  We have recently proposed a deterministic matrix dynamics at the Planck
scale, for gravity coupled to Dirac fermions, evolving in the so-called Connes
time. By coarse-graining this dynamics over time intervals much larger than
Planck time, we derived the space-time manifold, quantum theory, and classical
general relativity, as low energy emergent approximations to the underlying
matrix dynamics. In the present article, we show how to include Yang-Mills
gauge fields in this Planck scale matrix dynamics. We do this by appropriately
modifying the fundamental action for the previously introduced `atom' of
space-time-matter [which we now call an `aikyon']. This is achieved by
modifying the Dirac operator to include a `potential' for the Yang-Mills
aspect, and a `current' for the Yang-Mills charge. Our work opens up an avenue
for unification of gravity with gauge-fields and Dirac fermions. We show how
spontaneous localisation in the matrix dynamics gives rise to general
relativity coupled to gauge-fields and relativistic point particles, in the
classical limit. We use this formalism to explain the remarkable fact that the
Kerr-Newman black hole has the same value for the gyromagnetic ratio as that
for a Dirac fermion, both being twice the classical value.
