  Spontaneous localisation is a falsifiable dynamical mechanism which modifies
quantum mechanics, and explains the absence of position superpositions in the
macroscopic world. However, this is an ad hoc phenomenological proposal.
Adler's theory of trace dynamics, working on a flat Minkowski space-time,
derives quantum (field) theory, and spontaneous localisation, as a
thermodynamic approximation to an underlying non-commutative matrix dynamics.
We describe how to incorporate gravity into trace dynamics, by using ideas from
Connes' non-commutative geometry programme. This leads us to a new quantum
theory of gravity, from which we can predict spontaneous localisation, and give
an estimate of the Bekenstein-Hawking entropy of a Schwarzschild black hole.
