Terrell rotation or the Terrell effect is the visual distortion that a passing object would appear to undergo, according to the special theory of relativity, if it were travelling at a significant fraction of the speed of light. This behaviour was described independently by both Roger Penrose and James Edward Terrell. Penrose's article was submitted 29 July 1958 and published in January 1959.[1] Terrell's article was submitted 22 June 1959 and published 15 November 1959.[2] The general phenomenon was noted already in 1924 by Austrian physicist Anton Lampa.[3]
Due to an early dispute about priority and correct attribution, the effect is also sometimes referred to as the Penrose–Terrell effect, the Terrell–Penrose effect or the Lampa–Terrell–Penrose effect, but not the Lampa effect.
Further detail
By symmetry, it is equivalent to the visual appearance of the object at rest as seen by a moving observer. Since the Lorentz transform does not depend on the acceleration, the visual appearance of the object depends only on the instantaneous velocity, and not the acceleration of the observer.
Comparison of the measured length contraction of a cube versus its visual appearance. The view is from the front of the cube at a distance four times the length of the cube's sides, three-quarters of the way from bottom to top, as projected onto a vertical screen (so that the vertical lines of the cube may initially be parallel).
Terrell's and Penrose's papers pointed out that although special relativity appeared to describe an "observed contraction" in moving objects, these interpreted "observations" were not to be confused with the theory's literal predictions for the visible appearance of a moving object. Thanks to the differential timelag effects in signals reaching the observer from the object's different parts, a receding object would appear contracted, an approaching object would appear elongated (even under special relativity) and the geometry of a passing object would appear skewed, as if rotated. By R. Penrose: "the light from the trailing part reaches the observer from behind the sphere, which it can do since the sphere is continuously moving out of its way".[2][1]
A globe, moving at various speeds to the right, is observed from three diameters distance from its nearest point on the surface (marked by a red cross). The left image shows the globe's measured, Lorentz-contracted shape. The right image shows the visual appearance of the globe.
For images of passing objects, the apparent contraction of distances between points on the object's transverse surface could then be interpreted as being due to an apparent change in viewing angle, and the image of the object could be interpreted as appearing instead to be rotated. A previously popular description of special relativity's predictions, in which an observer sees a passing object to be contracted (for instance, from a sphere to a flattened ellipsoid), was wrong. A sphere maintains its circular outline since, as the sphere moves, light from further points of the Lorentz-contracted ellipsoid takes longer to reach the eye.[2][1]
Terrell's and Penrose's papers prompted a number of follow-up papers,[5][6][7][8][9][10][11][12] mostly in the American Journal of Physics, exploring the consequences of this correction. These papers pointed out that some existing discussions of special relativity were flawed and "explained" effects that the theory did not actually predict – while these papers did not change the actual mathematical structure of special relativity in any way, they did correct a misconception regarding the theory's predictions.
A representation of the Terrell effect can be seen in the physics simulator "A Slower Speed of Light," published by MIT.
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 paper, On the Electrodynamics of Moving Bodies, the theory is presented as being based on just two postulates:
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The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.
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The word "mass" has two meanings in special relativity: invariant mass is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to rest energy, while relativistic mass is equivalent to relativistic energy.
The ladder paradox is a thought experiment in special relativity. It involves a ladder, parallel to the ground, travelling horizontally at relativistic speed and therefore undergoing a Lorentz length contraction. The ladder is imagined passing through the open front and rear doors of a garage or barn which is shorter than its rest length, so if the ladder was not moving it would not be able to fit inside. To a stationary observer, due to the contraction, the moving ladder is able to fit entirely inside the building as it passes through. On the other hand, from the point of view of an observer moving with the ladder, the ladder will not be contracted, and it is the building which will be Lorentz contracted to an even smaller length. Therefore, the ladder will not be able to fit inside the building as it passes through. This poses an apparent discrepancy between the realities of both observers.
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This timeline describes the major developments, both experimental and theoretical, of:
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