Prof. Suvrat Raju (Centre for Theoretical Sciences, Tata Institute of Fundamental Research)
We describe an apparent paradox with state-dependent constructions of the black hole interior: excitations with small energy with respect to the boundary Hamiltonian can have strong effects on an infalling observer violating a principle of statistical mechanics that bounds the effect of low-energy sources. This is sometimes called a "Born rule" violation. We describe how this paradox is resolved by causality. As a result of a non-trivial property of position-space AdS correlators, no observer can create such an excitation and also observe its effect. This is an important check of the consistency of state-dependent maps between the black hole interior and boundary operators in AdS/CFT.