  Many modern cosmological scenarios feature large volumes of spacetime in a de
Sitter vacuum phase. Such models are said to be faced with a "Boltzmann Brain
problem" - the overwhelming majority of observers with fixed local conditions
are random fluctuations in the de Sitter vacuum, rather than arising via
thermodynamically sensible evolution from a low-entropy past. We argue that
this worry can be straightforwardly avoided in the Many-Worlds (Everett)
approach to quantum mechanics, as long as the underlying Hilbert space is
infinite-dimensional. In that case, de Sitter settles into a truly stationary
quantum vacuum state. While there would be a nonzero probability for observing
Boltzmann-Brain-like fluctuations in such a state, "observation" refers to a
specific kind of dynamical process that does not occur in the vacuum (which is,
after all, time-independent). Observers are necessarily out-of-equilibrium
physical systems, which are absent in the vacuum. Hence, the fact that
projection operators corresponding to states with observers in them do not
annihilate the vacuum does not imply that such observers actually come into
existence. The Boltzmann Brain problem is therefore much less generic than has
been supposed.
