  Here, the Abraham-Minkowski controversy on the correct definition of the
light momentum in a macroscopic medium is revisited with the purpose to
highlight that an effective medium formalism necessarily restricts the
available information on the internal state of a system, and that this is
ultimately the reason why the dilemma has no universal solution. Despite these
difficulties, it is demonstrated that in the limit of no material absorption
and under steady-state conditions, the time-averaged light (kinetic) momentum
may be unambiguously determined by the Abraham result, both for bodies at rest
and for circulatory flows of matter. The implications of these findings are
discussed in the context of quantum optics of moving media, and we examine in
detail the fundamental role of the Minkowski momentum in such a context.
