Statement
Problem 2.1 of Goto et al.: can we characterize gravitational observables as operational quantities on the boundary and/or via gravitational tasks? Diffeomorphism-invariant observables (extremal surfaces/volumes, dressed bulk local operators) are well-defined semiclassically, but it is unclear whether they remain meaningful in full quantum gravity — and whether each corresponds to a concrete boundary information-processing task.
Why It Matters
This is the umbrella problem of Theme 1 and the general form of a claim the group is already trying to prove in one case: that a geometric bulk quantity has an operational meaning. The generalized-entropy-as-capacity result is precisely an instance — generalized entropy characterized as the capacity for holographic embezzlement — so progress here is progress on the group’s most holographic project.
What We Know
- RT / QES already give entropic (hence semi-operational) readings of extremal surfaces.
- Subregion–subalgebra duality and entanglement-wedge reconstruction tie bulk operators to boundary subalgebras.
- A fully task-based dictionary (which task certifies which bulk observable) is missing.
Possible Approaches
- Prove operational characterizations case by case (generalized entropy ↔ embezzlement capacity; complexity ↔ volume; etc.).
- Use resource theory to attach monotones to bulk quantities — see holographic-resource-theory, resource-theory-monotones-in-qft.