Nine quasar absorption spectra at 21-cm and ultraviolet (UV) rest-frame wavelengths are used to estimate possible variations in x≡α2gpμ, where α is the fine structure constant, gp the proton g-factor and μ≡me/mp is the electron-to-proton mass ratio. We find 〈Δx/x〉weightedtotal= (0.63 ± 0.99) × 10−5 over a redshift range 0.23 ≲zabs≲ 2.35 which corresponds to look-back times of 2.7–10.5 billion years. A linear fit against look-back time, tied to Δx/x= 0 at z= 0, gives a best-fitting rate of change of . We find no evidence for strong angular variations in x across the sky. Our sample is much larger than most previous samples and demonstrates that intrinsic line-of-sight velocity differences between the 21-cm and UV absorption redshifts, which have a random sign and magnitude in each absorption system, limit our precision. The data directly imply that the average magnitude of this difference is Δvlos∼ 6 km s−1.
Combining our Δx/x measurement with absorption-line constraints on α-variation yields strong limits on the variation of μ. Our most conservative estimate, obtained by assuming no variations in α or gp is simply Δμ/μ=〈Δx/x〉weightedtotal. If we use only the four high-redshift absorbers in our sample, we obtain Δμ/μ= (0.58 ± 1.95) × 10−5, which agrees (2σ) with recent, more direct estimates from two absorption systems containing molecular hydrogen, also at high redshift, and which have hinted at a possible μ-variation, Δμ/μ= (−2.0 ± 0.6) × 10−5. Our method of constraining Δμ/μ is completely independent from the molecular hydrogen observations. If we include the low-redshift systems, our Δμ/μ result differs significantly from the high-redshift molecular hydrogen results. We detect a dipole variation in μ across the sky, but given the sparse angular distribution of quasar sight lines we find that 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 μ and x.