Relativity and decoherence of spacetime superpositions

It is univocally anticipated that in a theory of quantum gravity, there exist quantum superpositions of semiclassical states of spacetime geometry. Such states could arise, for example, from a source mass in a superposition of spatial configurations. In this paper, we introduce a framework for describing such "quantum superpositions of spacetime states." We introduce the notion of the relativity of spacetime superpositions, demonstrating that for states in which the superposed amplitudes differ by a coordinate transformation, it is always possible to re-express the scenario in terms of dynamics on a single, fixed background. Our result unveils an inherent ambiguity in labelling such superpositions as genuinely quantum-gravitational, which has been done extensively in the literature, most notably with reference to recent proposals to test gravitationally-induced entanglement. We apply our framework to the above-mentioned scenarios, looking at gravitationally-induced entanglement, the problem of decoherence of gravitational sources, and clarifying commonly overlooked assumptions. In the context of decoherence of gravitational sources, our result implies that the resulting decoherence is not fundamental, but depends on the existence of external systems that define a relative set of coordinates through which the notion of spatial superposition obtains physical meaning.