Local Conservation of Charge: Feynman's Thought Experiment Explained

[AlchemistK]

I was watching the messenger lectures by Feynman and in the third lecture he talks about conservation. In the beginning he talks about the conservation of charge, and at one point demonstrates a thought experiment in which two observers, one stationary and the other moving, see a charge disappear at one point in front of them and another similar charge reappear behind them. The person stationary with respect to the charges see the charge appear at the same time it disappears, but the second person disagrees because of his movement.
Then Feynman states that charge is conserved locally.
What does he mean by that?

(He also states that if something is conserved, it must also be conserved locally.)

 

[MrRobotoToo]

It means something like this: if the amount of charge at some point in space changes value from Q1 to Q2 in a time interval from T1 to T2, then there exists a surface surrounding the point such that an amount of charge equal to Q2-Q1 passes through the surface in the same time interval. It's just a way of saying that for a conserved quantity such as charge to change value at a point, it must do so by moving in a smooth and continuous way to some nearby point(s).