  Simultaneity is a well-defined notion in special relativity once a Minkowski
metric structure is fixed on the spacetime continuum (manifold) of events. In
quantum gravity, however, the metric is not expected to be a fixed, classical
structure, but a fluctuating quantum operator which may assume a coherent
superposition of two classically-distinguishable values. A natural question to
ask is what happens to the notion of simultaneity and synchronization when the
metric is in a quantum superposition. Here we show that the resource of
distributed entanglement of the same kind as used by Jozsa et al. [Phys. Rev.
Lett. 85, 2010 (2000)] gives rise to an experimental probe that is sensitive to
coherent quantum fluctuations in the spacetime metric.
