In our struggle to understand the physical world, certain dichotomies have been thematic foci of that struggle from ancient times: Atomicity versus Continuity, Being versus Becoming, Locality versus Global-ness, Order versus Chaos, Objectivity versus Subjectivity. These remain persistent themes into the present era. Today, 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 dichotomy of Atomicity versus Continuity. 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.
Public Lecture A meditation on General Relativity
I work on an approach to unifying physics---causal set theory---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 causal set theory 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.
Public lecture: Spacetime Atoms and the Unity of Physics
The other dichotomies are also embroiled in the development of causal set theory.
There are classically stochastic models of causal set cosmology in which the universe grows in a way that respects relativity and respects the non-existence of a global time coordinate. The atomicity of causal sets has therefore allowed 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. A major question is: Can Quantum Becoming be realised in causal set theory?
The Lorentz invariance and discreteness of Causal sets mean that they are radically non-locality in nature. How that non-locality might manifest itself and how and why the non-locality seems to be hidden in quantum field theory and GR as we know them is a puzzle seeking a solution. Closely connected to this local-global dichotomy, is the fact that a quantum causal set dynamics is framed in terms of the path integral. Path integrals are global in nature: they deal with whole spacetime histories. They can also explain how quantum mechanics can be non-local and yet still relativistically causal.
In Physics the struggle between Order and Chaos manifests itself in a primal struggle between Action and Entropy. In quantum gravity specifically, it takes the form of the ``cosmological constant problem''. Entropically, the cosmological constant Lambda should take the value 1 in natural units, which would result in a chaotic universe with no large scale structure at all. Instead, its physically observed value is 120 orders of magnitude smaller and is the smallest number in physics. For that to happen, the Action--the Dynamics--of quantum gravity must be powerful enough to reign in the entropic forces of chaos to produce the large ordered universe we see. The nonlocality of causal sets holds out the promise that this is possible.
Finally the Objectivity versus Subjectivity dichotomy lies at the heart of the scientific endeavour. The desire to understand the world as it is, independently of myself and other human beings, is what motivates me. However we cannot remove ourselves from the World of which we are a part. I have argued that conscious experience is the objective process of the birth of spacetime atoms in the brain in causal set theory and it is necessarily an internal view because of the relativistic structure of causal sets.
Seminar Causal Set Quantum Gravity and the Hard Problem of Consciousness
Dowker F, Sorkin RD, 2023, An intrinsic causality principle in histories-based quantum theory: a proposal, Journal of Physics A: Mathematical and Theoretical, Vol:56, ISSN:1751-8113
Dowker F, Zalel S, 2023, Observables for cyclic causal set cosmologies, Classical and Quantum Gravity, Vol:40, ISSN:0264-9381
Dowker F, Wilkes H, 2022, An argument for strong positivity of the decoherence functional in the path integral approach to the foundations of quantum theory, Avs Quantum Science, Vol:4, ISSN:2639-0213, Pages:012601-012601
Bento BV, Dowker F, Zalel S, 2022, If time had no beginning: growth dynamics for past-infinite causal sets, Classical and Quantum Gravity, Vol:39, ISSN:0264-9381
Dowker F, 2021, Boundary contributions in the causal set action, Classical and Quantum Gravity, Vol:38, ISSN:0264-9381