Cosmological variation of the fine-structure constant versus a new interaction

We show that using the modified form of the Dirac Hamiltonian as suggested by Bekenstein does not affect the analysis of QSO data pertaining to a measurement of $\alpha$ variation. We obtain the present time limit on Bekenstein’s parameter, ${\tan }^2\chi =(0.2\pm 0.7)\times {10}^{-6}$, from the measurement of the hydrogen $2p$ fine structure using a value of $\alpha$ obtained from different experiments.