Spaceship Approach

A spaceship is approaching Stephanie at the relativistic speed of v/c = 0.98974. What does she see as the spaceship nears and then passes? Hint: for simplicity, consider a cube approaching in place of the spaceship.

Answer

The observer sees the highly relativistic object approaching back side first! Therefore, the spaceship seems to be approaching tail first! What is often referred to as a contraction in the direction of motion for a relativistically approaching object is actually a rotation known as the Terrell effect.

We need to discuss some aspects of the Terrell effect to explain the behavior of the approaching spaceship. Consider a solid, opaque cube approaching. At low speeds, the light rays emitted off the back side of the approaching cube cannot pass through the box to reach the observer. At higher speeds nearing the speed of light, however, enough of the box moves out of the way for light emitted from part of the back side to reach the observer. When this behavior happens, the observer will not see all of the front side because some of the light rays from the front are intercepted by the extremely fast moving box. The box appears rotated, with the away side of the front hidden, and the near side of the back visible. The rotation angle increases with increasing speed, nearing c and with proximity to the trajectory. Additional complications also occur, such as non-rigidity, which we ignore in this simple explanation.

So the spaceship approaching at near light speed will appear rotated so that the back end is almost totally visible and the front end is almost totally hidden from view. J. Terrell in 1959 was the first to recognize that what physicists had been calculating as a Lorentz-Fitzgerald contraction is

actually a rotation for a real three dimensional object. What we have described above is a snapshot of the spaceship (and cube) that is, what photons from different parts of the object would imprint on a camera sensor simultaneously. E. Sheldon (see the reference below) discusses the stereoscopic appearance of a three dimensional object that involves shearing and other distortions in addition to rotation, all these effects first discussed by J. Terrell.

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