My work focuses on comparisons between quantum and classical physics in an attempt to understand the kind of world our best theories of physics describe.
I use the mathematical tools of strict deformation quantization to analyze the classical limit of quantum theories. These tools inform the interpretation of quantum theories in terms of particles as well as various continuity and symmetry conditions on quantum states. In addition to their specific role in the philosophy of quantum theories, the classical limit also provides a case study for various general issues in philosophy of science. I have argued that the classical limit constitutes an example of a kind of intertheoretic reduction, which helps us understand the kinds of explanations quantum mechanics can give of other domains. My work also analyzes whether quantization (the inverse procedure to the classical limit) might provide a rational basis for the construction of new scientific theories.
Book: The Classical-Quantum Correspondence, in the series "Cambridge Elements in Philosophy of Physics", Cambridge University Press, 2023.
The classical limit as an approximation. Philosophy of Science, 2020. [preprint, journal]
Extensions of Bundles of C*-algebras (with Jeremy Steeger). Reviews in Mathematical Physics, 2021. [preprint, journal]
Is the classical limit 'singular'? (with Jeremy Steeger). Studies in the History and Philosophy of Modern Physics, 2021. [preprint, journal]
Why Be Regular? Studies in the History and Philosophy of Modern Physics, 2019.
The classical limit of a state on the Weyl algebra. Journal of Mathematical Physics, 2018. [preprint, journal]
On Theory Construction in Physics: Continuity from Classical to Quantum. Erkenntnis, 2017. [preprint, journal]
Quantization as a Categorical Equivalence. Letters in Mathematical Physics, 2024. [preprint]
Classical Limits of Hilbert Bimodules as Symplectic Dual Pairs, forthcoming in Reviews in Mathematical Physics. [preprint]
The classical limit of a symmetry-invariant state. (with Thomas Browning). Letters in Mathematical Physics, 2020. [journal]
Reductive Explanation and the Construction of Quantum Theories. The British Journal for Philosophy of Science, 2022. [preprint, journal]
Classical limits of Unbounded Quantities by Strict Quantization. (with Thomas Browning, Robin Gates-Redburg, Jonah Librande, and Rory Soiffer) Journal of Mathematical Physics, 2020. [preprint, journal]
Localizable Particles in the Classical Limit of Quantum Field Theory. (with Jonah Librande and Rory Soiffer) Foundations of Physics, 2021. [preprint, journal]
One debate in the literature on the foundations of quantum theories focuses on the question of the appropriate mathematical setting for formulating quantum theories. While ordinary quantum theories with finitely many degrees of freedom can be formulated in an irreducible Hilbert space representation of certain canonical commutation relations, the mathematical results undergirding such a formulation break down for systems with infinitely many degrees of freedom. I have argued that in these circumstances, one ought to adopt a more general formulation of quantum theories in terms of C*-algebras and that Hilbert space representations are only auxiliary devices.
Deduction and Definability in Infinite Statistical Systems. Special Issue: Infinite Idealizations in Science in Synthese, 2019. [preprint, journal, erratum]
On the Choice of Algebra for Quantization. Philosophy of Science, 2017. [preprint, journal]
Toward an Understanding of Parochial Observables. The British Journal for the Philosophy of Science, 2016. [preprint, journal]
Unitary Inequivalence in Classical Systems. Synthese, 2016. [preprint, journal]
On broken symmetries in classical systems. Studies in the History and Philosophy of Modern Physics, 2015. [preprint, journal]
A number of "no-go" theorems suggest that the predictions of quantum mechanics cannot be reproduced by a hidden variable theory satisfying certain constraints. A number of authors have suggested that one of those constraints in particular is the culprit---that our hidden variable theories invoke classical Kolmogorovian probability theory. A number of alternative probability theories have arisen out of this suggestion, including negative and imaginary probability spaces as well as probability spaces violating various additivity axioms. My work shows that the "no-go" theorems can be generalized to rule out many of these alternative probability theories as well. Moreover, this approach demonstrates certain conceptual connections between the many existing "no-go" theorems in the literature by providing a unifying framework that pinpoints the source.
On Noncontextual, Non-Kolmogorovian Hidden Variable Theories (with Samuel C. Fletcher). Foundations of Physics, 2017. [preprint, journal]
Hidden Variables and Incompatible Observables in Quantum Mechanics. The British Journal for the Philosophy of Science, 2015. [preprint, journal]
Can the ontological models framework accommodate Bohmian mechanics? Studies in the History and Philosophy of Modern Physics, 2014. [journal]
Classical Limits of Hilbert Bimodules as Symplectic Dual Pairs (with Jer Steeger), in submission.
Quantization and the Preservation of Structure Across Theory Change, in preparation.
Quantum Probability via the Method of Arbitrary Functions (with Liam Bonds, Brooke Burson, Lynnx Cheng, Kade Cicchella, and Alia Yusaini), in preparation.
The Geometry of the 'Gauge Argument'. (with Jim Weatherall), in preparation.
I run undergraduate projects as part of the Washington Experimental Math Lab, which serves to bring talented math students to a research setting.
Probability via Arbitrary Functions for Quantum Multiple-Well Systems
Classical Limit of Fermionic Fields
Classical Rindler Particle Modes as Perfect Fluids
Probability via Arbitrary Functions for the Quantum Double Well
Probability via Arbitrary Functions for the Quantum Harmonic Oscillator
Do Classical Particle Modes Uniquely Determine the Klein-Gordon Field?
Classical Minkowski Particle Modes as Perfect Fluids
Classical Limit of the Electromagnetic Field
Classical Limit of Minkowski and Rindler Number Operators for a Klein-Gordon Field
Berezin Quantization of the Almost Periodic Functions
Quantization and Reduction for a Particle in an External Gauge Field