Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recen...

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Autores principales:	James M Chappell, Azhar Iqbal, Nicolangelo Iannella, Derek Abbott
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2012
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/5bda8289550a4ee18e8a0134f59d82c8
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spelling	oai:doaj.org-article:5bda8289550a4ee18e8a0134f59d82c82021-11-18T08:03:08ZRevisiting special relativity: a natural algebraic alternative to Minkowski spacetime.1932-620310.1371/journal.pone.0051756https://doaj.org/article/5bda8289550a4ee18e8a0134f59d82c82012-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/23300566/?tool=EBIhttps://doaj.org/toc/1932-6203Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.James M ChappellAzhar IqbalNicolangelo IannellaNicolangelo IannellaDerek AbbottPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 7, Iss 12, p e51756 (2012)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q James M Chappell Azhar Iqbal Nicolangelo Iannella Nicolangelo Iannella Derek Abbott Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
description	Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
format	article
author	James M Chappell Azhar Iqbal Nicolangelo Iannella Nicolangelo Iannella Derek Abbott
author_facet	James M Chappell Azhar Iqbal Nicolangelo Iannella Nicolangelo Iannella Derek Abbott
author_sort	James M Chappell
title	Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
title_short	Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
title_full	Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
title_fullStr	Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
title_full_unstemmed	Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
title_sort	revisiting special relativity: a natural algebraic alternative to minkowski spacetime.
publisher	Public Library of Science (PLoS)
publishDate	2012
url	https://doaj.org/article/5bda8289550a4ee18e8a0134f59d82c8
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Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.

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