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Special Relativity

  • Dieter LüstEmail author
  • Ward Vleeshouwers
Chapter
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Abstract

In non-relativistic settings, the symmetry group of space-time is the Galilean group, which consists of rotations and translations. These transformations leave spatial distances (as well as temporal intervals) invariant. For example, in two spatial dimensions with coordinates (xy), the squared distance \(s^2 = (\Delta x)^2 + (\Delta y)^2 \) is invariant under rotations, which are of the form \(\begin{pmatrix}x \\ y \end{pmatrix} \mapsto \begin{pmatrix}x' \\ y' \end{pmatrix} = \begin{pmatrix} \cos \alpha &{} \sin \alpha \\ -\sin \alpha &{} \cos \alpha \end{pmatrix}\begin{pmatrix}x \\ y \end{pmatrix}.\) The invariance of spatial (Euclidean) distance is then given by \(s'^2 = (\Delta x')^2 + (\Delta y')^2 = s^2\).

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Arnold-Sommerfeld-CenterLudwig-Maximilians-UniversitaetMunichGermany
  2. 2.Institute for Theoretical PhysicsUtrecht UniversityUtrechtThe Netherlands

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