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≡α²gₚμ, where α is the fine structure constant, gₚ the proton g factor, and mₑ/mₚ≡μ the electron/proton mass ratio. Over a redshift range 0.24zabs2.04, ⟨Δx/x⟩ₜₒₜₐₗʷᵉⁱᵍʰᵗᵉᵈ=(1.17±1.01)×10^-5. A linear fit gives ${ ̇ {}}{x}/x=({-}1.43±{}1.27)×{}{10}^{{-}15} {yr}^{{-}1}$. Two previous results on varying ${α}$ yield the strong limits ${Δ}{μ}/{μ}=(2.31±{}1.03)×{}{10}^{{-}5}$ and ${Δ}{μ}/{μ}=(1.29±{}1.01)×{}{10}^{{-}5}$. Our sample, $8×{}$ larger than any previous, provides the first direct estimate of the intrinsic 21-cm and UV velocity differences ${~}6 km {s}^{{-}1}$.