Editing Kennedy–Thorndike experiment (section)

==Recent experiments==
{{Further|Modern searches for Lorentz violation}}

=== Cavity tests ===
[[File:Braxmaier modern Kennedy Thorndike experiment.svg|thumb|350px|Figure 3. Simplified diagram of Braxmaier ''et al.'' 2002]]
In recent years, [[Michelson–Morley experiment#Recent experiments|Michelson–Morley experiments]] as well as Kennedy–Thorndike type experiments have been repeated with increased precision using [[laser]]s, [[maser]]s, and cryogenic [[optical resonator]]s. The bounds on velocity dependence according to the [[Test theories of special relativity|Robertson-Mansouri-Sexl test theory]] (RMS), which indicates the relation between time dilation and length contraction, have been significantly improved. For instance, the original Kennedy–Thorndike experiment set bounds on RMS velocity dependence of ~10<sup>−2</sup>, but current limits are in the ~10<sup>−8</sup> range.<ref name=sexl>{{Cite journal |author1=Mansouri R. |author2=Sexl R.U. | year=1977 | title= A test theory of special relativity: III. Second-order tests| journal =Gen. Rel. Gravit. |volume=8 |issue=10 |pages=809–814 | doi=10.1007/BF00759585|bibcode = 1977GReGr...8..809M |s2cid=121834946 }}</ref>

Fig. 3 presents a simplified schematic diagram of Braxmaier ''et al.'s'' 2002 repeat of the Kennedy–Thorndike experiment.<ref name=Braxmaier/> On the left, photodetectors (PD) monitor the resonance of a sapphire cryogenic optical resonator (CORE) length standard kept at liquid helium temperature to stabilize the frequency of a Nd:YAG laser to 1064&nbsp;nm. On the right, the 532&nbsp;nm absorbance line of a low pressure iodine reference is used as a time standard to stabilize the (doubled) frequency of a second Nd:YAG laser.

