Self-Energy of the Electron

The setf-energy of the electron is an old problem; it appeared in classical physics. If you assume that an electron is a ball of radius a with all its charge on the surface, then the total electrostatic energy E₀ = e²/2a. Maybe the mass m of the electron corresponds to this energy. However, if you compute the momentum P carried by the field when the electron is moving with velocity V (including the Lorentz contraction of the ball) you find P = (4/3)E₀ V/(1 – V²)^1/2. This corresponds to a particle of mass m = (2/3) × (e²/a). Poincaré suggested that something must hold the ball together and that the forces would contribute an additional amount of stored energy. But there is no reliable theory for these forces.