come up with this shit in another way: Write down a theory without electromagnetic interactions. Then REQUIRE your theory to be invariant under local phase transformations (i.e. U(1) transformations) and see what happens. It turns out that requiring local U(1) symmetry automatically gives you the correct interactions of your theory with the electromagnetic field. Cool, but basically we found a different way to derive something we already knew.
Fast forward some more years: People know from experiment that "weak" and "strong" interactions have to exist on the level of nuclei, but they do not have a satisfactory theory that describes these forces. Many theorists try to come up with a theory for these forces, but most of them fail. Some guy then remembers how another guy once re-derived electromagnetism by requiring invariance under some local transformations.
>mightgiveitatry.exeHe tries some other gauge groups and settles with SU(3), works out the theory and calculates some observables to compare to experiments
>holyshititworks.pngDo it also for the weak interaction. Due to the success of this approach, they then start to refer those theories as "gauge theories".
The important thing to note here is that there are no axioms involved, no meta-principles that dictated those guys to use gauge invariance. They just tried and it turned out it works. This is actually usually how physics works -- a lot of trial and error.
