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.

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