Preprint Article Version 2 This version is not peer-reviewed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)

How to cite: Merz, T. I: Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417 (doi: 10.20944/preprints201809.0417.v2). Merz, T. I: Geometric Interpretation of the Minkowski Metric. Preprints 2018, 2018090417 (doi: 10.20944/preprints201809.0417.v2).

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.

Subject Areas

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

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