This paper proposes a new way to write the gravitational path integral so that it is explicitly gauge‑invariant and tied to physical, relational measurements. The authors build the path integral out of quantum reference frames (QRFs) — coordinate systems made from the fields in the theory — and relational observables dressed to those frames. The result is a version of the gravitational path integral that needs no gauge fixing, produces no ghost fields or anomalies, and treats observables as local to a chosen frame.

Concretely, the authors combine a bundle picture of field space (a mathematical way to split gauge directions from physical directions) with dynamical, field‑dependent frames R[ϕ]. Given a covariant field quantity T, they push it forward into relational spacetime defined by a frame and obtain a frame‑dressed, gauge‑invariant observable OT|R. They then integrate over these relational observables with a measure induced by the DeWitt metric on field space. Written this way, the path integral Z is invariant under all internal frame changes. If one does choose to fix a frame, the construction reduces to standard Faddeev–Popov gauge‑fixed expressions and recovers the usual ghost determinants, so the new form is an equivalent, gauge‑invariant parent of the familiar formulas.

The framework makes a number of qualitative predictions. Because different frames define different relational spacetimes, a correlator or the time evolution that looks sharp in one QRF can look fuzzy in another. There is also a frame‑dependent family of vacuum states: what is a ground state in one frame often appears as an excited state from another frame’s viewpoint. The authors also show how to build gauge‑invariant but frame‑dependent effective actions by coupling sources only to relational observables. This opens a route to a relational notion of renormalization and to regularizing the path integral on relational spacetime rather than on the original manifold, which could preserve diffeomorphism (coordinate) invariance.