The second of our prize winners will be speaking in Geneva on Wednesday – and via video at UIC and on YouTube. Please join us!
Ko Sanders (University of Leipzig): What can (mathematical) categories tell us about space-time?
Abstract: It is widely believed that in quantum theories of gravity, the classical description of space-time as a manifold is no longer viable as a fundamental concept. Instead, space-time emerges as a suitable approximation. In order to understand what is required to explain this emergence, it is necessary to have a good understanding of the classical structure of space-time.
In this presentation I will focus on the concept of space-time as it appears in locally covariant quantum field theory (LCQFT), an axiomatic framework for describing quantum field theories in the presence of gravitational background fields. A key aspect of LCQFT is the way in which it formulates locality and general covariance, using the language of category theory.
I will argue that the use of category theory gives a precise and explicit statement of how space-time acts as an organizing principle in a systems view of the world. Along the way I will indicate how categories turn physical theories into a kind of models for modal logic, and how the categorical view of space-time shifts the emphasis away from the manifold structure. The latter point suggests that the view of space-time as an organizing principle may persist, even in a quantum theory of gravity, but it may raise new questions.