  We show that the usual Born-Oppenheimer type of approximation used in quantum
gravity, in which a semiclassical time parameter emerges from a weak-coupling
expansion of the Wheeler-DeWitt constraint, leads to a unitary theory at least
up to the next-to-leading order in minisuperspace models. As there are no
unitarity-violating terms, this settles the issue of unitarity at this order,
which has been much debated in the literature. Furthermore, we also show that
the conserved inner product is gauge-fixed in the sense that the measure is
related to the Faddeev-Popov determinant associated with the choice of
semiclassical time as a reparametrization gauge. This implies that the
Born-Oppenheimer approach to the problem of time is, in fact, an instance of a
relational quantum theory, in which transition amplitudes can be related to
conditional probabilities.
