A Vector Potential Description of Linear Momentum, and Consequences

The linear momentum of an elementary charged particle is normally written as mv. This paper shows that it can equally be written as qA. This A is the self−induced vector potential, acting on each tiny element of the charge, by virtue of all the rest of the charge (in motion). |qA| = (q2μ0v/4π)<1/|r|>, where |r| is comparable with the “classical radius” of the elementary particle, i.e. the radius of a sphere of unit charge having electrostatic energy equal to the rest mass. Why go to all this bother? Who needs “vector potentials?” The reason is that this alternate formulation opens up easy answers to several current problems in physics. One can demonstrate that inertial mass is wholly electromagnetic and that inertial forces are Coulombic. It facilitates the calculation of the magnetic flux accompanying the quantized motion of an elementary particle. Surprisingly, the amplitude of this oscillating magnetic flux is quantized, in units of h/4e. Since photons arise from quantum transitions, it appears that the photon carries away magnetic flux in the amount of h/4e. This helps illuminate the photoelectric law, with its photon energy content proportional to 1/λ.