Limits on the Variation of Fundamental Atomic Quantities over Cosmic Time Scales

Abstract

The detection of Mg ii fine structure and hydrogen hyperfine absorption lines toward the radio source AO 0235 + 164 allows us to place upper limits on the variability of three products of the fine-structure constant, the nuclear $g$ factor of the proton, and the ratio of electron to proton mass, viz. $\frac{{\alpha }^2{g}_{p}m}{M}$ $\frac{g_{p}m}{M}$, and $\alpha$. Since the spectral lines are observed at a high red shift, $z=0.5\mathrm{}$, the limits obtained on the variation with time of these quantities (adopting $z$ as a measure of the Hubble expansion) apply over at least 35% of the age of the universe.