  Recently a certain thought experiment was discussed which involves the
decoherence of a quantum system due to a black hole. Here we show how this
phenomenon is consistent with standard ideas about quantum black holes. In
other words, modeling the black hole as a quantum system at finite temperature
one obtains the same answer. We demonstrate this by analyzing the problem in
terms of an effective theory that can apply both for the black hole case and
for an ordinary matter system, showing that the same qualitative effect is
present for ordinary matter at finite temperature.
