  By analyzing the survival probability amplitude of an unstable state we show
that the energy corrections to this state in the long ($t \to \infty$) and
relatively short (lifetime of the state) time regions, are different. It is
shown that in the considered model the above corrections decrease to zero as $t
\to \infty$. It is hypothesized that this property could be detected by
analyzing the spectra of distant astrophysical objects. The above property of
unstable states may influence the measured values of possible deviations of the
fine structure constant $\alpha$ as well as other astrophysical and
cosmological parameters.
