# On a possible quantum contribution to the red shift

Source: [On a possible quantum contribution to the red shift](<https://www.sota2.com/research/paper/68fa21aa7a2b558e29338758>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:16.545Z

Authors: K. Urbanowski

Published: 2008-06-17T20:29:33.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0806.2870>)

[PDF](<https://arxiv.org/pdf/0806.2870.pdf>)