REMARKS ON LORENTZ CONTRACTION

There have appeared recently a number of interesting papers' concerning the impossibility of seeing or photographing the Lorentz contraction of fast-moving bodies. In these papers, the authors argue that, since the image on the retina of the eye or on the film of the camera is formed by light rays which enter simultaneously into the pupil or the lens, it must be distorted. This distortion is due. to the fact that these rays were not emitted simultaneously from different parts of the moving body at different distances from the observation point. The simple example of a fast-moving cube observed from the side is shown in Figure la. The rays emitted simultaneously from points A, B, C, and D will clearly take the same tine to reach the objective of the camera. But since points E and F are located farther away from the camera, light must be emitted from them somewhat earlier if it has to reach the objective at the same time as light from points A, B, C, and D. The distance by which the cube moves while light covers the distance equal to its side is apparently v (1/c) = 1 (v/c); thus, the picture will show the projection of the rear side of the cube with a length 1 (v/c). On the other hand, the face ABCD will be seen as being contracted by the factor \/l (v2/c2) in accordance with Lorentz transformations. Putting sin C = v/c; cos a Vi (v2/c2), we find that on the photograph the cube will appear as preserving its shape but being rotated by angle 0. Considering a sphere inscribed in that cube, we find that a fast-moving sphere will look on the photograph exactly as if it were at rest. It should be indicated here that the above conclusions depend essentially on the assumption that the object to be photographed is either self-luminous or illuminated by a constant outside source of light. 'If the photography of a fast-moving cube is performed by a flash-camera or by radar equipment, the situation will be quite different. The ports of the advancing wave which hit the front face of the cube will be reflected back, while those which passed just in front of or just behind it will never have a chance to get back. Thus, the flash camera or radar photographs will definitely show a correct Lorentz contraction. Another interesting case exists when the moving object is comparatively flat and is moving along an observable trajector like a bicycle (Fig. lb) riding along the curb of a street.2 In this case, observing the motion of the lower points of the two wheels which always follow the curb, we cannot possibly say that the bicycle is rotated. True, the license plate and the handle bar will look bent out of their normal position, but this deformation could be ascribed to a traffic accident. In the case of a streetcar running along a straight track,3 the situation is more difficult, and the fact that the rear of the car can easily be seen while all the wheels follow the track cannot be explained in any normal way except by assuming that the entire car suffered an unusual sheer deformation. It follows from the above examples that the apparent deformation compensates for the Lorentz contraction only in the case of special characteristics of motion and special methods of observation and that, in general, the interpretation of the observed effect as a rotation is not correct.