Holographic Thought Experiments

TL;DR

This paper explores the implications of boundary-only Hamiltonians in anti-de Sitter gravity for unitarity, causality, and potential paradoxes in holographic quantum gravity, highlighting the breakdown of semi-classical assumptions.

Contribution

It argues that boundary unitarity and information preservation lead to causality modifications and potential paradoxes, emphasizing the breakdown of semi-classical gravity in holographic measurements.

Findings

Boundary Hamiltonian is a pure boundary term on-shell.

Boundary observables evolve unitarily over time.

Short-timescale measurements can alter causality notions.

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.