Sanders, Ko (2015) What can (mathematical) categories tell us about spacetime? In: UNSPECIFIED.
This is the latest version of this item.

Text
SpacetimeEssay_v2.pdf Download (254kB)  Preview 
Abstract
It is widely believed that in quantum theories of gravity, the classical description of spacetime as a manifold is no longer viable as a fundamental concept. Instead, spacetime 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 spacetime.
In this essay I will focus on the concept of spacetime 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 spacetime 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 spacetime shifts the emphasis away from the manifold structure. The latter point suggests that the view of spacetime 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.
Export/Citation:  EndNote  BibTeX  Dublin Core  ASCII/Text Citation (Chicago)  HTML Citation  OpenURL 
Social Networking: 
Item Type:  Conference or Workshop Item (UNSPECIFIED)  

Creators: 


Keywords:  spacetime, 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:  28 Jul 2017 16:23  
Last Modified:  28 Jul 2017 16:23  
Item ID:  13265  
Subjects:  Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Relativity Theory 

Date:  10 December 2015  
URI:  http://philsciarchive.pitt.edu/id/eprint/13265 
Available Versions of this Item

What can (mathematical) categories tell us about spacetime? (deposited 23 Jun 2017 16:34)
 What can (mathematical) categories tell us about spacetime? (deposited 28 Jul 2017 16:23) [Currently Displayed]
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
View Item 