  Invariant Set Theory (IST) is a realistic, locally causal theory of
fundamental physics which assumes a much stronger synergy between cosmology and
quantum physics than exists in contemporary theory. In IST the (quasi-cyclic)
universe $U$ is treated as a deterministic dynamical system evolving precisely
on a measure-zero fractal invariant subset $I_U$ of its state space. In this
approach, the geometry of $I_U$, and not a set of differential evolution
equations in space-time $\mathcal M_U$, provides the most primitive description
of the laws of physics. As such, IST is non-classical. The geometry of $I_U$ is
based on Cantor sets of space-time trajectories in state space, homeomorphic to
the algebraic set of $p$-adic integers, for large but finite $p$. In IST, the
non-commutativity of position and momentum observables arises from number
theory - in particular the non-commensurateness of $\phi$ and $\cos \phi$. The
complex Hilbert Space and the relativistic Dirac Equation respectively are
shown to describe $I_U$, and evolution on $I_U$, in the singular limit of IST
at $p=\infty$; particle properties such as de Broglie relationships arise from
the helical geometry of trajectories on $I_U$ in the neighbourhood of $\mathcal
M_U$. With the p-adic metric as a fundamental measure of distance on $I_U$,
certain key perturbations which seem conspiratorially small relative to the
more traditional Euclidean metric, take points away from $I_U$ and are
therefore unphysically large. This allows (the $\psi$-epistemic) IST to evade
the Bell and Pusey et al theorems without fine tuning or other objections. In
IST, the problem of quantum gravity becomes one of combining the
pseudo-Riemannian metric of $\mathcal M_U$ with the p-adic metric of $I_U$. A
generalisation of the field equations of general relativity which can achieve
this is proposed.
