My project investigates the emergence of time and dynamics in algebraic approaches to quantum gravity, combining insights from physics and philosophy. Recent applications of algebraic quantum field theory to quantum gravity in the AdS/CFT correspondence have raised the prospect that similar algebraic methods could underpin a form of holography in cosmological, de Sitter-type spacetimes. In this setting, observable quantities cannot be defined in relation to an asymototic boundary. Rather, observables have to be related directly to an observer's wordline to produce a physically meaningful algebra, which gives the algebra an operational interpretation: it represents precisely what that observer can measure along their wordline. 

The relational dynamics governing these observables is encoded in the Page–Wootters mechanism, while tools from Tomita–Takesaki modular theory can be used to derive an emergent notion of time from the algebraic structure itself, in the spirit of the Thermal Time Hypothesis. Another key advantage of the algebraic framework is that, while Hilbert space representations depend sensitively on the choice of spacetime background, the underlying ∗-algebraic structure does not — suggesting a notion of background independence in which the background enters only at the level of a representation or state.

This project is part of the NWA-ORC Emergence at all scales, financed by the NWO.
Link: https://www.nwo.nl/en/projects/wbheu44297.