Cosmological Variation of the Fine Structure Constant versus a new   Interaction
  We show why a dynamically varying fine structure constant does not impact on the Webb group's analysis as suggested by Bekenstein. We also provide a limit on the size of a possible correction to the Dirac Hamiltonian caused by a perturbation due to a dynamically varying alpha in hydrogen. 
E.J. Angstmann, V.V. Flambaum and S.G. Karshenboim