Relativistic Charge and Cosmic Expansion: A Reformulation of Electromagnetism in Which the Proton Rest Charge is the Fundamental Invariant

We propose a reformulation of relativistic electromagnetism in which the rest charge of the proton is the fundamental Lorentz-invariant quantity e₀, while the electron's rest charge is velocity-dependent, q₀ (e) = e₀/gamma, in exact structural analogy with the relativistic mass relation m = gamma m₀. The electron's moving (observed) charge always equals e₀ in magnitude, preserving local electromagnetic neutrality. We prove that this reformulation is mathematically identical to standard relativistic electromagnetism at the classical level: the electromagnetic four-current JBᵐu is equal to the standard current Jᵐu, leaving Maxwell's equations, all field solutions, the Lorentz force, and every experimental prediction unchanged. We further demonstrate that the framework is consistent with quantum electrodynamics at all current levels of experimental precision, and identify two candidate regimes in which a full quantum extension would require non-trivial choices. Finally, we apply the reformulation to a cosmic hydrogen plasma (neglecting gravity) and show that the proton-electron rest-charge asymmetry, which arises naturally from the thermal velocity difference between the species, generates an effective repulsive pressure proportional to distance. This yields Hubble's recession law v = Hr with Hubble parameter H = sqrt (N e₀² epsilon / 3 epsilon₀ mH), where eps = 1-1/gmₑ encodes the electron thermal velocity. The mechanism requires no modification of Maxwell's equations, no dark energy, and no fine-tuned cosmological constant.