  Two quantum field theories whose Hilbert spaces do not overlap cannot
transmit a signal to one another. From this simple principle, we deduce some
highly nontrivial consequences for holographic quantum gravity. These include:
(1) certain cosmological bounces are forbidden, (2) generic singularities
inside black holes cannot be resolved, and (3) traversable wormholes do not
exist. At the classical level, this principle rules out certain types of naked
singularities and suggests that new singularity theorems should exist.
