On a possible quantum contribution to the red shift

Abstract

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 $\gamma(t)$ and then the Khalfin result means that this $\gamma(t)$ 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 ($t \to \infty$) and relatively short (lifetime of the state) time regions, are different. It is shown that these corrections decrease to ${\cal E} = {\cal E}_{min} < {\cal E}_{\phi}$ as $t \to \infty$, where ${\cal E}_{\phi}$ is the energy of the system in the state $|\phi>$ measured at times $t \sim \tau_{\phi}= \frac{\hbar}{\gamma}$. 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.