On a Possible Quantum Contribution to the Red Shift *

We consider an effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region: In 1957 Khalfin proved that this amplitude tends to zero as t goes to the infinity more slowly than any exponential function of t. This effect can be described in terms of time-dependent decay rate γ(t) and then the Khalfin result means that this γ(t) is not a constant for long times but that it tends to zero as t goes to the infinity. It appears that a similar conclusion can be drawn for the energy of the unstable state for a large class of models of unstable particles: This energy should be much smaller for suitably long times t than the energy of this state for t of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long (t → ∞) and relatively short (lifetime of the state) time regions, are different. It is shown that these corrections decrease to E = E min < E φ as t → ∞, where E φ is the energy of the system in the state |φ measured at times t ∼ τ φ = γ. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.