### 6.3 Emergent gravity

One of the more fascinating approaches to “quantum gravity” is the suggestion, typically attributed to
Sakharov [332, 393], that gravity itself may not be “fundamental physics”. Indeed it is now a relatively
common opinion, maybe not mainstream but definitely a strong minority opinion, that gravity (and in
particular the whole notion of spacetime and spacetime geometry) might be no more “fundamental” than is
fluid dynamics. The word “fundamental” is here used in a rather technical sense - fluid mechanics is not
fundamental because there is a known underlying microphysics, that of molecular dynamics, of which fluid
mechanics is only the low-energy low-momentum limit. Indeed the very concepts of density and velocity
field, which are so central to the Euler and continuity equations, make no sense at the microphysical level
and emerge only as one averages over timescales and distance-scales larger than the mean free time and
mean free path.
In the same way, it is plausible (even though no specific and compelling model of the relevant
microphysics has yet emerged) that the spacetime manifold and spacetime metric might arise only once one
averages over suitable microphysical degrees of freedom. Sakharov had in mind a specific model in which
gravity could be viewed as an “elasticity” of the spacetime medium, and was “induced” via
one-loop physics in the matter sector [332, 393]. In this way Sakharov had hoped to relate the
observed value of Newton’s constant (and the cosmological constant) to the spectrum of particle
masses.

More generally the phrase “emergent gravity” is now used to describe the whole class of theories in
which the spacetime metric arises as a low-energy approximation, and in which the microphysical degrees
of freedom might be radically different. Analogue models, and in particular analogue models
based on fluid mechanics or the fluid dynamic approximation to BECs, are specific examples of
“emergent physics” in which the microphysics is well understood. As such they are useful for
providing hints as to how such a procedure might work in a more fundamental theory of quantum
gravity.