I've just watched one of Feynman's lectures on the character of physical law where he was talking about conservation laws. In that particular part he was reasoning why a mass can't "jump" from one place to another (link) which he elegantly proved would be a violation of angular momentum. While I get this, is there no other way to prove this? It seems odd that all the laws of motion and conservation of momentum laws can't reason against a simple mass jump.
Does a jump violate the continuity equation? And maybe some other, more fundamental law? Also the angular momentum reasoning can't be used against the jump of a charge.