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We show that motion and gravity affect the precision of quantum clocks. Weconsider a localised quantum field as a fundamental model of a quantum clockmoving in spacetime and show that its state is modified due to changes inacceleration. By computing the quantum Fisher information we determine howrelativistic motion modifies the ultimate bound in the precision of themeasurement of time. While in the absence of motion the squeezed vacuum is theideal state for time estimation, we find that it is highly sensitive to themotion-induced degradation of the quantum Fisher information. We show thatcoherent states are generally more resilient to this degradation and that inthe case of very low initial number of photons, the optimal precision can beeven increased by motion. These results can be tested with current technologyby using superconducting resonators with tunable boundary conditions.

Motion and gravity effects in the precision of quantum clocks