The links of Pythagorean prime 137 to the fine structure constant, electrons’ Coulomb to gravitational force ratio, and the mass ratios of elementary particles

In this work, we present a model to unfold the century-old mysteries surrounding the fine structure constant and explain the physical origin of its value of ~1/137 due to gauge invariance, Einstein’s mass energy relation, and space time quantization. Using a generalized Dirac equation in a spacetime lattice, we obtain an estimate of an electron’s radius RRRR and also link the magic 137 beyond electromagnetism, to the ratio of the Coulomb and gravitational forces between a pair of electrons at , and t he m ass ratio s of an el ect ron to ot her particles such as a proton, Higgs boson, W/Z bosons, and quarks. With the proposed quantized space time, singularity divergence, and vacuum catastrophe problems in continuum quantum field theory can be avoided.