Preprint Article Version 3 This version is not peer-reviewed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)

How to cite: Merz, T. Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417 (doi: 10.20944/preprints201809.0417.v3). Merz, T. Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417 (doi: 10.20944/preprints201809.0417.v3).

Abstract

A novel geometric interpretation of the Minkowski metric is provided, which offers a different and more intuitive approach to phenomena in special relativity. First it is shown that a change of basis in Minkowski space is the equivalent of a change of basis in Euclidean space if a basis element is replaced by its dual element, constituting a mixed basis set. 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. Second, a measuring device called a local, flat observer is defined in Euclidean space and it is shown, that this device uses a mixed basis when measuring distances. Combining these steps, it is concluded that a local, flat observer in a four-dimensional Euclidean spacetime measures a Minkowski spacetime.

Subject Areas

Minkowski space; spacetime; contravariant transformation; mixed basis; geometric interpretation; special relativity

Comments (1)

Comment 1
Received: 5 September 2019
Commenter: Thomas Merz
Commenter's Conflict of Interests: Author
Comment: A second section providing an interpretation of the previous result was added.
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