Probing variations in fundamental constants with radio and optical   quasar absorption-line observations
  Nine quasar absorption spectra at 21-cm and UV rest-wavelengths are used to estimate possible variations in x=alpha^2 g_p mu, (alpha is the fine structure constant, g_p the proton g-factor and mu=me/mp the electron-to-proton mass ratio). We find <Delta x/x>^weighted_total(=Dxxwt)=(0.63+-0.99) 10^-5 over 0.23~<z_abs~<2.35 (2.7 to 10.5 Gyr, look-back time, t_lb). A linear best fit against t_lb, tied to Delta x/x=0 at z=0, gives (dot x)/x=(-0.6+-1.2) 10^-15 /yr. Our large sample demonstrates that intrinsic line-of-sight velocity differences between the 21-cm and UV absorption redshifts, (on average Delta_vlos~6km/s), with random sign and magnitude in each absorption system, limit our precision. Combining our Delta x/x measurement with absorption-line constraints on alpha-variation yields strong limits on the variation of mu. Our most conservative estimate, obtained by assuming no variations in alpha or g_p is Delta mu/mu(=Dmm)=Dxxwt. If we use only the four high-redshift absorbers in our sample, we obtain Dmm=(0.58+-1.95) 10^-5, which agrees (2sigma) with recent, more direct estimates from two absorption systems containing molecular hydrogen, also at high redshift, and which have hinted at a possible mu-variation, Dmm=(-2.0+-0.6) 10^-5. Our method of constraining Dmm is completely independent from the molecular hydrogen observations. If we include the low-redshift systems, our Dmm result differs significantly from the high-redshift molecular hydrogen results. We detect a dipole variation in mu across the sky, but this model is required by the data at only the 88 per cent confidence level. Clearly, much larger samples of 21-cm and molecular hydrogen absorbers are required to adequately resolve the issue of the variation of mu and x.(Abridged) 
P. Tzanavaris, M. T. Murphy, J. K. Webb, V. V. Flambaum, S. J. Curran