I listened to a lecture several years ago in which the speaker claimed that there is a theorem that shows that violation of charge conservation under classical electrodynamics is impossible in the strictest imaginable sense. I didn't think much of it at the time, but now I'm curious about it and cannot find references to this theorem anywhere.
The argument went something like this:
Assume that there is a region of spacetime in which the conservation of charge may be violated. Outside of this spacetime region, everything is normal, but inside all bets are off. Clearly, this special region must conserve charge as a whole since its temporal boundaries start and end with the traditional rules, but there might be events inside the region which violate charge conservation locally.
At this point, as I recall, he invoked conservation of energy (especially as it relates to electromagnetic radiation propagating out from this special region into the rest of the universe) and asserted that with all other laws of classical physics held in place the boundary of this special spacetime region would either have to be infinite or infinitesimal.
In other words, either the entire universe throughout all of time may violate charge conservation (and therefore violate all manner of other laws) or no part of it ever does. This is the theorem I am curious about. He called this special spacetime region on which the theorem is based an "Electromagnetic Miracle."
Can anyone say conclusively whether or not such a theorem exists?