According to observations leptons are always produced in pairs. Both particles can be electrically charged, or just one, in which case the charged particle is accompanied by a particle specific neutrino. The period doubling process in nonlinear dynamical systems creates stable pair structures from the Planck units. The electron-positron pair is one of the stable structures, and the rest mass, electric charge and magnetic moment can be accurately calculated by the period doubling process. That the pair structure is stable means, that e.g., an electron and a positron are always born together. In the muon decay one of the pair is charged, while the other remains chargeless because there is only one charge available. It is suggested in this article that neutrino is the chargeless part of the lepton pair.

In the Standard Model of elementary particles, the rest mass, magnetic moment and electric charge of the electron are considered to be natural constants. In this article it is proposed that these properties can be calculated in a simple way from the corresponding Planck units using the well-known period doubling phenomenon in nonlinear dynamical systems. Periods corresponding to the values of the electron and positron properties belong to a subset of stable periods. The periodic structures of the rest energy and magnetic moment consist of three internal degrees of freedom, whereas the Coulomb energy of the electric charge consists of four. The number of period doublings for the elementary charge determines the value of the fine structure constant alpha.

Our understanding and theoretical interpretation of observations in astrophysics and cosmology depends on our knowledge of the fundamental constants and their possible dependence on time and space. Atomic spectroscopy and radio astronomy give important information on the validity and stability of the fundamental constants. The possible dependence of the fine structure constant alpha on time and spatial direction is an active topic of research.Period doubling is a universal property of nonlinear dynamical systems, and the doubling is exact in principle. The value of the elementary charge squared can be calculated by the period doubling process from the Planck charge and thereby the value of alpha.If ‘old’ and ‘new’ electrons are identical, then the Planck charge, i.e. a set of natural constants, has remained constant over time. In this article we show that the value of alpha calculated from the Planck charge is 0.007 % smaller than the current accepted value of alpha.