Time variation of the fine structure constant driven by quintessence

There are indications from the study of quasar absorption spectra that the fine structure constant alpha may have been measurably smaller for redshifts z>2. Analyses of other data (Sm-149 fission rate for the Oklo natural reactor, variation of Re-187 beta-decay rate in meteorite studies, atomic clock measurements) which probe variations of alpha in the more recent past imply much smaller deviations from its present value. In this work we tie the variation of alpha to the evolution of the quintessence field proposed by Albrecht and Skordis, and show that agreement with all these data, as well as consistency with Wilkinson Microwave Anisotropy Probe observations, can be achieved for a range of parameters. Some definite predictions follow for upcoming space missions searching for violations of the equivalence principle.