  We provide evidence that strong quantum entanglement between Hilbert spaces
does not generically create semiclassical wormholes between the corresponding
geometric regions in the context of the AdS/CFT correspondence. We propose a
description of low-energy gravity probes as random operators on the space of
black hole states. We use this description to compute correlators between the
entangled systems, and argue that a wormhole can only exist if correlations are
large. Conversely, we also argue that large correlations can exist in the
manifest absence of a Lorentzian wormhole. Thus the strength of the
entanglement cannot generically diagnose spacetime connectedness, without
information on the spectral properties of the probing operators. Our random
matrix picture of probes also provides suggestive insights into the problem of
"seeing behind a horizon".
