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Terrell rotation

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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]

This phenomenon was popularized by Victor Weisskopf in a Physics Today article.[4]

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

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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.

See also

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References and further reading

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  1. ^ a b c Roger Penrose (1959). "The Apparent Shape of a Relativistically Moving Sphere". Proceedings of the Cambridge Philosophical Society. 55 (1): 137–139. Bibcode:1959PCPS...55..137P. doi:10.1017/S0305004100033776. S2CID 123023118.
  2. ^ a b c James Terrell (1959). "Invisibility of the Lorentz Contraction". Physical Review. 116 (4): 1041–1045. Bibcode:1959PhRv..116.1041T. doi:10.1103/PhysRev.116.1041.
  3. ^ Anton Lampa (1924). "Wie erscheint nach der Relativitätstheorie ein bewegter Stab einem ruhenden Beobachter?". Zeitschrift für Physik (in German). 27 (1): 138–148. Bibcode:1924ZPhy...27..138L. doi:10.1007/BF01328021. S2CID 119547027.
  4. ^ Victor F. Weisskopf (1960). "The visual appearance of rapidly moving objects". Physics Today. 13 (9): 24. Bibcode:1960PhT....13i..24W. doi:10.1063/1.3057105. S2CID 36707809.
  5. ^ Mary L. Boas (1961). "Apparent shape of large objects at relativistic speeds". American Journal of Physics. 29 (5): 283–286. Bibcode:1961AmJPh..29..283B. doi:10.1119/1.1937751.
  6. ^ Eric Sheldon (1988). "The twists and turns of the Terrell Effect". American Journal of Physics. 56 (3): 199–200. Bibcode:1988AmJPh..56..199S. doi:10.1119/1.15687.
  7. ^ James Terrell (1989). "The Terrell Effect". American Journal of Physics. 57 (1): 9–10. Bibcode:1989AmJPh..57....9T. doi:10.1119/1.16131.
  8. ^ Eric Sheldon (1989). "The Terrell Effect: Eppure si contorce!". American Journal of Physics. 57 (6): 487. Bibcode:1989AmJPh..57..487S. doi:10.1119/1.16144.
  9. ^ John Robert Burke and Frank J. Strode (1991). "Classroom exercises with the Terrell effect". American Journal of Physics. 59 (10): 912–915. Bibcode:1991AmJPh..59..912B. doi:10.1119/1.16670.
  10. ^ G. D. Scott and H. J. van Driel (1970). "Geometrical Appearances at Relativistic Speeds". American Journal of Physics. 38 (8): 971–977. Bibcode:1970AmJPh..38..971S. doi:10.1119/1.1976550.
  11. ^ P. M. Mathews and M. Lakshmanan (1972). "On the Apparent Visual Forms of Relativistically Moving Objects". Nuovo Cimento B. 12B (11): 168–181. Bibcode:1972NCimB..12..168M. doi:10.1007/BF02895571. S2CID 118733638.
  12. ^ G.D. Scott and M. R. Viner (1965). "The geometrical appearance of large objects moving at relativistic speeds". American Journal of Physics. 33 (7): 534–536. Bibcode:1965AmJPh..33..534S. doi:10.1119/1.1971890.
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