Electromagnetic Mass

Abstract

BY the modifications of Maxwell's field equations recently proposed¹ it is possible to revive the old idea of the electromagnetic origin of inertia. The mass of the electron can then be calculated from its charge and the constants of the field equations (the velocity of light c, and the absolute field a¹). It can be shown that the Lorentz equations for the motion of an electron in an external field are approximately true, and that the energy is given by mc². (The disagreement of these quantities stated in the Royal Society paper referred to above turned out to be a mistake.) The tensor S, the components of which are Maxwell's stresses, density of momentum and of energy, can be represented in two different forms, one using the Lagrangian, , the other the Hamiltonian, , where E is the electric and B the magnetic field vector. For example, the 44-component of S, representing density of energy, is given by , where the vectors H, D are connected with B, E by . For an electron at rest (H = B = 0) the mass m is related to the total energy by the equation , where r₀ = ae and is the value of the potential at the centre of the electron. By integrating the conservation law for S, we obtain the Lorentz equations of motion for external fields which contain only those wave-lengths which are large compared with r₀.