Editing Terrell rotation

{{Short description|Effect in special relativity}}
[[File:Experimental visualization of the Terrell effect.png|alt=A red sphere showing the rotation effect and distortion predicted by Terrell.|thumb|Experimental visualization of the Terrell effect using [[femtosecond pulse shaping]] and a gated [[Image intensifier|intensified]] camera.]]
'''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 first discussed by Austrian physicist {{ill|Anton Lampa|de}} in 1924, and  further developed independently by both [[Roger Penrose]] and [[Nelson James Terrell|James Terrell]] in 1959.  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.'''

== History ==
In 1924 by Anton Lampa discussed the effect for the first time for a moving rod,<ref name="Lampa1924" /><ref>{{Cite journal |last=de Hoop |first=Adrianus T. |date=January 2009 |title=Electromagnetic radiation from moving, pulsed source distributions: The 3D time-domain relativistic Doppler effect |url=https://doi.org/10.1016/j.wavemoti.2008.08.003 |journal=Wave Motion |volume=46 |issue=1 |pages=74–77 |doi=10.1016/j.wavemoti.2008.08.003 |bibcode=2009WaMot..46...74D |issn=0165-2125|url-access=subscription }}</ref> but this result was overlooked until its rediscovery by Penrose and Terrell.<ref>{{Cite book |last=Brown |first=Harvey R. |url=https://books.google.com/books?id=LbAUDAAAQBAJ&dq=terrell+rotation+lampa&pg=PA29 |title=Physical Relativity: Space-time Structure from a Dynamical Perspective |date=2005-11-24 |publisher=Clarendon Press |isbn=978-0-19-927583-0 |language=en}}</ref><ref name=":1">{{Cite book |last=Giulini |first=Domenico |url=https://books.google.com/books?id=7qO42uCcPcUC&dq=terrell+rotation+lampa&pg=PT87 |title=Special Relativity: A First Encounter: 100 years since Einstein |date=2011-04-07 |publisher=OUP Oxford |isbn=978-0-19-162086-7 |language=en}}</ref> Roger Penrose's article on the effect was submitted 29 July 1958 and published in January 1959.<ref name="Penrose1959" /> James Terrell's article was submitted 22 June 1959 and published 15 November 1959.<ref name="Terrell1959" /> Penrose specifically developed the case of a sphere.<ref name=":1" />

Terrell's and Penrose's papers prompted a number of follow-up papers,<ref name="Boas" /><ref name="Sheldon1989a" /><ref name="Terrell1989" /><ref name="Sheldon1989b" /><ref name="Burke1991" /><ref name="ScottvanDriel1970" /><ref name="MathewsLakshmanan1972" /><ref name="ScottViner1965" /> 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.

This phenomenon was popularized by [[Victor Weisskopf]] in a ''[[Physics Today]]'' article in 1960.<ref name="Weisskopf1960" />

In 2017, astronomer [[Avi Loeb]] suggested that the Terrell effect could have applications for measuring exoplanet masses.<ref name=":0" />

The effect was experimentally demonstrated in 2024 by [[Peter Schattschneider]] and his group of [[TU Wien]].<ref>{{cite arXiv |eprint=2409.04296 |last1=Hornof |first1=Dominik |last2=Helm |first2=Victoria |author3=Enar de Dios Rodriguez |last4=Juffmann |first4=Thomas |last5=Haslinger |first5=Philipp |last6=Schattschneider |first6=Peter |title=A Snapshot of Relativistic Motion: Visualizing the Terrell Effect |date=2024 |class=physics.optics }}</ref><ref name=":0">{{Cite web |date=2025-03-06 |title=Curious consequence of special relativity observed for the first time in the lab |url=https://physicsworld.com/a/curious-consequence-of-special-relativity-observed-for-the-first-time-in-the-lab/ |access-date=2025-03-07 |website=Physics World |language=en-GB}}</ref> They used femto-second laser to artificially reduce the speed of light to 2&nbsp;m/s, simulating the effect.<ref name=":0" />

== Description ==
By symmetry, it is equivalent to the visual appearance of the object at rest as seen by a moving observer. Since [[Lorentz transformation]]s do not depend on the acceleration, the visual appearance of the object depends only on the instantaneous velocity, and not the acceleration of the observer.[[File:Animated Terrell Rotation - Cube.gif|thumb|330px|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 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".<ref name=Terrell1959/><ref name=Penrose1959/>

[[File:Terrell Rotation Sphere.gif|thumb|330px|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.<ref name=Terrell1959/><ref name=Penrose1959/>

== In educational games ==
A representation of the Terrell effect can be seen in the physics simulator ''[[A Slower Speed of Light]]'', published by the [[Massachusetts Institute of Technology]] (MIT).<ref>{{Cite journal |last1=Sherin |first1=Zachary W. |last2=Cheu |first2=Ryan |last3=Tan |first3=Philip |last4=Kortemeyer |first4=Gerd |date=2016-05-01 |title=Visualizing relativity: The OpenRelativity project |journal=American Journal of Physics |volume=84 |issue=5 |pages=369–374 |doi=10.1119/1.4938057 |issn=0002-9505|doi-access=free |bibcode=2016AmJPh..84..369S }}</ref>

