Observing Spacetime

TL;DR

Balasubramanian and Yildirim demonstrate that generic boundary probes yield universal, state-agnostic responses in single- and two-boundary quantum gravity setups, while carefully tuned probes activate non-perturbative wormhole saddles that reveal the prepared shell-state. They show this detection works for black holes behind horizons as well as for disconnected baby universes, and it can be achieved with probes on one boundary or coordinated probes on both, with the latter sometimes producing exponential enhancements. By projecting onto microcanonical windows and analyzing saddles, they connect state-detection to QMA complexity, arguing that verifying a proposed gravity state is efficient, whereas finding the exact state is computationally hard. The work clarifies how Euclidean wormholes and entanglement structure shape what asymptotic observers can infer about highly complex gravitational states, with implications for black hole interiors, PETS, and baby universes in any GR-theory setting. It thus provides a concrete framework to test proposals about quantum gravity microstates using non-perturbative path-integral effects.

Abstract

Complex states of quantum gravity in flat and AdS gravity can have features that are inaccessible to classical asymptotic observers. The missing information appears to such observers to be hidden behind a horizon or in a baby universe. Here we use the gravitational path integral to ask whether quantum observables can access the hidden data. We show that generic probes give a universal result and contain no information about the state. However, a probe appropriately fine-tuned to the state can give a large signal because of novel wormhole saddles in the path integral. Thus, in these settings, asymptotic observers cannot easily determine the state of the universe, but can check a proposal for it. Using these fine-tuned probes we show that an asymptotic observer can detect information hidden in a disconnected baby universe. Furthermore we show that the state of a two-boundary black hole can be detected using Lorentzian operators localised on just one of the boundaries.

Figures (18)

• Figure 1: Path integral boundary condition defining the single-sided shell states. ( a) Euclidean boundary with topology $\mathbb{R}^{<0}\times\mathbb{S}^{d-1}$ for preparation of the shell states. The arrows indicate a half-infinite line. The shell operator $\mathcal{O}_{i}$ is pictured in red and $\beta_{}/2$ is the Euclidean "preparation time". ( b) Euclidean boundary with the $\mathbb{S}^{d-1}$ suppressed. We adopt this convention, and sometimes depict this boundary with a curve or a kink to clarify diagrams (images adapted from Balasubramanian:2025zey).
• Figure 2: Shell-strip asymptotic boundary condition for the overlap $\braket{j|i}$ consisting of the line $\lim_{\alpha \to \infty} [-\alpha, \beta + \alpha]$ on which $\mathcal{O}_{i}$ and $\mathcal{O}^{\dagger}_{j}$ are inserted at $\tau =0$ and $\tau=\beta$ respectively (images adapted from Balasubramanian:2025zey).
• Figure 3: The saddle for the norm $\overline{\braket{i|i}}$ is constructed by considering the shell propagating on a disk and strip separately for some propagation times $\Delta T_{S,D}$ and then gluing them together along the $i$-shell worldvolume by discarding the shell homology region (purple). The junction conditions dynamically determine $\Delta T_{S,D}$ to yield an on shell glued geometry. We have suppressed the angular directions in these diagrams, and represent the radius-time plane with the dashed line representing the origin (images adapted from Balasubramanian:2025zey).
• Figure 4: Analytic continuation of the single-sided shell state saddlepoints to Lorentzian signature, shown here with asymptotically AdS boundary conditions. For asymptotically flat boundary conditions the vertical lines are replaced by diamonds. ( a) Type A shell state corresponding to a single-sided black hole. ( b) Type B shell state consisting of thermal AdS (or thermal flat space) with and added disconnected compact Big-Crunch AdS cosmology. Images adapted from Balasubramanian:2025zey.
• Figure 5: Path integral boundary condition for $\braket{i|\mathcal{O}_P|i}\braket{i|\mathcal{O}_P^{\dagger}|i}$.