This is just an oddball question that's been rattling around in my head. What evidence do we have that the Coulomb force of, say, a spherical charge distribution Q, is actually nonzero at very large distances? I can easily imagine that the inverse square law is very accurate out to some incredible distance, but maybe has an as-yet-undetected correction that causes the force to actually hit zero at some finite distance. It seems likely that if this distance were large enough, we wouldn't be able to detect any deviation, but have we managed to put any empirical lower bounds on the distance over which the inverse square law holds? I imagine that changing the inverse square law would affect the propagation of light, so does the light from distant galaxies rule this out on the scale of the observable universe?