Gauge Symmetry in 60 Seconds!

Transcript

what is gauge symmetry to understand that let's take a look at the map integration is the inverse of differentiation but because differentiation treats all constants the same and counts as an out when we reverse the process with integration say to solve a differential equation we lose that bit of info and are left with an unfixed positive term C in Vector calculus the same logic applies to the curl operation but instead of just a single number we lose an entire conservative vector that means there's a diverse set of fields that can serve as the solution to single pde now imagine it feels like gravity take on any value they like but that kind of inconsistency physics would be impossible right well that's exactly what happens in certain theories of physics called H theories and even though Newton's gravity is in one Maxwell's electromagnetism is and not only does it work out the freedom to choose a certain range of fields without changing the result in physics the property we call gauge symmetry allows us to pick the simplest equations for any problem we find and even extend them the theories like special relativity and quantum mechanics [Music]