From state distinguishability to effective bulk locality

We provide quantitative evidence that the emergence of an effective notion of spacetime locality in black hole physics is due to restricting to the subset of observables that are unable to resolve black hole microstates from the maximally entangled state. We identify the subset of observables in the full quantum theory that can distinguish microstates, and argue that any measurement of such observables involves either long times or large energies, both signaling the breaking down of effective field theory where locality is manifest. We discuss some of the implications of our results for black hole complementarity and the existence of black hole interiors.