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 $x\equiv {\alpha }^2{g}_p\mu$, where $\alpha$ is the fine structure constant, $g_p$ the proton $g$ factor, and $m_e/m_p\equiv \mu$ the electron/proton mass ratio. Over a redshift range $0.24\lesssim z_{\mathrm{abs}}\lesssim 2.04$, $⟨\Delta x/x{⟩}_{\mathrm{total}}^{\mathrm{weighted}}=(1.17\pm 1.01)\times {10}^{-5}$. A linear fit gives $\dot{x}/x=(-1.43\pm 1.27)\times {10}^{-15}{\mathrm{yr}}^{-1}$. Two previous results on varying $\alpha$ yield the strong limits $\Delta \mu /\mu =(2.31\pm 1.03)\times {10}^{-5}$ and $\Delta \mu /\mu =(1.29\pm 1.01)\times {10}^{-5}$. Our sample, $8\times$ larger than any previous, provides the first direct estimate of the intrinsic 21-cm and UV velocity differences $\sim 6\mathrm{km}{\mathrm{s}}^{-1}$.