Next Article in Journal
System Framework for Cardiovascular Disease Prediction Based on Big Data Technology
Previous Article in Journal
Multi-Device to Multi-Device (MD2MD) Content-Centric Networking Based on Multi-RAT Device
Article Menu
Issue 12 (December) cover image

Export Article

Open AccessArticle
Symmetry 2017, 9(12), 292; https://doi.org/10.3390/sym9120292

Visualization of Thomas–Wigner Rotations

GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Received: 1 November 2017 / Revised: 7 November 2017 / Accepted: 8 November 2017 / Published: 27 November 2017
Full-Text   |   PDF [582 KB, uploaded 30 November 2017]   |  

Abstract

It is well known that a sequence of two non-collinear Lorentz boosts (pure Lorentz transformations) does not correspond to a Lorentz boost, but involves a spatial rotation, the Wigner or Thomas–Wigner rotation. We visualize the interrelation between this rotation and the relativity of distant simultaneity by moving a Born-rigid object on a closed trajectory in several steps of uniform proper acceleration. Born-rigidity implies that the stern of the boosted object accelerates faster than its bow. It is shown that at least five boost steps are required to return the object’s center to its starting position, if in each step the center is assumed to accelerate uniformly and for the same proper time duration. With these assumptions, the Thomas–Wigner rotation angle depends on a single parameter only. Furthermore, it is illustrated that accelerated motion implies the formation of a “frame boundary”. The boundaries associated with the five boosts constitute a natural barrier and ensure the object’s finite size. View Full-Text
Keywords: special relativity; Thomas–Wigner rotation; accelerated frame; visualization special relativity; Thomas–Wigner rotation; accelerated frame; visualization
Figures

Figure 1

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 (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Beyerle, G. Visualization of Thomas–Wigner Rotations. Symmetry 2017, 9, 292.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top