Visualization of Thomas-Wigner Rotations

It is well known that a sequence of two non-collinear Lorentz boosts (pure Lorentz 1 transformations) does not correspond to a Lorentz boost, but involves a spatial rotation, the Wigner 2 or Thomas-Wigner rotation. We visualize the interrelation between this rotation and the relativity of 3 distant simultaneity by moving a Born-rigid object on a closed trajectory in several steps of uniform 4 proper acceleration. Born-rigidity implies that the stern of the boosted object accelerates faster than 5 its bow. It is shown that at least five boost steps are required to return the object’s center to its starting 6 position, if in each step the center is assumed to accelerate uniformly and for the same proper time 7 duration. With these assumptions, the Thomas-Wigner rotation angle depends on a single parameter 8 only. Furthermore, it is illustrated that accelerated motion implies the formation of an event horizon. 9 The event horizons associated with the five boosts constitute a natural boundary to the rotated 10 Born-rigid object and ensure its finite size. 11