- The left-hand side
of the animation
shows the lengths that would be actually measured by a true measuring technique.
The cube
FitzGerald contracts
along the direction of horizontal motion of
velocity
v = (x * c).
- The FitzGerald contraction
formula is
L(v)=L_0*sqrt(1-v**2/c**2) , where v is the observer's velocity relative an object, L(v) is the observer's observed length for the object along the direction of motion, and L_0 is the length along the direction of motion measured in rest frame of the object. L_0 is called the proper length in Relativityspeak.

- Howsoever, what you measure by a true measuring technique
is
**NOT**what you see because of the finite vacuum light speed c = 2.99792458*10**8 m/s. There is a differential time delay for the light signals from different parts of the cube.If you correct for the differential time delay, then you get a true measurement of length and observe the FitzGerald contraction.

What you observe sans correction is a rotation, the Terrell-Penrose effect.

The Terrell-Penrose effect is illustrated by the right-hand side of the animation.

- The Terrell-Penrose effect
was fully worked out independently in
1959 by
James Terrell (1923--2009)
and
Roger Penrose (1931--)
(see Wikipedia: Terrell rotation).

Caption: "Comparison of the measured FitzGerald contraction of a cube versus its visual appearance as given by the Terrell-Penrose effect. The view is from the front of the cube at a distance four times the length of the cube's sides, three-quarters of the way from bottom to top, as projected onto a vertical screen (so that the vertical lines of the cube are initially parallel)." (Slightly edited.)

Features:

Image link: Wikimedia Commons: File:Animated Terrell Rotation - Cube.gif.

Local file: local link: terrell_rotation_effect.html.

File: Relativity file: terrell_rotation_effect.html.