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Quantum Clocks and Gravitational Time Dilation and the Quantum Interference

Takeshi ChibaShunichiro Kinoshita
Sep 2022
摘要
Recently, a proper time observable for a quantum clock is introduced and itis found that the proper time read by one clock conditioned on another clockreading a different proper time obeys classical time dilation in accordancewith special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order toinvestigate whether the weak equivalence principle holds for quantum matter. Wefind that for general quantum states the quantum time dilation in a weakgravitational field obeys a similar gravitational time dilation found inclassical relativity. However, unlike the special relativistic case, the timedilation involves the external time (a background coordinate time at theobserver on the earth) as well as the proper times of two clocks. We alsoinvestigate a quantum time dilation effect induced by a clock in asuperposition of wave packets localized in momentum space or in position spaceand propose the setup to observe the gravitational effect in the quantuminterference effect in the time dilation.
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