On the structure of space-time and matter as obtained from the Planck scale by period doubling in three and four dimensions

One of the most interesting questions in modern physics is the possible relation of the Planck scale to our perceived world. The Planck energy (10E22 MeV) is extremely large as compared to the rest energies of the elementary particles, and the Planck length (10E-35 m) is too short to be directly connected to any real world distances. The Planck scale is determined by the natural constants h, c, G and epsilon zero making it absolute and unadjustable. The Planck scale may also represent the ultimate graininess, i.e. the basic structure of the space-time. It is also well known that nonlinear systems show universal behavior in the form of period doubling, which is the same as frequency and energy halving. If period doubling is applied to the Planck energy E=h/t, an absolute and unadjustable set of sublevels is borne. It is shown here that the rest energies and magnetic moments of the basic elementary particles are given directly by the corresponding Planck sublevels. The value of the elementary electric charge squared, which is proportional to energy, results from the Planck charge squared by the same period doubling process. The planets in the Solar system occupy orbits, the radii of which can be calculated from the Planck length by spatial period doubling. A spectrum of velocities can be calculated from the speed of light by the same process. These velocities fit the consequent orbital velocities of the planets and the quantized redshifts of galaxies, if redshift is interpreted as velocity.