A charged photon and its light-speed helical trajectory form a surprising new solution to the relativistic electron's energy-momentum equation E^2 = p^2 c^2 + m^2 c^4. This charged photon is a new model for the electron, and quantitatively resembles the light-speed electron described by Dirac. His relativistic quantum mechanical equation for the electron was derived from the above energy-momentum equation. While the electron's energy is E = gamma mc^2, the charged photon's energy is E = gamma mc^2=hf . The electron's relativistic momentum p = gamma mv is the longitudinal component of the charged photon's helically circulating momentum p total = gamma mc . At any electron speed, the charged photon has an internally circulating transverse momentum p trans = mc , which at the helical radius Ro = L Compton/4pi =1.93 x 10^-13 m for a resting electron produces the z -component hbar/2 of the electron's spin. The right and left turning directions of the charged photon's helical trajectory correspond to a spin up (sz = +hbar/2) and spin down (sz = -hbar/2) electron. The negative and positive possible charges of the charged photon correspond to the electron and the positron. The circulating charged photon at the helical radius Ro produces one-half of the electron's pre-QED magnetic moment µ = µ Bohr predicted by the Dirac equation. There is a relativistic variation with the electron's speed v of the charged photon's helical radius R = Ro / (gamma)^2 and its helical pitch P = (2pi v/gamma c) Ro . The pitch has a maximum value P max = pi Ro when the electron's speed is v = c/sqrt(2) . The decreasing charged photon's helical radius R = Ro/gamma^2 with the electron's increasing speed v quantitatively explains why the electron appears so small (<10^-18 m) in high-energy electron scattering experiments, even though the characteristic radius of the circulating charged photon for a resting electron is Ro .