Children Are Source Of Embarrassment

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Krab says; "If you only understand it mathematically, then you don't really understand it...". Sir can you be kind & explain to me (not to my 8 years old gaughter) what is local gauge invariance means & how it works in field theory? I would love to see a "qualitative" explanation as to how this principle introduces interaction into the theory.
Thank you for the broom example! Can you do the same thing with the symmetrical spinning top? & tell me who order the littile toy to balance its centre of mass?
 
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