Limits on a Dynamically Varying Fine Structure Constant

We show that using the modified form of the Dirac Hamiltonian as suggested by Bekenstein, does not affect the analysis in [1-4] of QSO data pertaining to a measurement of alpha variation. We obtain the present time limit on Bekenstein's parameter, tan^{2}chi =(0.2 \pm 0.7)\times10^{-6}, from the measurement of the hydrogen 2p fine structure using value of alpha obtained from different experiments.