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What can (mathematical) categories tell us about space-time?

Sanders, Ko (2015) What can (mathematical) categories tell us about space-time? In: UNSPECIFIED.

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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 an approximation in appropriate regimes. 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 essay 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 certain systems view of the world. Along the way I will indicate how physical theories give rise to categories which act as 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, perhaps in a generalized way, even in a quantum theory of gravity. I will mention some new questions, which this shift in emphasis raises.


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Item Type: Conference or Workshop Item (UNSPECIFIED)
Creators:
CreatorsEmailORCID
Sanders, Kojacobus.sanders@dcu.ie0000000184905568
Keywords: space-time, category theory
Subjects: Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Relativity Theory
Depositing User: Dr. Ko Sanders
Date Deposited: 23 Jun 2017 16:34
Last Modified: 23 Jun 2017 16:34
Item ID: 13147
Subjects: Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Relativity Theory
Date: 10 December 2015
URI: http://philsci-archive.pitt.edu/id/eprint/13147

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