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

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.