Lorentz invariants

[QuArK21343]

Why is it that charge is Lorentz invariant (it's a scalar, independent of the frame of reference) whereas mass is not? Does this mean that the gravitational force a body exerts depends on the frame of reference, whereas the electric force doesn't?

[Bill_K]

The mass of a particle is also a Lorentz invariant. You may be thinking of the relativistic mass γm.

[QuArK21343]

Ok, since this is new to me, could you clarify the difference between the two? Do you mean the rest mass is Lorentz invariant? Anyway, there is no analogue to relativistic mass as far as charge is concerned (no relativistic charge), right?

[Bill_K]

"Relativistic mass" is a highly misleading concept and should be avoided. Its use arose simply because the relativistic expression for the momentum happens to be p = γmv, and in trying to make look like the nonrelativistic formula it was written p = Mv where M = γm.

The Lorentz force equation can be written (τ is proper time)

dp/dτ = γe(E + v/c x B)

and sure enough there's the combination γe, but I would not recommend defining this as the "relativistic charge" either!