Hi all, my 13yro student dropped a bomb on me asking me what are Gauge Theories.. How do I explain it to him in a meaningful way?
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Gauge theories are about simmetries and “change of coordinates”.
For example, if you take the phenomenon of “uniform motion”, it doesn’t matter where exactly it’s taking place. The physical laws are exactly the same. It also doesn’t matter *when* it happens. Again, the physical laws are always the same. So uniform motion in 2021 New York is exactly the same as uniform motion in 1800 Tokyo. From a mathematical standpoint, if you “change coordinates” (in space-time) you’re simply moving a phenomenon in space and time but you’re not changing how that works from a physics standpoint.
Of course this is a very simple example, but gauge theories are essentially about simmetries and how you can “change coordinates” (not just space and time, it’s an abstract concept where you apply a function to any mathematical variable you want) and still keep the same physical laws, and what this implies.
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