Article
Version 4
Preserved in Portico This version is not peer-reviewed
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 4 : Received: 17 May 2024 / Approved: 17 May 2024 / Online: 20 May 2024 (00:03:03 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 4 : Received: 17 May 2024 / Approved: 17 May 2024 / Online: 20 May 2024 (00:03:03 CEST)
How to cite: Merz, T. Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417. https://doi.org/10.20944/preprints201809.0417.v4 Merz, T. Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417. https://doi.org/10.20944/preprints201809.0417.v4
Abstract
In this article it is shown, first, that a change of basis in Minkowski space is equivalent to a change of basis in Euclidean space if a basis element is replaced by its dual element, constituting a mixed basis set. Second, that such mixed bases can be interpreted as a measurement system used by local, flat observers whose direct distance measurements are restricted to an (n−1)-dimensional submanifold in an n-dimensional Euclidean space. Combining these steps, it is concluded that a local, flat observer in a four-dimensional Euclidean space measures a Minkowski spacetime. This interpretation could be useful for theories in special relativity and related fields that rely on spacetime concepts, as it offers a more intuitive geometric understanding of the Minkowski metric.
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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