On the apparent visual forms of relativistically moving objects

Abstract

The question of the apparent visual shape of an object moving at relativistic speeds, as perceived by a single observer, is analysed afresh. It is shown by qualitative arguments that the apparent shape is related to the shape at rest through a combination of nonuniform shear and extension/contraction parallel to the direction of motion, which does not reduce to a rotation even in the case of distant objects subtending a small angle at the observer. The two-dimensional projection (as in a photograph) of this distorted shape may coincide with that of the object (suitably rotated) at rest; but we emphasize that it would be grossly misleading to conclude from this, as is generally done in the literature, that distant relativistically moving objects appear as if simply lotated. The ≪ train paradox ≫ is discussed in illustration of this point. Analytical formulae relating the apparent visual shape to the shape at rest are given. Also the striking fact that the apparent speed of the object as seen by visual observation may well exceed the speed of light is brought out. Finally it is pointed out that the phenomenon is closely analogous to the relativistic Doppler effect.