  In ordinary gravitational theories, any local bulk operator in an
entanglement wedge is accompanied by a long-range gravitational dressing that
extends to the asymptotic part of the wedge. Islands are the only known
examples of entanglement wedges that are disconnected from the asymptotic
region of spacetime. In this paper, we show that the lack of an asymptotic
region in islands creates a potential puzzle that involves the gravitational
Gauss law, independently of whether or not there is a non-gravitational bath.
In a theory with long-range gravity, the energy of an excitation localized to
the island can be detected from outside the island, in contradiction with the
principle that operators in an entanglement wedge should commute with operators
from its complement. In several known examples, we show that this tension is
resolved because islands appear in conjunction with a massive graviton. We also
derive some additional consistency conditions that must be obeyed by islands in
decoupled systems. Our arguments suggest that islands might not constitute
consistent entanglement wedges in standard theories of massless gravity where
the Gauss law applies.
