Charge invariance

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Charge invariance refers to the fixed electrostatic charge of a particle, regardless of speed. For example, an electron has a specific charge at rest. At a velocity v, the charge remains the same (as opposed to the energy increasing). Some particle characteristics are relativisticly invariant (charge and mass). Others, like energy, change with velocity. Typically, we write:

Ev = γmc2,

mv = m

ev = e.,

where the subscript v represent the quantity at speed v. The key factor is

\gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}},

which is a function of speed (relative to some rest frame. The first equation above describes relativistic energy, the second – invariant mass, the third – charge invariance. Notice that γ does not appear in the second and third lines. where E0 = mc2 and m0 refers to rest energy). So, to say "rest charge" or "rest mass" is redundant. Notice also that as v (speed) increases, γ increases, and so E (and increases too.

The property of charge invariance follows from the vanishing divergence of the charge-current four-vector j^\mu=(c\rho,{\vec j}), with \partial_\mu j^\mu=0.

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