Universal quantum modifications to general relativistic time dilation in delocalised clocks

Author:

Khandelwal Shishir12,Lock Maximilian P.E.3,Woods Mischa P.14

Affiliation:

1. Institute for Theoretical Physics, ETH Zürich, Switzerland

2. Group of Applied Physics, University of Geneva, Switzerland

3. Institute for Quantum Optics and Quantum Information (IQOQI), Vienna, Austria

4. Department of Computer Science, University College London, United Kingdom

Abstract

The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

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