John Baez
Duality in Logic and Physics

Duality has many manifestations in logic and physics. In classical logic, propositions form a partially ordered set and negation is an order-reversing involution which switches "true" and "false". The same holds in quantum logic, with propositions corresponding to closed subspaces of a Hilbert space. But the full structure of quantum physics involves more: at the very least, the category of Hilbert spaces and bounded linear operators. This category has another kind of duality, a contravariant involution that switches "preparation" and "observation". Other closely related dualities in quantum physics include "time reversal" (switching future and past) and "charge conjugation" (switching matter and antimatter). The quest to find a unified mathematical framework for dualities in logic and physics leads to a fascinating variety of structures: star-autonomous categories, n-categories with duals, and more. We give a tour of these, with an effort to focus on conceptual rather than technical issues.

John Barrett
State sum models, induced gravity and the spectral action

I will give a new proposal for the spectral action for gravity coupled to matter, taking into account the phenomenon of induced gravity. This is then used to give some perspectives for the construction of a quantum theory of gravity coupled to matter using state sum models based on a tricategory.

Louis Crane
The category of spacetime regions

The purpose of this talk is to propose a connection between the spin foam approach to quantum gravity and a branch of abstract homotopy theory called model category theory. The spin foam approach models regions in spacetime by four dimensional simplicial complexes. The quantum theory of the metric on them is constructed by putting representations of the Lorentz group on the triangulation and combining them in a specific way, called a categorical state sum. Recently a technical advance has removed the problems that plagued the theory, so that a finite computational theory of quantum general relativity seems to be available. The deeper interpretational problems remain: what do the specific complexes mean? Are they triangulations of an underlying point set, or Feynman diagrams of a fundamental theory? If they are just approximations, how does the exact theory emerge? How does the Bekenstein bound relate to this picture? How does the classical limit of the models approach general relativity? What we are going to propose is that the state sum models on different simplicial complexes can be modified to fit together to form what is called a model category. We can then incorporate the Bekenstein bound into the model by using a technique from model category theory called localization. The flow of information from a system to its exterior would be a map in the category, and the localization of a model of the system with respect to this map would give a simplicial complex on which the exact effective theory would be computed.

Benjamin Schumacher
What is information? Reversibility and simulation

Over the last two decades, quantum physics has introduced new concepts of information and computation based on physical laws. This has required a re-examination of our old notions of information and information processing. In what sense can we regard quantum entanglement as a kind of "information", or the dynamical evolution of a quantum system (a computer) as a kind of "computation"? This talk will draw on the lessons of the quantum realm to suggest a general framework for thinking about information and physics. We will argue that the idea of "information" describes the reversible and irreversible transformations of a physical state, while "computation" addresses how one physical process may act as a simulation of another.

Last modified: April 1, 2010 by Bob Coecke