AdS/CFT is a duality
relating the degrees of freedom in a D dimensional bulk gravity theory to a (D-1) dimensional theory living on the boundary. I will argue that in fact the boundary theory contains only a subset of the bulk observables. For each state of the boundary theory, there are multiple bulk states dual to it, which can be operationally distinguished by observers who fall across event horizons. Based on arXiv:1210.3590.