Apparent Shape of Large Objects at Relativistic Speeds

Abstract

It has been recently recognized that there is a difference between the measured Lorentz contracted shape of an object moving at relativistic speed and the shape as seen by a single observer. The case of an object which subtends a small solid angle at the observer has been discussed by several authors. This paper discusses objects so large or so near that the subtended solid angle cannot be considered small, and gives simple proofs that spheres always present a circular outline and that straight lines may appear curved. These results are applied to revise Gamow's well-known picture of the bicyclist seen by Mr. Tompkins.

A direct test of the Lorentz length contraction

“…Three of these are noted in the references [2,3,4] In the current study, the factors of greatest importance are the following: 1) the field of regard or field of view, extending from one degree to fifteen degrees, is not trivial, thus we are not dealing with differential subtended angles; 2) the observer always has some nonzero velocity with respect to the object(s) of view. For example, while motion may be in the same direction as a line joining two stars in one viewing, it always comparing the image as viewed by one moving observer with that as viewed by another moving observer, and never by an observer stationary with respect to the stars.…”

Illumination and acceleration in the visualization of special relativity: a comment on fast rendering of relativistic objects

“…Apart from a previously disregarded article by Lampa 2 in 1924 about the invisibility of the Lorentz contraction, the ®rst solutions to this problem were given by Penrose 3 and Terrell 4 in 1959. Later, this issue was addressed in more detail by Weisskopf, 5 Boas, 6 Scott and Viner 7 and Scott and van Driel. 8 Hsiung and Dunn 9 are the ®rst to use advanced visualization techniques for image shading of fastmoving objects.…”

“…radiance has to be considered according to equations (1) and (6). For ®nal image synthesis, three tristimulus values RGB can be obtained from the wavelength-dependent radiance that reaches the eye point.…”

Searchlight and Doppler effects in the visualization of special relativity

“…Apart from a previously disregarded article by Lampa [1924] about the invisibility of the Lorentz contraction, the first solutions to this problem were given by Penrose [1959] and Terrell [1959]. Various aspects were discussed by Weisskopf [1960]; Boas [1961]; Scott and Viner [1965]; Scott and van Driel [1970]; and Kraus [2000]. Hsiung and Dunn [1989] were the first to use advanced visualization techniques for image shading of fast moving objects.…”