  We study the change of the effective fine structure constant in the
cosmological models of a scalar field with a non-vanishing coupling to the
electromagnetic field. Combining cosmological data and terrestrial observations
we place empirical constraints on the size of the possible coupling and explore
a large class of models that exhibit tracking behavior. The change of the fine
structure constant implied by the quasar absorption spectra together with the
requirement of tracking behavior impose a lower bound of the size of this
coupling. Furthermore, the transition to the quintessence regime implies a
narrow window for this coupling around $10^{-5}$ in units of the inverse Planck
mass. We also propose a non-minimal coupling between electromagnetism and
quintessence which has the effect of leading only to changes of alpha
determined from atomic physics phenomena, but leaving no observable
consequences through nuclear physics effects. In doing so we are able to
reconcile the claimed cosmological evidence for a changing fine structure
constant with the tight constraints emerging from the Oklo natural nuclear
reactor.
