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Length contraction
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==Experimental verifications== {{See also|Tests of special relativity}} Any observer co-moving with the observed object cannot measure the object's contraction, because he can judge himself and the object as at rest in the same inertial frame in accordance with the principle of relativity (as it was demonstrated by the [[Trouton–Rankine experiment]]). So length contraction cannot be measured in the object's rest frame, but only in a frame in which the observed object is in motion. In addition, even in such a non-co-moving frame, ''direct'' experimental confirmations of length contraction are hard to achieve, because (a) at the current state of technology, objects of considerable extension cannot be accelerated to relativistic speeds, and (b) the only objects traveling with the speed required are atomic particles, whose spatial extensions are too small to allow a direct measurement of contraction. However, there are ''indirect'' confirmations of this effect in a non-co-moving frame: *It was the negative result of a famous experiment, that required the introduction of length contraction: the [[Michelson–Morley experiment]] (and later also the [[Kennedy–Thorndike experiment]]). In special relativity its explanation is as follows: In its rest frame the interferometer can be regarded as at rest in accordance with the relativity principle, so the propagation time of light is the same in all directions. Although in a frame in which the interferometer is in motion, the transverse beam must traverse a longer, diagonal path with respect to the non-moving frame thus making its travel time longer, the factor by which the longitudinal beam would be delayed by taking times ''L''/(''c''−''v'') and ''L''/(''c''+''v'') for the forward and reverse trips respectively is even longer. Therefore, in the longitudinal direction the interferometer is supposed to be contracted, in order to restore the equality of both travel times in accordance with the negative experimental result(s). Thus the two-way speed of light remains constant and the round trip propagation time along perpendicular arms of the interferometer is independent of its motion & orientation. * Given the thickness of the atmosphere as measured in Earth's reference frame, [[muon]]s' extremely short lifespan shouldn't allow them to make the trip to the surface, even at the speed of light, but they do nonetheless. From the Earth reference frame, however, this is made possible only by the muon's time being slowed down by time dilation. However, in the muon's frame, the effect is explained by the atmosphere being contracted, shortening the trip.<ref name=sexl /> *Heavy [[ion]]s that are spherical when at rest should assume the form of "pancakes" or flat disks when traveling nearly at the speed of light{{px2}}{{mdash}}{{hsp}}and in fact, the results obtained from particle collisions can only be explained when the increased nucleon density due to length contraction is considered.<ref>{{cite web|author=Brookhaven National Laboratory|url=http://www.bnl.gov/rhic/physics.asp|title=The Physics of RHIC|access-date=2013-01-01}}</ref><ref>{{cite web|author=Manuel Calderon de la Barca Sanchez|url=http://nuclear.ucdavis.edu/~calderon/Research/physicsResearch.html|title=Relativistic heavy ion collisions|access-date=2013-01-01}}</ref><ref>{{Cite journal|author=Hands, Simon|title=The phase diagram of QCD|year=2001|journal=Contemporary Physics|volume=42|issue=4|pages=209–225|doi=10.1080/00107510110063843|arxiv=physics/0105022|bibcode = 2001ConPh..42..209H |s2cid=16835076}}</ref> * The [[ionization]] ability of electrically charged particles with large relative velocities is higher than expected. In pre-relativistic physics the ability should decrease at high velocities, because the time in which ionizing particles in motion can interact with the electrons of other atoms or molecules is diminished; however, in relativity, the higher-than-expected ionization ability can be explained by length contraction of the [[Coulomb's law|Coulomb field]] in frames in which the ionizing particles are moving, which increases their electrical field strength normal to the line of motion.<ref name=sexl>{{Citation|author1=Sexl, Roman |author2=Schmidt, Herbert K.|title=Raum-Zeit-Relativität|year=1979|publisher=Vieweg|location=Braunschweig| bibcode=1979raum.book.....S| isbn=3-528-17236-3}}</ref><ref>{{Citation|author=Williams, E. J.|title=The Loss of Energy by β -Particles and Its Distribution between Different Kinds of Collisions|year=1931|journal=Proceedings of the Royal Society of London. Series A|volume=130|issue=813|pages=328–346|doi=10.1098/rspa.1931.0008|bibcode = 1931RSPSA.130..328W |doi-access=free}}</ref> * In [[synchrotron]]s and [[free-electron laser]]s, relativistic electrons were injected into an [[undulator]], so that [[synchrotron radiation]] is generated. In the proper frame of the electrons, the undulator is contracted which leads to an increased radiation frequency. Additionally, to find out the frequency as measured in the laboratory frame, one has to apply the [[relativistic Doppler effect]]. So, only with the aid of length contraction and the relativistic Doppler effect, the extremely small wavelength of undulator radiation can be explained.<ref>{{cite web|author=DESY photon science|url=http://photon-science.desy.de/research/studentsteaching/primers/synchrotron_radiation/index_eng.html|title=What is SR, how is it generated and what are its properties?|access-date=2013-01-01|url-status=dead|archive-url=https://web.archive.org/web/20160603161837/http://photon-science.desy.de/research/studentsteaching/primers/synchrotron_radiation/index_eng.html|archive-date=2016-06-03}}</ref><ref>{{cite web|author=DESY photon science|url=http://flash.desy.de/sites2009/site_vuvfel/content/e395/e2188/FLASH-Broschrefrs_web.pdf|title=FLASH The Free-Electron Laser in Hamburg (PDF 7,8 MB)|access-date=2013-01-01}}</ref>
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