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Visible form of moving bodies

 a,  b
a Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
b Institute of Applied Physics, Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

It is shown that when an extended object moves not only with relativistic, but even with nonrelativistic speed, due to the different lag of light emitted by different parts of the object, motionless the observer sees the shape of this object distorted, and this distortion of shape depends on the method of observation. In addition, the stationary observer sees the spatial position and speed of the object incorrectly. When driving extended object with relativistic velocity, the phenomenon considered by A. Einstein relativistic aberration, which leads to the fact that a stationary observer sees an image of a moving small body rotated by some angle. It was shown that in the well-known papers of J. Terrell and R. Penrose, consideration of these phenomena were not fully correctly taken into account the effects associated with different delays light emitted by different parts of an extended object, which simultaneously come to a stationary to the observer. From these works, in particular, it followed that a stationary observer sees an image of a moving extended object — for example, a cube or a ball, not flattened in the direction of motion (as follows from Lorentz transformations), but only "rotated" by the angle of relativistic aberration. The correct expressions are given for the image of rods observed by a fixed observer, which are parallel and perpendicular to the velocity movement. In particular, it is shown that, if the cube moves quite quickly past a remote stationary observer, the image of its face that faces the observer will be reduced in the direction of movement in accordance with transformations of Lorentz, but not "turn around"; the image of its back (in the direction of motion) faces "will turn" to some angle. Therefore, the cube image will look distorted. The history is considered theoretical prediction and experimental observation of this phenomenon. The actual Gamow's paradox about the relativistic tram, showing that the results of J. Terrell and R. Penrose for the general case of the movement of the object are not correct. It is shown that the use of the results of this work clearly explains the paradox about the "Gamow tram". Specific physical problems are given for which the application of expressions for relativistic aberration and the effect of light retardation greatly simplifies their solution. Shown, that the assertions of some astronomers about the observation of the superluminal motions of certain galaxies of supernova jets are erroneous, because in the process of calculations they ignored the effects under consideration.

Text is available here.

Keywords: light delay, relativistic aberration, Gamow paradox, velocity of galaxies
DOI: 10.3367/UFNe.2018.08.038407
Citation: Bolotovskii B M, Malykin G B "Visible form of moving bodies" Phys. Usp., accepted

Received: 17th, May 2018, revised: 5th, August 2018, 7th, August 2018

Оригинал: Болотовский Б М, Малыкин Г Б «Видимая форма движущихся тел» УФН, принята к публикации; DOI: 10.3367/UFNr.2018.08.038407

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