42.8503{\ldots}A Theory of the Unification of Gravitation and Electromagnetism

The GEM (Gravity Electro-Magnetism)(1), theory is presented as an alloy of Sakharov (2)and Kaluza-Klien approaches to field unification. The metric tensor becomes: g$_{ab}$ = 4(F$^{c}_{a}$F$_{cb}$ )/(F$^{ab}$F$_{ab})$, where F$_{cb}$ is the EM field due to theZPF(Zero Point Fluctuation).It is found that this results in a massless ground state vacuum. It is found that a flat-space metric is recovered in the limit of a full spectrum ZPF. The vacuum ZPF energy and vacuum quantities G , h, and c give birth to particles quantities m$_{p}$, m$_{e}$, and e, in a process triggered by the appearance of the Kaluza-Klein fifth dimension. Where also, the EM and gravity forces split from each other in a process correlated to the splitting apart of protons and electrons. This leads to the formula ln(r$_{o}$/r$_{p})$ = $\sigma $ =42.8503{\ldots}, where $\sigma $ = (m$_{p}$/m$_{e})^{1/2}$, where m$_{p}$ and m$_{e}$ are the electron and proton masses respectively and where r$_{o}$ =e$^{2}$/m$_{o}$c$^{2}$, r$_p$ is the Planck length, and where m$_{o}$ = (m$_{p}$m$_{e})^{1/2}$ and the formula: G=(e$^{2}$/m$_{o}^{2})\alpha $exp(-2$\sigma )$=6.668x10$^{-8}$ dynes-cm$^{2}$/g$^{2}$ (esu). The splitting of the electron and proton occurs as the splitting of a light-like space-time interval into a time-like part, the electron, and a space-like part, the proton, with three inseparable sub-dimensions, the quarks. (1) Brandenburg, J.E. (2007), IEEE Trans. On Plasma Sci.,Vol.35, No. 4., p845. (2) Sakharov A.D. Sov. Phys. Doklady 12,1040, (1968).