Relativity visualized

Fast objects seen nearby

a

b

c
Abb. 9: A cubic lattice a: at rest, b/c approaching/receding at 90% of the speed of light.
Approaching lattice (slow), MPEG1 320×240 (409 kB), MPEG1 640×480 (4.3 MB)
Approaching lattice (0.9 c), MPEG1 320×240 (436 kB), MPEG1 640×480 (5.0 MB)
Receding lattice (0.9 c), MPEG1 320×240 (774 kB), MPEG1 640×480 (12.9 MB)
Abb. 10: A rod approaches the camera at 90% of the speed of light. Among all the light rays that reach the camera at the same instant, those coming from the ends of the rod have been emitted first (a), the one coming from the middle last (c). The points of emission lie on a curved line in the shape of a hyperbola. Thin solid lines mark the distances already covered by the light rays, dotted lines indicate the remainders of the light paths.
Rod (0.9 c), MPEG1 320×240 (796 kB), MPEG1 640×480 (2.6 MB)

When we observe material moving at extremely high velocities in space, we always watch from a very large distance. Only in computer simulations we get the chance to watch fast moving objects nearby. Take, e.g., a cubic lattice (Fig. 9a) approaching at 90% of the speed of light (Fig. 9b). The elongation in the direction of motion is clearly visible. Equally conspicuous: the rods appear curved. Curved rods are also seen when the lattice moves away from us (Fig. 9c), appearing shortened at the same time, as expected. Thus, seen from close by, fast objects appear not only elongated, shortened or tilted, but also distorted.

This phenomenon, as the others, is a consequence of the finite light travel times. Fig. 10 illustrates the principle for the example of a single vertical rod. The emission points of the light rays which reach the camera simultaneously, lie on a curved line. This is due to the motion of the rod and it can easily be shown that this line is in fact a hyperbola. Since any rod perpendicular to its direction of motion appears as a hyperbola, a plane perpendicular to the motion is seen in the shape of a hyperboloid. This explains the bulging shape of the lattice planes.

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Authors: Ute Kraus, Date: July 14, 2005