Atomic Clocks and the Search for Variation of the Fine Structure   Constant
  Evidence that the fine structure constant, alpha, was different in an early epoch has recently been found in quasar (QSO) absorption spectra. An accurate laboratory measurement of alpha variation could help to distinguish between space and time variation of alpha and possibly confirm the QSO results. We have performed calculations of the relativistic energy shifts that a variation of alpha would cause in a wide range of atomic spectra. A laboratory measurement of how these transition frequencies vary over time is vital in determining whether alpha is varying today. 
E. J. Angstmann, V. A. Dzuba and V. V. Flambaum