  The emergent semiclassical time approach to resolving the problem of time in
quantum gravity involves heavy slow degrees of freedom providing via an
approximately Hamilton-Jacobi equation an approximate timestandard with respect
to which the quantum mechanics of light fast degrees of freedom can run. More
concretely, this approach involves Born-Oppenheimer and WKB ansatze and some
accompanying approximations. In this paper, I investigate this approach for
concrete scaled relational particle mechanics models, i.e. models featuring
only relative separations, relative angles and relative times. I consider the
heavy-light interaction term in the light quantum equation - necessary for the
semiclassical approach to work, firstly as an emergent-time dependent
perturbation of the emergent-time-dependent Schrodinger equation for the light
subsystem. Secondly, I consider a scheme in which the backreaction is small but
non-negligible, so that the l-subsystem also affects the form of the emergent
time. I also suggest that the many terms involving expectation values of the
light wavefunctions in both the (unapproximated) heavy and light equations
might require treatment in parallel to the Hartree--Fock self-consistent
approach rather than merely being discarded; for the moment this paper provides
a counterexample to such terms being smaller than their unaveraged
counterparts. Investigation of these ideas and methods will give us a more
robust understanding of the suggested quantum-cosmological origin of microwave
background inhomogeneities and galaxies.
