Causality explains why spatial and temporal translations commute: A remark
type: Item
instance of: scholarly article
title: Causality explains why spatial and temporal translations commute: A remark
zbMATH Open document ID: 0852.53075
DOI: 10.1007/BF02082831
published in: International Journal of Theoretical Physics
publication date: 1996-12-01T00:00:00Z
review text: The author defines a spacetime as a pair \((M,\leq)\) with \(M\) a set and \(\leq \) an order. (The exact properties of \(\leq\) are not specified but it is to be regarded as a ``causality'' ordering. Also a ``non-trivial'' restriction which the reviewer does not understand is imposed on \(M\).) A 1-1 map \(g : M \to M\) is called a symmetry if for \(a,b \in M\), \(a \leq b \Leftrightarrow g(a) \leq g(b)\). A map \(x : M \to \mathbb{R}\) is called a coordinate and it is an inertial coordinate if for each \(q \in G\) there exists a number \(S_x(g)\) such that \(x(g(a)) = x(a) + S_x(g)\) for all \(a \in M\). A coordinate \(t\) is called temporal if \(a \leq b \Rightarrow t(a) \leq t(b)\). Finally, the pair \((M,G)\) is called natural if, given \(a,b \in M\), the condition \(t(a) \leq t(b)\) for all inertial temporal coordinates \(t\) implies \(a \leq b\). The author then proves that if \((M,G)\) is such a natural pair, \(G\) is an abelian group.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83C99
zbMATH DE Number: 889807
zbMATH Keywords: order relations
zbMATH Keywords: causality
author: Vladik Kreinovich
reviewed by: G. S. Hall
MaRDI profile type: Publication
cites work: Q5538720
cites work: Maximale Untersemigruppen und Konvexität in Gruppen
cites work: Q5527790
cites work: Q5603156
full work available at URL: https://doi.org/10.1007/bf02082831
OpenAlex ID: W1993301929
description: scientific article; zbMATH DE number 889807