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By analyzing the survival probability amplitude of an unstable state we showthat the energy corrections to this state in the long ($t \to \infty$) andrelatively short (lifetime of the state) time regions, are different. It isshown that in the considered model the above corrections decrease to zero as $t\to \infty$. It is hypothesized that this property could be detected byanalyzing the spectra of distant astrophysical objects. The above property ofunstable states may influence the measured values of possible deviations of thefine structure constant $\alpha$ as well as other astrophysical andcosmological parameters.Comment: LaTeX2e, 16 pages, new comments adde

A quantum long time energy red shift: a contribution to varying α theories