Anne-Catherine de la Hamette - Identification is pointless

Abstract: A first step towards scenarios at the interface of quantum theory and gravity is to consider a quantum superposition of semiclassical spacetimes, such as the one, arguably, sourced by a gravitating object in superposition. But what does it mean that a gravitational source is in a superposition of “different” locations? How can one compare points across the different manifolds? 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 a system or 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 an explicit application of this formalism, we explore how the localisation of events is relative to the choice of QRF and formulate a quantum generalisation of Einstein’s famous hole argument. The latter calls into question the metaphysical meaning of not just spacetime points but also the identification between spacetime points across manifolds in superposition. Finally, we discuss the implications of QRF changes for indefinite causal order, the locality of interaction, and potential empirical consequences in interference experiments.
Talk page: researchsemina...
Paper: arxiv.org/abs/...
3C-QFS, 11 June 2024