Quantum clocks observe classical and quantum time dilation.

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. The usual definition of external time is unlikely to survive if we want to unite quantum mechanics and relativity. Here the authors consider two quantum clocks moving in curved spacetime and formulate the probability distribution that relates their proper times, allowing them to explore quantum time dilation. [ABSTRACT FROM AUTHOR]