I have been reading Purcell's electromagnetism. In the text, he talks about conservation of mass, and charge; and invariance of mass, and charge. He says that charge is invariant because results of experiments support it. Mass is not invariant because when a matter moves with constant velocity relative to a stationary observer, it gains some mass (actualy energy).
However, I cannot fully understand invariance of charges. What is the deep meaning of this? It is invariance because of our definition of charge?
When we apply Gauss' Law both mass and charge should be same relative to every refference system (I think).
Can we explain this phenomenon without experiments' result, can we connect this to a fundamental physics?
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