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The theory of relativity associates a proper time with each moving object viaits world line. In quantum theory however, such well-defined trajectories areforbidden. After introducing a general characterisation of quantum clocks, wedemonstrate that, in the weak-field, low-velocity limit, all "good" quantumclocks experience time dilation as dictated by general relativity when theirstate of motion is classical (i.e. Gaussian). For nonclassical states ofmotion, on the other hand, we find that quantum interference effects may giverise to a significant discrepancy between the proper time and the time measuredby the clock. The universality of this discrepancy implies that it is notsimply a systematic error, but rather a quantum modification to the proper timeitself. We also show how the clock's delocalisation leads to a largeruncertainty in the time it measures -- a consequence of the unavoidableentanglement between the clock time and its center-of-mass degrees of freedom.We demonstrate how this lost precision can be recovered by performing ameasurement of the clock's state of motion alongside its time reading.

Universal quantum modifications to general relativistic time dilation in delocalised clocks