We analyse a gedankenexperiment previously considered by Mari et al. [1] that involves quantum superpositions of charged and/or massive bodies ("particles") under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice's particle) and vacuum fluctuations of the electromagnetic field (which limits Bob's ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We correct an error in the analysis of Mari et al. [1] and of Baym and Ozawa [2], who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.

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.

Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of opto-mechanical quantum oscillators is characterised by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the non-locality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.

We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.