Do observer-dependent gravitational algebras persist beyond leading order in G?
In plain words
Recent work shows that including an observer with a clock makes the set of measurable quantities in de Sitter space and near black holes well behaved, with finite entropies. These results hold only to leading order in the strength of gravity.
Precise statement
Chandrasekaran, Longo, Penington and Witten (2022) showed that adding an observer with a clock Hamiltonian to the de Sitter static patch yields a type $\mathrm{II}_1$ von Neumann algebra of gravitationally dressed observables as $G \to 0$, with a maximal-entropy state matching the Gibbons-Hawking entropy. Determine whether a consistent algebra with a trace (finite entropy) exists at higher orders in $G\hbar/c^{3}$, and whether the observer must be treated as a dynamical subsystem. An answer is a construction at second order or a demonstration of breakdown.
What would settle it
A construction of the dressed observable algebra at next order in the gravitational coupling, with its type and trace determined.