Limits on variations in fundamental constants from 21-cm and ultraviolet quasar absorption lines

Quasar absorption spectra at 21-cm and UV rest-wavelengths are used to estimate the time variation of x=alpha^2 g_p mu, where alpha is the fine structure constant, g_p the proton g factor, and m_e/m_p=mu the electron/proton mass ratio. Over a redshift range 0.24 ~< z_abs ~< 2.04, <Delta x/x>_total_weighted=(1.17+-1.01) x 10^-5. A linear fit gives d/dt{x}/x=(-1.43+-1.27) x 10^-15 yr^-1. Two previous results on varying alpha yield the strong limits Delta mu/mu=(2.31+-1.03) x 10^-5 and Delta mu/mu=(1.29+-1.01) x 10^-5. Our sample, 8x larger than any previous, provides the first direct estimate of the intrinsic 21-cm and UV velocity differences ~6 km s^-1.