Speaker
Description
Consider a scenario involving a superposition of semiclassical spacetimes. How can one compare points on the different manifolds across the superposition? Due to the diffeomorphism invariance of general relativity, there is a priori no notion of the “same” or “different” points across the branches. In fact, there are multiple ways of relating points or events on the different spacetimes. Here, we make this concrete by using coincidences of four scalar fields to construct a comparison map between all spacetimes in superposition, which allows us to determine whether an event is located at the “same” or “different” points across the branches. Different choices of scalar fields can be understood as different instantiations of quantum reference frames (QRFs), connecting the construction to recent research in the field of quantum foundations. As explicit applications of this formalism, we explore how the localization of events is relative to the choice of QRF and will discuss the implications thereof for indefinite causal order and the locality of interaction. After examining the construction of relational observables, we conclude with a quantum generalization of the famous hole argument. This argument calls into question the metaphysical meaning of not just spacetime points but also the identification between spacetime points across manifolds in superposition.
