Is Time the Real Line? View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2022-09-20

AUTHORS

Bruno F. Rizzuti, Luca M. Gaio, Lucas T. Cardoso

ABSTRACT

This paper is devoted to discussing the topological structure of the arrow of time. In the literature, it is often accepted that its algebraic and topological structures are that of a one-dimensional Euclidean space E1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {E}^1$$\end{document}, although a critical review on the subject is not easy to be found. Hence, leveraging on an operational approach, we collect evidences to identify it structurally as a normed vector space (Q,|·|)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathbb {Q}, \vert \cdot \vert )$$\end{document}, and take a leap of abstraction to complete it, up to isometries, to the real line. During the development of the paper, the space-time is recognized as a fibration, with the fibers being the sets of simultaneous events. The corresponding topology is also exposed: open sets naturally arise within our construction, showing that the classical space-time is non-Hausdorff. The transition from relativistic to classical regimes is explored too. More... »

PAGES

105

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10701-022-00623-4

DOI

http://dx.doi.org/10.1007/s10701-022-00623-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1151156059


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