量子对红移的可能贡献
On a possible quantum contribution to the red shift
摘要：
我们考虑的影响所产生的非指数行为的生存幅度的不稳定状态在很长的时间区域：在1957年哈尔芬证明，这一幅度趋于零，因为$t$去无穷慢于任何指数函数的$t$。这种效应可以用随时间变化的衰减率$γ(t)$来描述，然后Khalfin的结果意味着这个$γ(t)$在很长时间内不是一个常数，而是随着$t$走向无穷大而趋于零。对于一大类不稳定粒子模型的不稳定态的能量，似乎也可以得出类似的结论：对于适当长的时间$t$，这个能量应该比对于所考虑状态的寿命量级的$t$，这个状态的能量小得多。在一个给定的模型，我们表明，在长（$t \to \infty$）和相对较短的（状态的寿命）时间区域的能量校正，是不同的。结果表明，这些修正减少到${\cal E} = {\cal E}_{min} < {\cal E}_ϕ$作为$t \to \infty$，其中${\cal E}_ϕ$是在时间$t \sim τ_ϕ= \frac{\hbar}γ$测量的系统在状态$|ϕ>$的能量。这是纯粹的量子力学效应。据推测，有可能通过分析遥远天体的光谱来检测这种效应。不稳定态的上述性质可能影响天体物理学和宇宙学参数的测量值。
英文摘要：
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 ($t \to \infty$) and relatively short (lifetime of the state) time regions, are different. It is shown that these corrections decrease to ${\cal E} = {\cal E}_{min} < {\cal E}_ϕ$ as $t \to \infty$, where ${\cal E}_ϕ$ is the energy of the system in the state $|ϕ>$ measured at times $t \sim τ_ϕ= \frac{\hbar}γ$. 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.
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