Area as a quantum reference frame

Abstract

Elementary quantum reference frames (QRFs) such as clocks have recently led to surprising insights into quantum gravity. But far richer structures should emerge once we consider more full-fledged gravitational QRFs, i.e. quantum coordinate systems. A complete theory of such objects remains elusive, largely due to the subtleties in quantizing diffeomorphism symmetry. Null surfaces provide an ideal simplified setting to explore the properties of quantum coordinates. In this talk, I will show how one may form a useful QRF out of the area/spin 0 degrees of freedom on each light ray: the quantum dressing time. This construction permits relational observables and frame reorientations within an algebraic structure generalizing the crossed product, and consistent with established QRF approaches such as the perspective-neutral formalism. Along the way, I will discuss how diffeomorphism anomalies can be cancelled by the introduction of a suitable classical counterterm; I will describe some implications of the fact that QRFs made from fields (such as the quantum dressing time) must be Kähler-quantised; and I will comment on the consequences of our construction for gravitational entropies. Based on 2510.26589 and WIP with Laurent Freidel.