Images of objects moving at relativistic speed
and the Lampa-Terrell-Penrose effect

How does an object look like which flies by an observer at relativistic speed? Does one really see a Lorentz contracted object, e.g. a flat ellipsiod instead of a sphere? The answer is no, as illustrated in the following movie:

The movie lampa_trick.mpg shows the subsequent emission of light from the rim of a rapidly moving, Lorentz compressed sphere (e.g. a nucleus in an ultrarelativistic heavy ion collision). Even though this light is emmitted at different times, it arrives at the same time at the observer. This is due, of course, to the finite speed of light and the large speed of the sphere.

The speed of the sphere is v = 0.95 c, its motion is from the left to the right, and at the time t = 0, its center reaches the origin of the coordinate system. Light which would be absorbed underway by an opaque sphere is shown in orange.

The observer sees (i.e. observes at the same time) light which was emitted by the moving sphere at different times, thus when the sphere was at different positions. Hence, the observer sees a rotated and slightly distorted image of the sphere. In fact, the "back side" of the sphere is visible to the observer.
This is the Lampa-Terrell-Penrose effect.

(click on the picture to get the movie)

Taking into account the Lampa-Terrell-Penrose effect makes large differences for the visualization of ultrarelativistic heavy ion collisions as compared to the traditional way this is done.

Literature:

• A. Lampa, Wie erscheint nach der Relativitätstheorie ein bewegter Stab einem ruhenden Beobachter?, Z. Physik 27 (1924) 138-148.
• R. Penrose, The Apparent Shape of a Relativistically Moving Sphere, Proc. Cambridge. Phil. Soc. 55 (1959) 137.
• J. Terrell, Invisibility of the Lorentz contraction, Phys. Rev. 116 (1959) 1041-1045.

11.03.2002, Stefan Scherer, e-mail: scherer@th.physik.uni-frankfurt.de