Visible shape of moving bodies
B.M. Bolotovskii^{ a},
G.B. Malykin^{ b}
^{a }Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
^{b }Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
We show that if an extended object moves with a not only relativistic but even a nonrelativistic speed, the observer at rest sees the shape of this object distorted, and the distortion depends on the way the object is observed. This phenomenon is due to different retardation of light emitted by various parts of the object. Moreover, the observer at rest sees the objects' spatial position and speed in an incorrect way. If an extended object moves with a relativistic speed, the relativistic aberration phenomenon occurs, which was analyzed by A. Einstein. The essence of the effect is that the observer at rest sees the image of a moving small body rotated by some angle. The analysis of these phenomena reported in J. Terrell' and R. Penrose's wellknown papers fails to correctly take into account the effects related to different retardation of light, which is emitted by various parts of the extended object, but comes to the observer at rest at the same time. A conclusion could be drawn, in particular, from their studies that the observer at rest sees the image of a moving extended object, for example, a cube or a sphere, not flattened in the direction of motion (as follows from the Lorentz transformations) but only 'rotated' by the relativistic aberration angle. We report correct expressions for the images of rods parallel and perpendicular to the speed of motion that are seen by the observer at rest. In particular, if a cube moving sufficiently fast passes by a remote observer at rest, the image of the cube face turned to the observer will be contracted in the direction of motion in accordance with the Lorentz transformations but will not be 'rotated', while the image of its rare face (with respect to direction of motion) will 'rotate' by some angle. The image of the cube, therefore, will be distorted. A history of theoretical predictions and experimental observations of this phenomenon is presented. We discuss G. Gamov's relativistic street car paradox that shows that J. Terrell' and R. Penrose's results are incorrect in the general case of motion of objects. Results of our study explain the "Gamov's street car" paradox in an easily comprehensible way. Physical problems are presented that may be solved significantly easier if the formulas for relativistic aberration and light retardation effect are used. We show that assertions made by some astronomers regarding observation of superluminal motion of some galaxies and supernova jets are incorrect, inasmuch as the effects reviewed here are ignored.
