Variation of the fine-structure constant caused by expansion of the Universe

In this paper, we evaluate the fine-structure constant variation that should take place as the pseudo-Riemannian Universe expands and its curvature is changed adiabatically. Such variation of the fine-structure constant is attributed to an energy loss by an extended physical system (consisting of baryonic component and electromagnetic (EM) field) due to expansion of our Universe. Obtained ratio alpha/alpha = 1 . 10(-18) (per second) is only five times smaller than actually reported experimental limit on this value. For this reason, the obtained variation can probably be measured within a couple of years. To argue the correctness of our approach, we calculate the Planck constant as adiabatic invariant of the EM field propagated on the pseudo-Riemannian manifold characterized by slowly varied geometry. Finally, we discuss the double clock experiment based on Al+ and Hg+ clocks carried out by Rosenband et al. (Science 2008). We show that in this case (when the fine-structure constant is changed adiabatically), the method based on double clock experiment cannot be applied to measure the fine-structure constant variation.