We present a novel formula for the mass of the electron as a function of four fundamental constants of electromagnetism and gravitation: the fine structure constant, Planck's constant, the speed of light, and the gravitational constant. We derive the formula in three major steps.
First, we model the electron as a decreasing standing wave, solution of the propagation equation coming from Maxwell's relations. We consider its wave number k0 as a key value of electromagnetism. The internal energy is distributed according to the square of the amplitude of the wave.
Second, we make the hypothesis that the field of the wave has lower and upper bounds. Assuming quantization of kinetic momentum we find that the logarithm of the quotient of these bounds can be assimilated to the inverse of the fine structure constant. Third, we propose that vacuum space is a granular fluid medium. The value k0 is such that it implies opacity of the electron wave to gravitons, which are the elementary dynamic corpuscles of the fluid.
