Editing Special relativity (section)

=== Measurement versus visual appearance ===
{{main|Terrell rotation}}
[[File:Animated Terrell Rotation - Cube.gif|thumb|330px|Figure 5–4. Comparison of the measured length contraction of a cube versus its visual appearance.]]
Time dilation and length contraction are not optical illusions, but genuine effects. Measurements of these effects are not an artifact of [[Doppler shift]], nor are they the result of neglecting to take into account the time it takes light to travel from an event to an observer.

Scientists make a fundamental distinction between ''measurement'' or ''observation'' on the one hand, versus ''visual appearance'', or what one ''sees''. The measured shape of an object is a hypothetical snapshot of all of the object's points as they exist at a single moment in time. But the visual appearance of an object is affected by the varying lengths of time that light takes to travel from different points on the object to one's eye.

[[File:Terrell Rotation Sphere.gif|thumb|330px|Figure 5–5. Comparison of the measured length contraction of a globe versus its visual appearance, as viewed from a distance of three diameters of the globe from the eye to the red cross.]]
For many years, the distinction between the two had not been generally appreciated, and it had generally been thought that a length contracted object passing by an observer would in fact actually be ''seen'' as length contracted. In 1959, James Terrell and [[Roger Penrose]] independently pointed out that differential time lag effects in signals reaching the observer from the different parts of a moving object result in a fast moving object's visual appearance being quite different from its measured shape. For example, a receding object would ''appear'' contracted, an approaching object would ''appear'' elongated, and a passing object would have a skew appearance that has been likened to a rotation.<ref name="Terrell" group=p>{{cite journal |last1=Terrell |first1=James |title=Invisibility of the Lorentz Contraction |journal=[[Physical Review]] |date=15 November 1959 |volume=116 |issue=4 |pages=1041–1045 |doi=10.1103/PhysRev.116.1041 |bibcode=1959PhRv..116.1041T }}</ref><ref name="Penrose" group=p>{{cite journal |last1=Penrose |first1=Roger | authorlink1=Roger Penrose |title=The Apparent Shape of a Relativistically Moving Sphere |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |date=24 October 2008 |volume=55 |issue=1 |pages=137–139 |doi=10.1017/S0305004100033776|bibcode=1959PCPS...55..137P |s2cid=123023118 }}</ref><ref>{{cite web |last1=Cook|first1=Helen |title=Relativistic Distortion |url=http://www.math.ubc.ca/~cass/courses/m309-01a/cook/ |publisher=Mathematics Department, University of British Columbia |access-date=12 April 2017 }}</ref><ref>{{cite web |last1=Signell |first1=Peter |title=Appearances at Relativistic Speeds |url=https://stuff.mit.edu/afs/athena/course/8/8.20/www/m44.pdf |website=Project PHYSNET |publisher=Michigan State University, East Lansing, MI |access-date=12 April 2017 |archive-url=https://web.archive.org/web/20170413153459/https://stuff.mit.edu/afs/athena/course/8/8.20/www/m44.pdf |archive-date=13 April 2017 |url-status=dead }}</ref> A sphere in motion retains the circular outline for all speeds, for any distance, and for all view angles, although
the surface of the sphere and the images on it will appear distorted.<ref>{{cite web |last1=Kraus |first1=Ute |title=The Ball is Round |url=http://www.spacetimetravel.org/fussball/fussball.html |website=Space Time Travel: Relativity visualized |publisher=Institut für Physik Universität Hildesheim |access-date=16 April 2017 |archive-url=https://web.archive.org/web/20170512165032/http://www.spacetimetravel.org/fussball/fussball.html |archive-date=12 May 2017 |url-status=dead }}</ref><ref name="Boas_1961">{{cite journal |last1=Boas |first1=Mary L. |title=Apparent Shape of Large Objects at Relativistic Speeds |journal=American Journal of Physics |date=1961 |volume=29 |issue=5 |page=283 |doi=10.1119/1.1937751|bibcode=1961AmJPh..29..283B }}</ref>

