Sanders, Ko (2015) What can (mathematical) categories tell us about space-time? 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 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.
Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
Social Networking: |
Item Type: | Conference or Workshop Item (UNSPECIFIED) | ||||||
---|---|---|---|---|---|---|---|
Creators: |
|
||||||
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: | 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: | https://philsci-archive.pitt.edu/id/eprint/13265 |
Available Versions of this Item
-
What can (mathematical) categories tell us about space-time? (deposited 23 Jun 2017 16:34)
- What can (mathematical) categories tell us about space-time? (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 |