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. α²gₚmM gₚmM, and α. Since the spectral lines are observed at a high red shift, $z=0.5$, 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.