Relativity visualized

# Rolling Wheels

Corvin Zahn, May 23, 2002

In his book "Mr. Tompkins in Wonderland" George Gamow describes the adventures of Mr. Tompkins in a fictitious world, in which the speed of light is only 30km/h. Motivated by the scene of Mr. Tompkins riding a bike along the street, the movies below show what a relativistically rolling wheel "really" looks like.

In his book "Mr. Tompkins in Wonderland" George Gamow describes the adventures of Mr. Tompkins in a fictitious world, in which the speed of light is only 30km/h. Motivated by the scene of Mr. Tompkins riding a bike along the street, the movies below show what a relativistically rolling wheel "really" looks like.

They are calculated with a four dimensional ray tracing method which takes into account the finite speed of light and the Lorentz contraction.

A more detailed explanation can be found in the paper

Sights that Einstein could not yet see - visualization of relativistic effects

## The Scene

The following MPEG movies show the same scene from three different viewing angles.

The red wheel in the background is at rest, the green one is in stationary rotation (a point on the rim moves with a speed of 0.93c) and the blue one in the foreground is rolling at a speed of 0.93c from left to the right through the scene.

The shadows are due to a light source which illuminates the scene from a great distance from behind and above.

## Movies

 Movie: Rolling wheel (0.93 c, right view) The wheel is rolling towards the observer. MPEG1 320×240 (444 kB), MPEG1 640×480 (4.1 MB)
 Movie: Rolling wheel (0.93 c, front view) The wheel is rolling from left to the right. MPEG1 320×240 (892 kB), MPEG1 640×480 (7.9 MB)
 Movie: Rolling wheel (0.93 c, left view) The wheel is rolling away. MPEG1 320×240 (1.0 MB), MPEG1 640×480 (10.2 MB)
 Movie: Rolling wheel (0.93 c, rotation around vertical axis) A wheel rotating around the vertical axis. MPEG1 320×240 (412 kB)