My PhD research at Flinders University centred upon Process Physics and was carried out under the supervision of Professor Reg Cahill. The apparent success of Process Physics in generating interesting, and possibly complex, emergent behaviour led to many of my current research interests. Rather than the static 4-dimensional modelling of present day (non-process) physics, Process Physics attempts to construct a dynamic model where space and matter are seen to emerge from a fundamentally random but self-organising system. The key insight is that to adequately model reality we must move on from the traditional non-process syntactical information modelling to a process semantic information modelling; such information is "internally meaningful".
We start with a relational network of links, represented as a matrix B
(where node i is connected to node j if there is a nonzero entry in the matrix).
We then model the evolution in time of this matrix (which represents the pre-geometric universe)
using equation that is inspired from quantum field theory (in particular the Global Color model of QCD),
but with all of the details (like spatial coordinates, colour charge etc.) stripped away:
Over time, we see the system link up, to form trees of a particular form. The figure alongside shows that most of the trees can be fairly well embedded in a three dimensional hypersphere. This is because the distance Dk between nodes is best fitted by the equation , when the dimensionality of the sphere, d=3.16, for a distance from tree to leaf of around 40 nodes. The "extra dimensionality" of the fit (the .16 value) represents overconnected space, which in this model is taken to represent matter. This extra structure is very difficult to model though, and this led to my interests in Complex Systems Science, and in particular, my attempts to model the dynamical formation of hierarchical structures.
More Recent Details
I have not worked on this stuff for quite a while... I suggest you go to the Process Physics homepage to find out what is going on now.