### Abstract

The standard formulation of quantum theory relies on a fixed space-time metric determining
the localisation and causal order of events. In general relativity, the metric is influenced by
matter, and is expected to become indefinite when matter behaves quantum mechanically.
Here, we develop a framework to operationally define events and their localisation with
respect to a quantum clock reference frame, also in the presence of gravitating quantum
systems. We find that, when clocks interact gravitationally, the time localisability of events
becomes relative, depending on the reference frame. This relativity ia a signature of an
indefinite metric, where events can occur in an indefinite causal order. Even if the metric is
indefinite, for any event we can find a reference frame where local quantum operations take
their standard unitary dilation form. This form is preserved when changing clock reference
frames, yielding physics covariant with respect to quantum reference frame transformations.

Original language | English |
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Number of pages | 12 |

Journal | Nature Communications |

Early online date | 29 May 2020 |

DOIs | |

Publication status | Early online date - 29 May 2020 |

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## Cite this

Castro-Ruiz, E., Giacomini, F., Belenchia, A., & Brukner, Č. (2020). Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems.

*Nature Communications*. https://doi.org/10.1038/s41467-020-16013-1