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Holographic Thought Experiments

Donald Marolf

TL;DR

The paper studies how information encoded at the AdS boundary can remain accessible under unitary boundary evolution and how this holographic encoding interacts with bulk causality. By constructing two-boundary (A and B) setups and analyzing thought experiments that couple to the boundary flux $\Phi_A$, it shows that certain strong couplings push the system beyond semi-classical gravity, potentially altering causal structure to reconcile boundary unitarity with interior measurements. It then introduces the concept of an operationally finite density of states $S(E)$, which can allow exact past information retrieval via long, controlled experiments without invoking drastic causal changes. The work also discusses alternative protocols using quantum memories and considers black-hole contexts, arguing that AdS/CFT provides a dual lens in which high-precision boundary energy measurements are possible, while the full quantum-gravity regime may require new principles. Overall, it clarifies when and how holographic unitarity can coexist with bulk causality and highlights the role of boundary conditions and spectral finiteness in resolving potential paradoxes relevant to holography and quantum gravity.

Abstract

The Hamiltonian of classical anti-de Sitter gravity is a pure boundary term on-shell. If this remains true in non-perturbative quantum gravity then i) boundary observables will evolve unitarily in time and ii) the algebra of boundary observables is the same at all times. In particular, information available at the boundary at any one time t_1 remains available at any other time t_2. Since there is also a sense in which the equations of motion propagate information into the bulk, these observations raise what may appear to be potential paradoxes concerning simultaneous (or spacelike separated) measurements of non-commuting observables, one at the asymptotic boundary and one in the interior. We argue that such potentially paradoxical settings always involve a breakdown of semi-classical gravity. In particular, we present evidence that making accurate holographic measurements over short timescales radically alters the familiar notion of causality. We also describe certain less intrinsically paradoxical settings which illustrate the above boundary unitarity and render the notion more concrete.

Holographic Thought Experiments

TL;DR

The paper studies how information encoded at the AdS boundary can remain accessible under unitary boundary evolution and how this holographic encoding interacts with bulk causality. By constructing two-boundary (A and B) setups and analyzing thought experiments that couple to the boundary flux , it shows that certain strong couplings push the system beyond semi-classical gravity, potentially altering causal structure to reconcile boundary unitarity with interior measurements. It then introduces the concept of an operationally finite density of states , which can allow exact past information retrieval via long, controlled experiments without invoking drastic causal changes. The work also discusses alternative protocols using quantum memories and considers black-hole contexts, arguing that AdS/CFT provides a dual lens in which high-precision boundary energy measurements are possible, while the full quantum-gravity regime may require new principles. Overall, it clarifies when and how holographic unitarity can coexist with bulk causality and highlights the role of boundary conditions and spectral finiteness in resolving potential paradoxes relevant to holography and quantum gravity.

Abstract

The Hamiltonian of classical anti-de Sitter gravity is a pure boundary term on-shell. If this remains true in non-perturbative quantum gravity then i) boundary observables will evolve unitarily in time and ii) the algebra of boundary observables is the same at all times. In particular, information available at the boundary at any one time t_1 remains available at any other time t_2. Since there is also a sense in which the equations of motion propagate information into the bulk, these observations raise what may appear to be potential paradoxes concerning simultaneous (or spacelike separated) measurements of non-commuting observables, one at the asymptotic boundary and one in the interior. We argue that such potentially paradoxical settings always involve a breakdown of semi-classical gravity. In particular, we present evidence that making accurate holographic measurements over short timescales radically alters the familiar notion of causality. We also describe certain less intrinsically paradoxical settings which illustrate the above boundary unitarity and render the notion more concrete.

Paper Structure

This paper contains 11 sections, 25 equations, 2 figures.

Table of Contents

  1. Introduction
  2. A tale of two boundaries
  3. Measuring the past
  4. A more physical measurement
  5. Operationally discrete spectra
  6. A return to projections
  7. Quantum computers and generic couplings
  8. Experiments inside Black Holes
  9. Discussion
  10. Diffeomorphism invariance and the Hamiltonian
  11. Time-dependent Boundary conditions: An example

Figures (2)

  • Figure 1: A conformal diagram of global AdS${}_{4}$ with the $S^2$ suppressed. A signal leaves the boundary at time $t_1$. The information is still present in the CFT at time $t_2$ though no signal has returned to the boundary.
  • Figure 2: Our AdS system lives in a (conformal) box in Alice's laboratory. Outside the AdS box are various ancilla. A clock and a measuring device with adjustable coupling are shown.