Observables beyond scattering in quantum gravity

Determine whether quantum gravity admits gauge‑invariant observables beyond S‑matrix scattering amplitudes and, if so, explicitly construct relational observables that can be consistently defined without a fixed background.

Background

In the first panel, participants debated whether the quantum field theory framework is sufficient for quantum gravity and, crucially, what counts as an observable. While several panelists argued that scattering amplitudes may be the only well-defined observables, others emphasized relational observables as necessary in a background-independent context.

This led to the explicit recognition of a gap: the community lacks consensus and concrete constructions for observables beyond scattering amplitudes, especially in relational formulations compatible with diffeomorphism invariance.

References

Whether there are other observables beyond scattering amplitudes emerged as an open question, but there was an emerging agreement on the fact that observables should be relational.

— Visions in Quantum Gravity  (2412.08696 - Buoninfante et al., 2024) in Panel 1 (Subsection "Quantum field theory framework for Quantum Gravity: yes or no?")

However, in the Hamiltonian formalism with the $(d+1)$-decomposition, it is not clear how to implement such smearing while respecting the full diffeomorphism invariance.

— On the (Non)Unitarity with respect to the Clock of a Dynamical Local Observer and the Einstein Equivalence Principle  (2608.16762 - Shimada, 17 Aug 2026) in Section 7, “Challenges with dynamical gravity” (subsection Challenges with dynamical gravity)