A trio of dichotomies, Atomicity versus Continuity, Locality versus Global-ness and, Being versus Becoming, are persistent themes in our struggle to understand the physical world. In the present era, they are finding concrete expression in the attempt to create a theory of "quantum gravity", which phrase is a shorthand for a framework in which all of physics will find unified expression. In my research these ancient tensions reveal themselves to be intertwined one with another and I am attempting, not so much to resolve them but to put them to work as heuristics in discovering quantum gravity. Consider the first dichotomy: we now know that ponderable matter is atomic and, since the work of Einstein, we know that space-time is a physical, 4-dimensional substance which bends, warps and ripples, an apparent continuum. I work on an approach to unifying physics in which this material space-time fabric is itself fundamentally granular or `atomic' and in which the smooth continuum of our current theory of space-time is an approximation to a discrete substructure. Space-time discreteness appears in several approaches to the problem of quantum gravity; what sets the approach I work on apart is that the atomicity respects the relativistic causal principle that physical influence cannot propagate faster than light. This causal spacetime atomicity takes the concrete form of a discrete partial order or causal set.
The other dichotomies become entangled in the quest as causal sets both necessitate a radical non-locality in nature and potentially enable physics to reclaim the notion of Becoming that seemed to have been lost with the advent of relativity and the rise of the block universe view. In another thread, quantum causal set dynamics (QCD) requires that quantum theory be conceived in terms of the path integral. Path integrals are global in nature: they deal with whole spacetime histories. Only in the classical limit does exactly local physics emerge, as the Euler Lagrange equations arise in the stationary phase limit. In the full quantum theory, it is unlikely that locality can be exactly achieved and this adds another layer to the challenge of recovering approximately local physics and a notion of Becoming, from quantum gravity.
Public lecture on my research Spacetime Atoms and the Unity of Physics
Short set of lectures on Causal Set Quantum Gravity
Personal Website atomsofspacetime
Belenchia A, Benincasa DMT, Dowker F, The continuum limit of a 4-dimensional causal set scalar d'Alembertian
et al., 2015, Boundary terms for causal sets, Classical and Quantum Gravity, Vol:32, ISSN:0264-9381
et al., 2014, Quantum information processing and relativistic quantum fields, Classical and Quantum Gravity, Vol:31, ISSN:0264-9381
Dowker F, 2014, The birth of spacetime atoms as the passage of time, Flow of Time, Vol:1326, ISSN:0077-8923, Pages:18-25