Smith Alexander R H, Ahmadi Mehdi
Department of Physics, Saint Anselm College, Manchester, NH, 03102, USA.
Department of Physics and Astronomy, Dartmouth College, Hanover, NH, 03755, USA.
Nat Commun. 2020 Oct 23;11(1):5360. doi: 10.1038/s41467-020-18264-4.
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.
在量子理论与相对论的交叉点上，存在着时钟经历固有时间叠加的可能性。我们考虑由在弯曲时空里运动的相对论性粒子的内禀自由度构建的量子时钟。推导了一个时钟在读取一个固有时间的条件下，另一个时钟读取不同固有时间的概率。从这个条件概率分布可以看出，当这些时钟的质心在局域化动量波包中移动时，它们会观测到经典的时间膨胀效应。然后，我们阐述了对在局域化动量波包叠加态中运动的时钟所观测到的时间膨胀效应的量子修正，这种效应有可能在实验中被观测到。利用赫尔斯特罗姆 - 霍列沃下界推导出一个固有时间 - 能量/质量不确定性关系。
