  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.
