Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/102998
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Type: Journal article
Title: Time as a geometric property of space
Author: Chappell, J.
Hartnett, J.
Iannella, N.
Iqbal, A.
Abbott, D.
Citation: Frontiers in Physics, 2016; 4:44-1-44-6
Publisher: Frontiers Media S.A.
Issue Date: 2016
ISSN: 2296-424X
Statement of
Responsibility: 
James M.Chappell, John G.Hartnett, Nicolangelo Iannella, Azhar Iqbal and Derek Abbott
Abstract: The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which “flows equably without relation to anything external.” In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that he could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation of 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Keywords: Time; geometric algebra; quaternions; Minkowski; spacetime
Rights: Copyright © 2016 Chappell, Hartnett, Iannella, Iqbal and Abbott. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
RMID: 0030058584
DOI: 10.3389/fphy.2016.00044
Appears in Collections:Electrical and Electronic Engineering publications

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