Revision of VLT/UVES constraints on a varying fine-structure constant

We critically review the current null results on a varying fine-structure constant, alpha, derived from VLT/UVES quasar absorption spectra, focusing primarily on the many-multiplet analysis of 23 absorbers from which Chand et al. (2004) reported a weighted mean relative variation of da/a=(-0.06+/-0.06) x 10^{-5}. Our analysis of the same reduced data, using the same fits to the absorption profiles, yields very different individual da/a values with uncertainties typically larger by a factor of ~3. We attribute the discrepancies to flawed parameter estimation techniques in the original analysis and demonstrate that the original da/a values were strongly biased towards zero. Were those flaws not present, the input data and spectra should have given a weighted mean of da/a=(-0.44+/-0.16) x 10^{-5}. Although this new value does reflect the input spectra and fits (unchanged from the original work -- only our analysis is different), we do not claim that it supports previous Keck/HIRES evidence for a varying alpha: there remains significant scatter in the individual da/a values which may stem from the overly simplistic profile fits in the original work. Allowing for such additional, unknown random errors by increasing the uncertainties on da/a to match the scatter provides a more conservative weighted mean, da/a=(-0.64+/-0.36) x 10^{-5}. We highlight similar problems in other current UVES constraints on varying alpha and argue that comparison with previous Keck/HIRES results is premature.