Talks

The transformation of a narrow beam into a hollow cone when incident along the optic axis of a biaxial crystal, predicted by Hamilton in 1832, created a sensation when observed by Lloyd soon afterwards. It was the first application of his concept of phase space, and the prototype of the conical intersections and fermionic sign changes that now pervade physics and chemistry. But the fine structure of the bright cone contains many subtle features, slowly revealed by experiment, whose definitive explanation, involving new mathematical asymptotics, has been achieved only recently, along with definitive experimental test of the theory. Radically different phenomena arise when chirality and absorption are incorporated in addition to biaxiality.

The notion of a conditional probability is critical for Bayesian reasoning. Bayes’ theorem, the engine of inference, concerns the inversion of conditional probabilities. Also critical are the concepts of conditional independence and sufficient statistics. The conditional density operator introduced by Leifer is a natural generalization of conditional probability to quantum theory. This talk will pursue this generalization to define quantum analogues of Bayes' theorem, conditional independence and sufficient statistics. These can be used to provide simple proofs of certain well-known results in quantum information theory, such as the isomorphism between POVMs and convex decompositions of a mixed state and the remote collapse postulate, and to prove some novel results on how to pool quantum states. This is joint work with Matt Leifer. I will also briefly discuss the possibility of a diagrammatic calculus for classical and quantum Bayesian inference (joint work with Bob Coecke).

Since Einstein first applied his equations of General Relativity to Cosmology, Dark Energy has had a major role in physicists’ efforts to explain the observations of our Universe. Many red herrings have been followed over the past 90 years, where Dark Energy has gone in and out of fashion. However, starting in the 1990s, a broadly supported and sustained view has emerged that the Universe is dominated by Dark Energy – a form of matter with negative pressure. I will give a brief overview of the history of Dark Energy, describe the range of observations that have lead to the adoption of Dark Energy in the standard model of Cosmology, and look to future observations that will refine our understanding of Dark Energy.

We study a simple model of a black hole in AdS and obtain a holographic description of the region inside the horizon,as seen by an infalling observer. For D-brane probes, we construct a map from physics seen by an infalling observer to physics seen by an asymptotic observer that can be generalized to other AdS black holes.

Work on formulating general probabilistic theories in an operational context has tended to concentrate on the probabilistic aspects (convex cones and so on) while remaining relatively naive about how the operational structure is built up (combining operations to form composite systems, and so on). In particular, an unsophisticated notion of a background time is usually taken for granted. It pays to be more careful about these matters for two reasons. First, by getting the foundations of the operational structure correct it can be easier to prove theorems. And second, if we want to construct new theories (such as a theory of Quantum Gravity) we need to start out with a sufficiently general operational structure before we introduce probabilities. I will present an operational structure which is sufficient to provide a foundation for the probabilistic concepts necessary to formulate quantum theory. According to Bob Coecke, this operational structure corresponds to a symmetric monoidal category. I will then discuss a more general operational framework (which I call Object Oriented Operationalism) which provides a foundation for a more general probabilistic framework which may be sufficient to formulate a theory of Quantum Gravity. This more general operational structure does not admit an obvious category theoretic formulation.

I will rephrase the question, "What is a quantal reality?" as "What is a quantal history?" (the word history having here the same meaning as in the phrase sum-over-histories). The answer I will propose modifies the rules of logical inference in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical logic, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular.