Space as a ''bucket of dust''
type: Item
instance of: scholarly article
title: Space as a ''bucket of dust''
zbMATH Open document ID: 0564.53045
DOI: 10.1007/BF00763048
author: G. Nagels
published in: General Relativity and Gravitation
publication date: 1985-01-01T00:00:00Z
review text: Wheeler has suggested the need for pre-geometry, that is, a prior structure from which continuous space can be constructed (at least approximately). This paper takes seriously the idea of starting with a large number of elements which can be connected; it claims that with very few assumptions such a set will exhibit properties usually associated with a three-dimensional space of constant positive curvature. It assumes that the elements are the vertices of a random graph, with each edge having constant small probability p of existing; distance is then defined in the usual graph-theoretic way. The probability distribution of the ''shape'' of the universe (that is, the assemblage of distances) is then found, and a rather complex analysis of the most probable distribution shows a ln N/ln L relation \((N=number\) of elements, \(L=size)\) approaching 3, independent of p so long as it is small. The result appears to depend critically on p being both small and constant.
reviewed by: C. W. Kilmister
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81Q15
Mathematics Subject Classification ID: 83E05
zbMATH DE Number: 3899713
zbMATH Keywords: dimensionality of space
zbMATH Keywords: pre-geometry
zbMATH Keywords: continuous space
zbMATH Keywords: probability distribution
MaRDI profile type: Publication
cites work: Q5328018
cites work: Q5527782
cites work: Q4157839
description: scientific article; zbMATH DE number 3899713