  We describe a kinetic theory approach to quantum gravity -- by which we mean
a theory of the microscopic structure of spacetime, not a theory obtained by
quantizing general relativity. A figurative conception of this program is like
building a ladder with two knotted poles: quantum matter field on the right and
spacetime on the left. Each rung connecting the corresponding knots represent a
distinct level of structure. The lowest rung is hydrodynamics and general
relativity; the next rung is semiclassical gravity, with the expectation value
of quantum fields acting as source in the semiclassical Einstein equation. We
recall how ideas from the statistical mechanics of interacting quantum fields
helped us identify the existence of noise in the matter field and its effect on
metric fluctuations, leading to the establishment of the third rung: stochastic
gravity, described by the Einstein-Langevin equation. Our pathway from
stochastic to quantum gravity is via the correlation hierarchy of noise and
induced metric fluctuations. Three essential tasks beckon: 1) Deduce the
correlations of metric fluctuations from correlation noise in the matter field;
2) Reconstituting quantum coherence -- this is the reverse of decoherence --
from these correlation functions 3) Use the Boltzmann-Langevin equations to
identify distinct collective variables depicting recognizable metastable
structures in the kinetic and hydrodynamic regimes of quantum matter fields and
how they demand of their corresponding spacetime counterparts. This will give
us a hierarchy of generalized stochastic equations -- call them the
Boltzmann-Einstein hierarchy of quantum gravity -- for each level of spacetime
structure, from the macroscopic (general relativity) through the mesoscopic
(stochastic gravity) to the microscopic (quantum gravity).
