Preprint Article Version 1 This version is not peer-reviewed

Visualization of Thomas-Wigner Rotations

Version 1 : Received: 1 November 2017 / Approved: 2 November 2017 / Online: 2 November 2017 (03:11:49 CET)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Symmetry 2017, 9, 292
DOI: 10.3390/sym9120292

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 an event horizon. The event horizons associated with the five boosts constitute a natural boundary to the rotated Born-rigid object and ensure its finite size.

Subject Areas

special relativity; Thomas-Wigner rotation; visualization

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