On the variation of the fine-structure constant in Friedmann Universes
  The fine-structure constant alpha does not vary as Friedmann Universes evolve, a conclusion based on assessments of quantum mechanics and electrodynamics. alpha = e^2/(4pi epsilon hbar c), where e is the charge of the electron, epsilon is vacuum permittivity, c is the speed of light, and hbar is Planck's constant divided by 2pi. This inquiry was motivated by Schrodinger's (1939) prediction that all quantum wave functions coevolve with Friedmann geometry and a similar prediction by Sumner (1994) for vacuum permittivity. The functional form of variations in quantum wave functions found by Schrodinger is enough to show that alpha does not vary. Electrodynamics also predicts that alpha does not vary. Evolutionary changes in c exactly cancel those in vacuum permittivity and other factors in alpha do not change. Since alpha appears in all first-order perturbation formulas for atomic energy levels, comparisons of the atomic spectra of distant atoms with those in laboratories provide an experimental measure of this prediction. Most experiments find changes in alpha that are either statistically zero or very small. These results and estimates of the Hubble constant and deceleration parameter from precision redshift/magnitude data support a major assumption of this paper that the Friedmann solution to Einstein's theory of general relativity without cosmological constant is an adequate approximation to spacetime geometry and its long term evolution at quantum scales. 
William Q. Sumner