  It has recently been proposed that quantum gravity might lead to the
decoherence of superpositions in energy, corresponding to a discretization of
time at the Planck scale. At first sight the proposal seems amenable to
experimental verification with methods from quantum optics and atomic physics.
However, we argue that the predicted decoherence is unobservable in such
experiments if it acts globally on the whole experimental setup. This is
related to the unobservability of the global phase in interference. We also
show how local energy decoherence, which acts separately on system and phase
reference, could be detected with remarkable sensitivity and over a wide range
of length scales by long-distance Ramsey interferometry with metastable atomic
states. The sensitivity of the experiments can be further enhanced using
multi-atom entanglement.
