Abstract

Invariant properties and structures of matter are modeled by internal period-like degrees of freedom. Invariance then means periods, which remain unaltered over time. Period doubling is a phenomenon common to nonlinear dynamical systems. In this model the doubling process is generalized into multiple dimensions and utilized to bring about sub-harmonic frequencies, which generate decreasing energies and increasing sizes. It is assumed that period doubling takes place at the Planck scale, and therefore the Planck units are used as reference. The sub-harmonics can be converted into several other physical quantities by well known physical relations. A certain class of sub-harmonics is stable and the elementary electric charge (squared), rest energies and magnetic moments of the electron-positron and proton-antiproton pairs are shown to belong to this class. It is suggested that the structure of the Solar system results from period doubling, too.