  The possibility of reconstructing the dark energy equation of state from
variations in the fine structure constant is investigated for a class of models
where the quintessence field is non-minimally coupled to the electromagnetic
field. For given classes of couplings and quintessence interaction potentials,
it is typically found that variations in alpha would need to be measured to
within an accuracy of at least $5 \times 10^{-7}$ to obtain a reconstructed
equation of state with less than a twenty per cent deviation from the true
equation of state between redshifts 0 and 3. In this case, it is argued that
the sign of the first derivative of the equation of state can be uncovered from
the reconstruction, thus providing unique information on how the universe
developed into its present dark energy dominated phase independent of high
redshift surveys. Such information would complement future observations
anticipated from the Supernova Acceleration Probe.
