Translation:Elementary geometric representation of the formulas of the special theory of relativity

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Elementary geometric representation of the formulas of the special theory of relativity (1921)
by Paul Gruner, translated from French by Wikisource

In French: Représentation géométrique élémentaire des formules de la théorie de la relativité, Archives des sciences physiques et naturelles (5) 3: 295–296, Scans

1576016Elementary geometric representation of the formulas of the special theory of relativity1921Paul Gruner


Gruner, P. and Sauter J. (Berne). – Elementary geometric representation of the formulas of the special theory of relativity.


The theory of special relativity, applied to two one-dimensional systems, moving relatively to each other with velocity , gives the following formulas:

where

The geometric representation given in a general manner by Minkowski, becomes particularly simple and elegant by choosing the axes of and for two mutually orthogonal systems.

From the attached figure, the axis is perpendicular to axis , and axis is rotated by an angle , such as

Posing , we immediately find that the coordinates of a point satisfy the requirements of the theory of relativity:

With this mode of representation which contains no imaginary quantity, it is easy and simple to graphically demonstrate the different results of the theory of relativity (length contraction, dilatation of clocks, change in mass, energy, volume, etc. ).

Fig. 1

Furthermore, the figure immediately gives the covariant and contravariant components of a vector ; it is easy to find geometrically the law of the invariance of the square of the vector:



 This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.

Original:

This work is in the public domain in the United States because it was published before January 1, 1929.


The longest-living author of this work died in 1957, so this work is in the public domain in countries and areas where the copyright term is the author's life plus 66 years or less. This work may be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works.

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Translation:

This work is released under the Creative Commons Attribution-ShareAlike 3.0 Unported license, which allows free use, distribution, and creation of derivatives, so long as the license is unchanged and clearly noted, and the original author is attributed.

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