== See also ==
* [[Length contraction]]
* [[Stellar aberration]]

== References and further reading ==
{{reflist|refs=

<ref name=Terrell1959>{{cite journal |author=James Terrell |year=1959 |title=Invisibility of the Lorentz Contraction |journal=[[Physical Review]] |volume=116 |issue=4 |pages=1041–1045 |doi=10.1103/PhysRev.116.1041|bibcode = 1959PhRv..116.1041T }}</ref>

<ref name=Penrose1959>{{cite journal |last1=Penrose | first1=Roger |authorlink1=Roger Penrose |year=1959 |title=The Apparent Shape of a Relativistically Moving Sphere |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |volume=55 |issue=1 |pages=137–139 |doi=10.1017/S0305004100033776|bibcode = 1959PCPS...55..137P |s2cid=123023118 }}</ref>

<ref name=Lampa1924>{{cite journal | author = Anton Lampa | year = 1924 | title = Wie erscheint nach der Relativitätstheorie ein bewegter Stab einem ruhenden Beobachter? | language = German | journal = [[Zeitschrift für Physik]] | volume = 27 | issue = 1 | pages = 138–148 | doi = 10.1007/BF01328021 |bibcode = 1924ZPhy...27..138L | s2cid = 119547027 }}</ref>

<ref name=Weisskopf1960>{{cite journal |author=Victor F. Weisskopf |year=1960 |title=The visual appearance of rapidly moving objects |journal=[[Physics Today]] |volume=13 |issue=9 |page=24 |doi=10.1063/1.3057105|bibcode=1960PhT....13i..24W |s2cid=36707809 |author-link=Victor F. Weisskopf }}</ref>

<ref name=Boas>{{cite journal |author=Mary L. Boas |year=1961 |title=Apparent shape of large objects at relativistic speeds |journal=[[American Journal of Physics]] |volume=29 |issue=5 |pages=283–286 |doi=10.1119/1.1937751|bibcode = 1961AmJPh..29..283B |author-link=Mary L. Boas }}</ref>

<ref name=Sheldon1989a>{{cite journal |author=Eric Sheldon |year=1988 |title=The twists and turns of the Terrell Effect |journal=[[American Journal of Physics]] |volume=56 |issue=3 |pages=199–200 |doi=10.1119/1.15687|bibcode = 1988AmJPh..56..199S }}</ref>

<ref name=Terrell1989>{{cite journal |author=James Terrell |title=The Terrell Effect |journal=[[American Journal of Physics]] |volume=57 |issue=1 |pages=9–10 |doi=10.1119/1.16131 |year=1989|bibcode = 1989AmJPh..57....9T }}</ref>

<ref name=Sheldon1989b>{{cite journal |author=Eric Sheldon |title=The Terrell Effect: Eppure si contorce! |journal=[[American Journal of Physics]] |volume=57 |issue=6 |pages=487 |doi=10.1119/1.16144 |year=1989|bibcode = 1989AmJPh..57..487S }}</ref>

<ref name=Burke1991>{{cite journal |author=John Robert Burke and Frank J. Strode |year=1991 |title=Classroom exercises with the Terrell effect |journal=[[American Journal of Physics]] |volume=59 |issue=10 |pages=912–915 |doi=10.1119/1.16670|bibcode = 1991AmJPh..59..912B }}</ref>

<ref name=ScottvanDriel1970>{{cite journal |author=G. D. Scott and H. J. van Driel |year=1970 |title=Geometrical Appearances at Relativistic Speeds |journal=[[American Journal of Physics]] |volume=38 |issue=8 |pages=971–977 |doi=10.1119/1.1976550|bibcode =1970AmJPh..38..971S |doi-access=free }}</ref>

<ref name=MathewsLakshmanan1972>{{cite journal |author=P. M. Mathews and M. Lakshmanan |year=1972 |title=On the Apparent Visual Forms of Relativistically Moving Objects |journal=[[Nuovo Cimento B]] |volume=12B |issue=11 |pages=168–181 |doi=10.1007/BF02895571 |bibcode = 1972NCimB..12..168M |s2cid=118733638 }}</ref>

<ref name=ScottViner1965>{{cite journal |author=G.D. Scott and M. R. Viner |year=1965 |title=The geometrical appearance of large objects moving at relativistic speeds |journal=[[American Journal of Physics]] |volume=33 |issue=7 | pages=534–536 |doi=10.1119/1.1971890|bibcode = 1965AmJPh..33..534S }}</ref>

}}

== External links ==
* [http://math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html A webpage explaining the Penrose-Terrell Effect]
* [http://www.spacetimetravel.org/ Extensive explanations and visualizations of the appearance of moving objects]
* [https://github.com/jkcuk/Dr-TIM/releases/tag/Terrell-rotation_explorer_v1.0.0 Interactive simulation of the Penrose-Terrell Effect]
{{Roger Penrose|state=collapsed}}
{{Relativity|state=collapsed}}

[[Category:Special relativity]]
[[Category:Roger Penrose]]