
20180711: Quantum Invariance & The Origin of The Standard Model
 05:16: This position dependent phase shift is called a local phase shift, instead of a global phase shift.
 05:21: We'll try this because, well, we already know that the magnitude squared of the wave function should still stay the same under local phase shifts.
 05:38: ... if we do a local phase shift, say, only this point here, only that location changes, as if it ...
 05:50: If you allow this sort of local phase shift, you can change each point in a different way and really mess up the wave function.
 06:08: Among other things, messing with local phase really screws up our prediction for the particle's momentum.
 06:19: Change the shape of that wave function with local phase shifts and you actually break conservation of momentum.
 06:26: Local phase is not a gauge symmetry of the basic Schrodinger equation.
 06:38: Just for funsies, maybe we can change the Schrodinger equation to find a version that really is invariant to local phase shifts.
 07:34: ... we've discovered that the only way for particles to have local phase invariance is for us to introduce a new fundamental field that pervades ...
 08:24: Any particle that has this kind of charge will interact with and be affected by the electromagnetic field and be granted local phase invariance.
 08:35: In order to have this particular type of local phase invariance, particles must possess electric charge.
 08:48: In this case, the symmetry is local phase invariance and the conserved quantity is electric charge.
 09:41: It turns out that local phase invariance is just the simplest of the larger suite of gauge symmetries of the standard model.
