I have just learned that sunlight traveling through the earth's atmosphere picks up a net polarization by collisions with molecules ($O_2$, $N_2$, etc.) that the photons encounter. One would think that those molecules would have to possess some degree of common alignment in order to produce light...

Symmetries that have non-trivial effects on observables must be preserved by dualities (equivalences between different-looking quantum field theories), because the equivalence relation preserves observables by definition. Gauge symmetries don't affect observables, so two quantum field theories ca...