Article
Version 1
Preserved in Portico This version is not peer-reviewed
I: Geometric Interpretation of the Minkowski Metric
Version 1
: Received: 20 September 2018 / Approved: 20 September 2018 / Online: 20 September 2018 (15:21:21 CEST)
Version 2 : Received: 22 January 2019 / Approved: 23 January 2019 / Online: 23 January 2019 (10:20:53 CET)
Version 3 : Received: 4 September 2019 / Approved: 5 September 2019 / Online: 5 September 2019 (11:19:21 CEST)
Version 2 : Received: 22 January 2019 / Approved: 23 January 2019 / Online: 23 January 2019 (10:20:53 CET)
Version 3 : Received: 4 September 2019 / Approved: 5 September 2019 / Online: 5 September 2019 (11:19:21 CEST)
How to cite: Merz, T. I: Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417. https://doi.org/10.20944/preprints201809.0417.v1 Merz, T. I: Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417. https://doi.org/10.20944/preprints201809.0417.v1
Abstract
A geometric interpretation of the Minkowski metric and thus of phenomena in special relativity is provided. It is shown that a change of basis in Minkowski space is the equivalent of a change of basis in Euclidean space if one basis element is replaced by its dual element. The methodology of the proof includes infinitesimal changes of basis using the Lie-algebras of the involved groups. As a consequence, a direct mapping between Euclidean and Minkowski space is defined.
Keywords
Minkowski space; spacetime; contravariant transformation; mixed basis; geometric interpretation; special relativity
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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