My dissertation work was focused on exploring and clarifying the way that time gets represented in quantum mechanics. This has led me to a distinctive view of quantum theory, and I'm busy exploring the consequences of this view for our conceptions of time, space, and matter, as well as working out how to extend these insights to relativistic quantum theory and relativistic space-times.
As a result, I've become interested in the metaphysics conceived by Alfred. N. Whitehead and Bertrand Russell in response to relativity and quantum physics. I think the distinctive event-based ontology of their later work deserves a twenty-first century renaissance. With Riccardo Pinosio I am working on an updated version of Russell's relational theory of time.
I'm interested in questions in the philosophy of science having to do with representation, fundamentality, and realism. I'm also interested in metaphysics generally, and in particular theories of persistence. I have interests in the history of modern physics too, especially concerning the incomparable Paul Dirac.
2012. "Dirac's Prediction of the Positron: A Case Study for the Current Realism Debate." Perspectives on Science, Vol. 20, No. 4. Article.
"At what time does a quantum experiment have a result?" (preprint)
"Saving Schrödinger's Cat: It's About Time (Not Measurement)" (draft)
"Quantum Mechanics for Event Ontologists" (conference paper)
"Rovelli's Relational Quantum Mechanics and the Relative State Interpretation are Equivalent"
"Towards a Resolution of the Problem of Relativistic Localization"
"Dirac's Geometrical Approach to the Electron Equation"
"Pauli's Theorem in Classical and Quantum Mechanics" (with Bryan Roberts)
"Digital Topology and the Relational Theory of Time" (with Riccardo Pinosio)
My dissertation, Time and the Foundations of Quantum Mechanics, is about the way that quantum mechanics seems to have a lot of trouble making sense of time and temporal processes, and what we can do to set it right. Some of the best known and most compelling examples of quantum behaviour—like the time of decay of a radioactive atom—require the theory to provide predictions for when something will happen. However, the usual Dirac-von Neumann formalism of quantum mechanics (named after Paul Dirac and John von Neumann) isn't very good at making predictions for processes which happen over a long period of time. In fact, I show that it is only good for making predictions about instantaneous measurements. But that's not at all like the sort of experiments we do in the lab, which usually involve a detector that's sensitive over a long period of time. Well, certainly more than an instant! What's more, it turns out that experiments involving the time at which something happens really can't be described by quantum mechanics unless we're prepared to bend the rules about what sort of physical quantities get interpreted as probabilities.
I argue that these sort of considerations (to do with time) provide a compelling reason to consider a generalization of quantum mechanics that mathematicians have been working on since the 1980s. Applying some of these mathematical tools to the problems that quantum mechanics has with time leads to an interesting new perspective on quantum phenomena. In particular, there's a sense in which giving predictions for the time that something happens means giving up on the idea that a quantum system has an instantaneous state. This actually makes for quite a distinctive way of thinking about quantum theory: rather than being a theory of instantaneous things described by wave-functions, we can think about quantum theory instead as just a way of making predictions of when some event will happen, given that other events have already happened (or will happen). These sort of events could be the decay of an atom, the detection of an electron at a luminescent screen, in a cloud chamber, or some more elaborate detector (like these).
In fact, the view of quantum theory I end up at closely resembles Paul Dirac's first attempts to write down a relativistically invariant form of the theory in 1926, and suggests an interpretation reminiscent of Heisenberg and Jordan's early idea of quantum jumps (inspired by their formalism of matrix mechanics). It also suggests a distinctive event-based ontology for quantum theory like those of Russell (1927) and Whitehead (1925), and is compatible with a Leibnizian view of time as a temporal order on events. I also suggest that these events could form the relata for a structural realist position similar to Russell's original ideas for structuralism.