On the apparent visual forms of relativistically moving objects

  title={On the apparent visual forms of relativistically moving objects},
  author={Paul M. Mathews and M. Lakshmanan},
  journal={Il Nuovo Cimento B (1971-1996)},
SummaryThe 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… 

The appearance, apparent speed, and removal of optical effects for relativistically moving objects

Because various parts of an object are different distances from an observer, and light takes a finite time to reach the observer, the appearance of a relativistically moving object will be very

Gamow’s cyclist: a new look at relativistic measurements for a binocular observer

A rigorous re-analysis of the cyclist, this time in three dimensions, is undertaken for a binocular observer, accounting for both the distortion in apparent position and the relativistic colour and intensity shifts undergone by a fast-moving object.

Projection of relativistically moving objects on a two-dimensional plane, the `train' paradox and the visibility of the Lorentz contraction

Although many papers have appeared on the theory of photographing relativistically moving objects, pioneered by the classic work of Penrose and Terrell, three problems remain outstanding. (1) There

Gamow's bicycle: The Appearance of Bodies at Relativistic Speeds and Apparent Superluminal Velocities

A human creates an image basing on the information delivered by photons that arrived at his retina simultaneously. Due to finite and constant velocity of light these photons left the moving body at

Minkowski diagram in relativity and holography.

The Minkowski diagram is revived, which was invented in 1908 to visualize relativistic relations between time and space, and it is shown how this diagram in a modified form can be used to derive both the static and dynamic holodiagram.

Computational visualization of retardation effects on observed particle distributions

The retardation equation for straight line signal propagation is solved analytically for the two-dimensional case and used to plot the retarded positions graphically for a variety of particle

Virtual pulse effect in incoherent scattering

During incoherent scattering of a radar pulse from an extended volume region it is appropriate, because of transit-time considerations, to work with a virtual pulse which differs from the true

Measurement and the interpretation of quantum mechanics and relativity theory

The necessity of generalizing the formalisms of both quantum mechanics and relativity theory so as to encompass more realistic nonideal measurements is discussed and it is argued that this generalization favours an empiricist interpretation of the mathematical formalisms over a realist one.



The apparent shape of a relativistically moving sphere

  • R. Penrose
  • Physics, Art
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1959
It would be natural to assume that, according to the special theory of relativity, an object moving with a speed comparable with that of light should appear to be flattened in the direction of motion

The visual appearance of rapidly moving objects

I would like to draw the attention of physicists to a recent paper by James Terrell in which he does away with an old prejudice held by practically all of us. We all believed that, according to

Invisibility of the Lorentz Contraction

It is shown that, if the apparent directions of objects are plotted as points on a sphere surrounding the observer, the Lorentz transformation corresponds to a conformal transformation on the surface

Apparent Shape of Large Objects at Relativistic Speeds

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

The Apparent Shape of Rapidly Moving Objects in Special Relativity

Summary A review is presented of previous papers on the apparent shape of bodies travelling with speeds comparable to that of light. It is shown that the visibility or otherwise of the Lorentz

Geometrical Appearances at Relativistic Speeds

Geometrical appearances at relativistic speeds (β = 0.5, 0.9, and 0.995) are illustrated for the following examples: (i) the celestial sphere with a number of constellations, (ii) the surface