  In present paper we evaluate the fine structure constant variation, that
should take place as the Universe expands and its curvature is changed
adiabatically. Such variation of the fine structure constant is attributed to
an energy losses by an extended physical system (consist of baryonic component
and electromagnetic field) due to expansion of our Universe.
  Obtained ratio (d alpha)/alpha = 1. 10{-18} (per second) is only five times
smaller than actually reported experimental limit on this value. For this
reason 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 electromagnetic field propagated on a manifold
characterized by slowly varied geometry, in the framework of the pseudo-
Riemannian geometry. Finally we discuss the double clock experiment based on
Al+ and Hg+ clocks carried out by T. 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 can not be applied to measure the
fine structure constant variation.
