Quantum Physics and Fractal Space Time

Abstract

We argue for a new fractal space-time which is different from that of Nottale, Ord and El Naschie. The fractal here is a deterministic fractal, where a fractal seed on an M+1 th scale, let us say, is about 10 40 times the diameter of the fractal seed on the M th fractal scale. At each scale, the fractal seed is the most fundamental particle on that scale and is the single Z 00 source in the Einstein equations, all other particles with mass are either excited states or multibody states of this particle. We take the M th fractal scale to be the electron and the M+1 th scale to be the Hubble universe. Next, we use the selfsimilarity between these two objects to solve for the metric, comoving with the Hubble expansion of the M+1 scale (The Dirac equation can be derived here also) . Plug these metric elements back into the metric equation (which then also derives a 1/ (1− r) potential) and then back into the Dirac equation. You then get tauon, muon, electron masses and QED results, but with only one vertex. The S matrix for this Dirac equation gives the W and Z masses as resonance energies. Applying the M+2 perturbation in the same way as the M+1 perturbation, gives the three neutrino masses. Combining the M+1 th and M+2 solution into the zero energy vacuum, gives the beta decay left, handedness and SU (2) XU (1) gauge. Applying this theory within the r<1 region, gives the quarks and QCD assymptotic freedom is implied by the 1/ (1− r) potential. We do a radial coordinate transformation of the Z αβ source to the expanding cosmological metric and get a new term added to Z 00. From this new term, we calculate the value of the Newtonian gravitational constant.