Holographic Thought Experiments

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.