Incoming links: Gauge theory
This shows that viewing electromagnetism as gauge theory does have experimentally observable consequences. TODO understand what that means.
In more understandable terms, it shows that the magnetic vector potential matters where the magnetic field is 0.
The Quantum Experiment that ALMOST broke Locality by The Science Asylum (2019)
Source. Published on the session reports of the Royal Prussian Academy of Sciences at Berlin 1918 page 464.
Is about Maxwell's equations in curved spacetime, and notably introduces gauge theory.
Viewable for free at: archive.org/details/mobot31753002089727/page/464/mode/2up.