My current research involves two general topics.
First, I am interested in attempts to resolve the measurement problem in quantum mechanics. The measurement problem arises from the fact that the standard theory’s two dynamical laws are incompatible: one is linear and the other nonlinear. Since they constitute contradictory descriptions of the time-evolution of physical states, they threaten to render the standard theory logically inconsistent if one is unable to specify strictly disjoint conditions for when each applies. The theory tells us that the linear dynamics is to be used in all situations except when a measurement is made in which case the nonlinear collapse dynamics is to be used; but since it does not tell us what constitutes a measurement, we do not know when to apply the linear dynamics and when to apply the collapse dynamics. I am particularly interested in solutions to the measurement problem that drop the collapse dynamics altogether.
Second, I am interested in using decision theory and evolutionary game theory to model basic features of empirical and mathematical inquiry. In particular, I have been modeling the coevolution of descriptive language and predictive theory in the context of Skyrms-Lewis sender-receiver games. Recent models have examined how effective priors and the very notions of truth and probability might coevolve with language. Most recently, I have been working with Brian Skyrms to show how such evolutionary games get started then interact with each other to form more complex games. This is the theory of self-assembling games.
A recent talk on Hugh Everett III’s many-worlds theory