Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. The lifetime of an excited hydrogenlike atom can be used as a clock, which we use to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared with the emission rate of an atom prepared in a mixture of momentum wave packets at order $v^2/c^2$. This effect is accompanied by a quantum correction to the Doppler shift due to the coherence between momentum wave packets. This quantum Doppler shift affects the spectral line shape at order $v/c$. However, its effect on the decay rate is suppressed when compared with the effect of quantum time dilation. We argue that spectroscopic experiments offer a technologically feasible platform to explore the effects of quantum time dilation.

中文翻译：

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原子光谱中的量子时间膨胀

当时钟在相对论动量波包的叠加中移动时，就会发生量子时间膨胀。激发的类氢原子的寿命可以用作时钟，我们可以用来证明量子时间膨胀是如何在自发发射过程中表现出来的。与在动量波包混合物中按顺序制备的原子的发射率相比，产生的发射率不同$v^{\mathrm{2个}}/C^{\mathrm{2个}}$。由于动量波包之间的相干性，该效应伴随着对多普勒频移的量子校正。量子多普勒频移会按顺序影响光谱线的形状$v/C$。但是，与量子时间膨胀效应相比，它对衰减率的效应被抑制了。我们认为光谱实验提供了一个技术上可行的平台来探索量子时间膨胀的影响。