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.