The fine-structure constant \alpha does not vary as Friedmann Universes evolve , a conclusion based on assessments of quantum mechanics and electrodynamics . \alpha is the dimensionless number \alpha \equiv e ^ { 2 } / { 4 \pi \varepsilon _ { o } \hbar c } \approx 1 / 137 , where e is the charge of the electron , \varepsilon _ { o } is vacuum permittivity , c is the speed of light , and \hbar is Planck ’ s constant divided by 2 \pi .
This inquiry was motivated by Schrödinger ’ s ( 1939 ) prediction that all quantum wave functions coevolve with Friedmann geometry and a similar prediction by Sumner ( 1994 ) for \varepsilon _ { o } .
The functional form of variations in quantum wave functions found by Schrödinger 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 \varepsilon _ { o } 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 H _ { o } and deceleration parameter q _ { o } 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 .