[[File:M87 jet (1).jpg|thumb|Figure 5–6. Galaxy [[Messier 87|M87]] sends out a black-hole-powered jet of electrons and other sub-atomic particles traveling at nearly the speed of light.]]
Both Fig.&nbsp;5-4 and Fig.&nbsp;5-5 illustrate objects moving transversely to the line of sight. In Fig.&nbsp;5-4, a cube is viewed from a distance of four times the length of its sides. At high speeds, the sides of the cube that are perpendicular to the direction of motion appear hyperbolic in shape. The cube is actually not rotated. Rather, light from the rear of the cube takes longer to reach one's eyes compared with light from the front, during which time the cube has moved to the right. At high speeds, the sphere in Fig.&nbsp;5-5 takes on the appearance of a flattened disk tilted up to 45° from the line of sight. If the objects' motions are not strictly transverse but instead include a longitudinal component, exaggerated distortions in perspective may be seen.<ref name="Muller_2014">{{cite journal |last1=Müller |first1=Thomas |last2=Boblest |first2=Sebastian |title=Visual appearance of wireframe objects in special relativity |journal=European Journal of Physics |date=2014 |volume=35 |issue=6 |page=065025 |doi=10.1088/0143-0807/35/6/065025|arxiv=1410.4583 |bibcode=2014EJPh...35f5025M |s2cid=118498333 }}</ref> This illusion has come to be known as ''[[Terrell rotation]]'' or the ''Terrell–Penrose effect''.<ref group=note>Even though it has been many decades since Terrell and Penrose published their observations, popular writings continue to conflate measurement versus appearance. For example, Michio Kaku wrote in ''Einstein's Cosmos'' (W. W. Norton & Company, 2004. p. 65): "...&nbsp;imagine that the speed of light is only 20 miles per hour. If a car were to go down the street, it might look compressed in the direction of motion, being squeezed like an accordion down to perhaps 1 inch in length."</ref>

Another example where visual appearance is at odds with measurement comes from the observation of apparent [[superluminal motion]] in various [[radio galaxies]], [[BL Lac objects]], [[quasars]], and other astronomical objects that eject [[astrophysical jet|relativistic-speed jets]] of matter at narrow angles with respect to the viewer. An apparent optical illusion results giving the appearance of faster than light travel.<ref>{{cite book|last1=Zensus|first1=J. Anton|last2=Pearson|first2=Timothy J.|title=Superluminal Radio Sources|date=1987|publisher=Cambridge University Press|location=Cambridge, New York|isbn=9780521345606|page=3|edition=1st}}</ref><ref>{{cite web|last1=Chase|first1=Scott I.|title=Apparent Superluminal Velocity of Galaxies|url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/Superluminal/superluminal.html|website=The Original Usenet Physics FAQ|publisher=Department of Mathematics, University of California, Riverside|access-date=12 April 2017}}</ref><ref>{{cite web|last1=Richmond|first1=Michael|title="Superluminal" motions in astronomical sources|url=http://spiff.rit.edu/classes/phys200/lectures/superlum/superlum.html|website=Physics 200 Lecture Notes|publisher=School of Physics and Astronomy, Rochester Institute of Technology|access-date=20 April 2017|archive-url=https://web.archive.org/web/20170216155045/http://spiff.rit.edu/classes/phys200/lectures/superlum/superlum.html|archive-date=16 February 2017|url-status=dead}}</ref> In Fig.&nbsp;5-6, galaxy [[Messier 87|M87]] streams out a high-speed jet of subatomic particles almost directly towards us, but Penrose–Terrell rotation causes the jet to appear to be moving laterally in the same manner that the appearance of the cube in Fig.&nbsp;5-4 has been stretched out.<ref>{{cite web|last1=Keel|first1=Bill|title=Jets, Superluminal Motion, and Gamma-Ray Bursts|url=http://pages.astronomy.ua.edu/keel/galaxies/jets.html|website=Galaxies and the Universe – WWW Course Notes|publisher=Department of Physics and Astronomy, University of Alabama|access-date=29 April 2017|archive-url=https://web.archive.org/web/20170301030027/http://pages.astronomy.ua.edu/keel/galaxies/jets.html|archive-date=1 March 2017|url-status=dead}}</ref>