Inside the Hologram: Reconstructing the bulk observer's experience

TL;DR

The paper proposes an observer-centered holographic framework to describe bulk experiences in AdS/CFT, encoding proper time and energy measurements along bulk worldlines via boundary modular dynamics without requiring explicit bulk geometry. It models the bulk observer as a black hole entangled with a reference, and uses modular Hamiltonians, modular Berry transport, and code-subspace dynamics to relate initial and final boundary data. Proper time emerges from the modular evolution coefficient while infalling energy manifests through maximal modular chaos via scrambling modes, resolving the Marolf-Wall puzzle in suitable setups. The approach is tested with moving and accelerating black holes, explored for twin-observer time dilation, and extended to particle detection and maximal chaos, with a discussion of emergent time, the frozen vacuum problem, and the feasibility of sub-AdS probes through microcanonical ensembles.

Abstract

We develop a holographic framework for describing the experience of bulk observers in AdS/CFT, that allows us to compute the proper time and energy distribution measured along any bulk worldline. Our method is formulated directly in the CFT language and is universal: It does not require knowledge of the bulk geometry as an input. When used to propagate operators along the worldline of an observer falling into an eternal black hole, our proposal resolves a conceptual puzzle raised by Marolf and Wall. Notably, the prescription does not rely on an external dynamical Hamiltonian or the AdS boundary conditions and is, therefore, outlining a general framework for the emergence of time.

Figures (8)

• Figure 1: An illustration of our setup. The red line represents the worldline of an ideal observer. We replace them by a small black hole of radius $r_{BH}$ much smaller than the spacetime's curvature features which we thermally entangle with a reference system, assumed to be another AdS black hole for simplicity. The black hole propagates along the original geodesic due to the equivalence principle. The green tube of radius $\ell$ around the black hole represents its "atmosphere": The operators our observer can manipulate at any given time.
• Figure 2: Our black hole is introduced geometrically by cutting a hole of size $\ell$ around the ideal observer's worldline in the initial Cauchy slice and a small time band $\Sigma_0(\epsilon)$ about it and replacing the interior with a black hole metric. The local killing vector generating the worldline's proper time is glued to the local generator of Schwarzschild time which, in turn, is modular time. As long as nothing falls in the black hole, this identification is valid everywhere along the worldline, suggesting that modular time is correlated to proper time.
• Figure 3: Illustration of the three different flows appearing in our discussion. $H$ is the CFT Hamiltonian generating global AdS evolution. $V_H$ is modular flow which maps the $t_i=0$ atmosphere operators (green disk on $t_i=0$ slice) to the Heisenberg picture atmosphere operators at $t_f=t$. $V_S$ describes the evolution of the atmosphere operators in the Schrodinger picture and captures the motion of the black hole relative to the boundary.
• Figure 4: LEFT: A black hole in AdS that receives a kick at $t_0$. Arbitrary trajectories in AdS can be generated by a dense sequence of such instantaneous kicks, allowing us to describe proper time evolution in any weakly curved spacetime. RIGHT: Twin black holes. The left twin is static while the right twin is the accelerated black hole of the LEFT panel. The time dilation experienced by the twins is computed by the modular Berry holonomy of the "loop" of modular Hamiltonians describing the two trajectories and the integral of the zero mode projection of the CFT Hamiltonian along the loop via eq. (\ref{['timedilationloop']}), (\ref{['timedilation']}).
• Figure 5: Free field vs shock contributions to the modular flow of a local "atmosphere" operator $\phi$ in the state (\ref{['PsiJ']})