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(abridged) Quasar absorption lines provide a precise test of the assumedconstancy of the fundamental constants of physics. We have investigatedpotential changes in the fine-structure constant, alpha, and theproton-to-electron mass ratio, mu.  The many-multiplet method allows one to use optical fine-structuretransitions to constrain (Delta alpha)/alpha at better than the 10^(-5) level.We present a new analysis of 154 quasar absorbers with 0.2 < z <3.7 in VLT/UVESspectra. From these absorbers we find 2.2 sigma evidence for angular variationsin alpha under a dipole+monopole model. Combined with previous Keck/HIRESobservations, we find 4.1 sigma evidence for angular (and therefore spatial)variations in alpha, with maximal increase of alpha occurring in the directionRA=(17.3 +/- 1.0) hr, dec=(-61 +/- 10) deg. Under a model where the observedeffect is proportional to the lookback-time distance the significance increasesto 4.2 sigma. Dipole models fitted to the VLT and Keck samples and modelsfitted to z<1.6 and z>1.6 sub-samples independently yield consistent estimatesof the dipole direction, which suggests that the effect is not caused bytelescope systematics. We consider a number of systematic effects and show thatthey are unable to explain the observed dipole effect.  We have used spectra of the quasars Q0405-443, Q0347-383 and Q0528-250 fromVLT/UVES to investigate the absorbers at z=2.595, 3.025 and 2.811 in thesespectra respectively. We find that (Delta mu)/mu=(10.1 +/- 6.6) x 10^(-6), (8.2+/- 7.5) x 10^(-6) and (-1.4 +/- 3.9) x 10^(-6) in these absorbersrespectively. A second spectrum of Q0528-250 provides an additional constraintof (Delta mu)/mu=(0.2 +/- 3.2_stat +/- 1.9_sys) x 10^(-6). The weighted mean ofthese values yields (Delta mu)/mu=(1.7 +/- 2.4) x 10^(-6), the most preciseconstraint on evolution in mu at z>1.

Searching for variations in the fine-structure constant and the proton-to-electron mass ratio using quasar absorption lines