Timeline for How the continuity equation $\partial_\mu j^\mu=0$ means current conservation?

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Jul 27, 2017 at 18:08	comment	added	Jahan Claes		@Soap Intuitively, global conservation says that total charge is conserved, but doesn't forbid charge from spontaneously teleporting across the universe. Local conservation says that to decrease the charge, you need to have a finite current density out of a volume. So things can't teleport instantaneously.
Jul 27, 2017 at 18:07	comment	added	Jahan Claes		@Soap No, local conservation of charge is strictly stronger than global conservation of charge. It's possible to go from local conservation to global conservation, but if you only know global conservation you can't derive local conservation.
Jul 27, 2017 at 13:08	comment	added	soap		But is conservation of charge equivalent to $\partial_\mu j^\mu=0$? How can you go from $\frac{d}{dt}\int\rho=0$ to $\partial_\mu j^\mu=0$? i.e. does the global conservation of charge imply what apparently one calls conservation of current (which is local in some sense)? Peskin and Schroeder seem to suggest this.
Jul 27, 2017 at 7:49	vote	accept	soap
Jul 27, 2017 at 1:01	history	answered	Jahan Claes	CC BY-SA 3.0