I just learned the scalar and vector potentials arising from the electric and magnetic fields have a physical reality in relation to quantum mechanical effects, such as the Aharonov-Bohm effect. Contrary to what I've learned from my course on electrodynamics (Griffiths) this sure must mean they propagate with a finite speed. Can you say that from maxwells equations they must have the same velocity as the fields? Are there any other effects than a change in phase of a particles wavefunction observed or found? And is the velocity at wich the potential propagate experimentally measured?