  There are not many tools to quantitatively monitor the emergence of classical
geometric features from a quantum spacetime, whose microscopic structure may be
a highly quantum-fluctuating "spacetime foam". To improve this situation, we
introduce new quantum observables that allow us to measure the absolute and
relative homogeneity of geometric properties of a nonperturbative quantum
universe, as function of a chosen averaging scale. This opens a new way to
compare results obtained in full quantum gravity to descriptions of the early
universe that assume homogeneity and isotropy at the outset. Our construction
is purely geometric and does not depend on a background metric. We illustrate
the viability of the quantum homogeneity measures by a nontrivial application
to two-dimensional Lorentzian quantum gravity formulated in terms of a path
integral over Causal Dynamical Triangulations, and find some evidence of
quantum inhomogeneity.
