Research/

Quantization Lab

Research

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.

Quantization and the Classical Limit

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.


Reduction

Continuity Conditions

Symmetry

Particles

Algebraic Representations of Physical Systems

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.

Hidden Variables and Alternative Probability Theories

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.


Works in Progress



Quantization Lab

I run undergraduate projects as part of the Washington Experimental Math Lab, which serves to bring talented math students to a research setting.

Current Projects

Past Projects