Causal sets and frame-valued set theory

Abstract
In spacetime physics any set C of events—a causal set—is taken to be partially ordered by the relation ≤ of possible causation: for p, q ∈ C, p ≤ q means that q is in p’s future light cone. In her groundbreaking paper The internal description of a causal set: What the universe looks like from the inside, Fotini Markopoulou proposes that the causal structure of spacetime itself be represented by “sets evolving over C” —that is, in essence, by the topos SetC of presheaves on Cop. To enable what she has done to be the more easily expressed within the framework presented here, I will reverse the causal ordering, that is, C will be replaced by Cop, and the latter written as P—which will, moreover, be required to be no more than a preordered set. Specifically, then: P is a set of events preordered by the relation ≤, where p ≤ q is intended to mean that p is in q’s future light cone—that q could be the cause of p, or, equally, that p could be an effect of q. In that case, for each event p, the set p↓ = {q: q ≤ p} may be identified as the causal future of p, or the set of potential effects of p. In requiring that ≤ be no more than a preordering—in dropping, that is, the antisymmetry of ≤—I am, in physical terms, allowing for the possibility that the universe is of Gödelian type, containing closed timelike lines.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,986
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA

No citations found.

Similar books and articles
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

10 ( #146,014 of 1,100,989 )

Recent downloads (6 months)

1 ( #290,337 of 1,100,989 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.