  Exactly soluble models can serve as excellent tools to explore conceptual
issues in non-perturbative quantum gravity. In perturbative approaches, it is
only the two radiative modes of the linearized gravitational field that are
quantized. The goal of this investigation is to probe the `Coulombic' aspects
of quantum geometry that are governed entirely by matter sources. Since there
are no gravitational waves in 3 dimensions, 3-d gravity coupled to matter
provides an ideal arena for this task. Our analysis will reveal novel aspects
of quantum gravity that bring out limitations of classical and semi-classical
theories in unforeseen regimes: non-linearities of general relativity can
magnify small quantum fluctuations in the matter sector to large effects in the
gravitational sector. Finally, this analysis leads to thought experiments that
bring out rather starkly why understanding of the nature of physical reality
depends sensitively on the theoretical lens with which it is probed. As
theories becomes richer, new scales emerge, triggering novel effects that could
not be imagined before. The model provides a concise realization of this
well-known chain.