{| class=wikitable
! Author !! Year !! Description !! Maximum<br />velocity dependence
|-
|Hils and Hall<ref>{{cite journal|author1=Hils, Dieter |author2=Hall, J. L. |title=Improved Kennedy–Thorndike experiment to test special relativity|journal=Phys. Rev. Lett.|volume=64|pages=1697–1700|year=1990|doi=10.1103/PhysRevLett.64.1697|bibcode = 1990PhRvL..64.1697H|issue=15|pmid=10041466 }}</ref>|| 1990 || Comparing the frequency of an optical [[Fabry–Pérot interferometer|Fabry–Pérot]] cavity with that of a laser stabilized to an [[iodine|I<sub>2</sub>]] reference line.||rowspan=2 style="text-align:center;" |<math>\lesssim10^{-5}</math>
|-
| nowrap="nowrap" | Braxmaier ''et al.''<ref name=Braxmaier>{{cite journal|author1=Braxmaier, C.|author2=Müller, H.|author3=Pradl, O.|author4=Mlynek, J.|author5=Peters, A.|author6=Schiller, S.|title=Tests of Relativity Using a Cryogenic Optical Resonator|journal=Phys. Rev. Lett.|volume=88|issue=1|pages=010401|year=2002|doi=10.1103/PhysRevLett.88.010401|pmid=11800924|bibcode=2001PhRvL..88a0401B|url=http://www.exphy.uni-duesseldorf.de/Publikationen/2002/Braxmaier-2002-PRL10401.pdf|access-date=2012-07-21|archive-date=2021-03-23|archive-url=https://web.archive.org/web/20210323200106/http://www.exphy.uni-duesseldorf.de/Publikationen/2002/Braxmaier-2002-PRL10401.pdf|url-status=dead}}</ref>|| 2002 || Comparing the frequency of a cryogenic optical resonator with an [[iodine|I<sub>2</sub>]] frequency standard, using two [[Nd:YAG laser]]s.
|-
|Wolf ''et al.''<ref>{{cite journal|author=Wolf|title=Tests of Lorentz Invariance using a Microwave Resonator|journal=Physical Review Letters|volume=90|issue=6|year=2003|pages=060402|doi=10.1103/PhysRevLett.90.060402|arxiv=gr-qc/0210049|bibcode = 2003PhRvL..90f0402W|pmid=12633279 |display-authors=etal}}</ref>|| 2003 || The frequency of a stationary cryogenic microwave oscillator, consisting of sapphire crystal operating in a [[Whispering-gallery wave|whispering gallery mode]], is compared to a [[hydrogen maser]] whose frequency was compared to [[caesium]] and [[rubidium]] [[atomic fountain]] clocks. Changes during Earth's rotation have been searched for. Data between 2001–2002 was analyzed.||rowspan=2 style="text-align:center;" |<math>\lesssim10^{-7}</math>
|-
|Wolf ''et al.''<ref>{{cite journal|author1=Wolf, P. |author2=Tobar, M. E. |author3=Bize, S. |author4=Clairon, A. |author5=Luiten, A. N. |author6=Santarelli, G. |title=Whispering Gallery Resonators and Tests of Lorentz Invariance|journal=General Relativity and Gravitation|volume=36|issue=10|year=2004|pages=2351–2372|doi=10.1023/B:GERG.0000046188.87741.51|arxiv=gr-qc/0401017|bibcode=2004GReGr..36.2351W|s2cid=8799879 }}</ref>|| 2004 || See Wolf ''et al.'' (2003). An active temperature control was implemented. Data between 2002–2003 was analyzed.
|-
|Tobar ''et al.''<ref>{{cite journal|author1=Tobar, M. E. |author2=Wolf, P. |author3=Bize, S. |author4=Santarelli, G. |author5=Flambaum, V. |title=Testing local Lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser|journal=Physical Review D|volume=81|issue=2|year=2010|pages=022003|doi=10.1103/PhysRevD.81.022003|arxiv=0912.2803|bibcode = 2010PhRvD..81b2003T |s2cid=119262822 }}</ref>|| 2009 || See Wolf ''et al.'' (2003). Data between 2002–2008 was analyzed for both sidereal and annual variations.||{{center|1=<math>\lesssim10^{-8}</math>}}
|-
|Gurzadyan and Margaryan <ref name=gm18>{{cite journal |author1=Gurzadyan, V.G. |author2=Margaryan, A.T. |title=The light speed versus the observer: the Kennedy–Thorndike test from GRAAL-ESRF|journal=Eur. Phys. J. C |volume=78|issue=8 |year=2018|pages=607|doi=10.1140/epjc/s10052-018-6080-x|arxiv=1807.08551|bibcode=2018EPJC...78..607G |s2cid=119374401 }}</ref>|| 2018 ||Compton Edge data of GRAAL experiment at European Synchrotron Radiation Facility (ESRF, Grenoble) and of the calorimeter via the 1.27 MeV photons are analysed.||{{center|1=<math>\lesssim 7\, 10^{-12}</math>}}
|}

=== Lunar laser ranging ===
In addition to terrestrial measurements, Kennedy–Thorndike experiments were carried out by Müller & Soffel (1995)<ref>{{cite journal|author1=Müller, J. |author2=Soffel, M. H. |title=A Kennedy–Thorndike experiment using LLR data|journal=Physics Letters A|volume=198|year=1995|pages=71–73|doi=10.1016/0375-9601(94)01001-B|issue=2|bibcode = 1995PhLA..198...71M }}</ref> and Müller et al. (1999)<ref name=muell99>{{cite journal|author=Müller, J., Nordtvedt, K., Schneider, M., Vokrouhlicky, D.|title=Improved Determination of Relativistic Quantities from LLR|journal=Proceedings of the 11th International Workshop on Laser Ranging Instrumentation|volume=10|year=1999|pages=216–222|url=http://cddis.gsfc.nasa.gov/lw11/docs/lrw_llrpan.pdf|archive-date=2012-07-22|access-date=2012-07-18|archive-url=https://web.archive.org/web/20120722040448/http://cddis.gsfc.nasa.gov/lw11/docs/lrw_llrpan.pdf|url-status=dead}}</ref> using [[Lunar Laser Ranging experiment|Lunar Laser Ranging]] data, in which the Earth-Moon distance is evaluated to an accuracy of centimeters. If there is a [[preferred frame]] of reference and the speed of light depends on the observer's velocity, then anomalous oscillations should be observable in the Earth-Moon distance measurements. Since time dilation is already confirmed to high precision, the observance of such oscillations would demonstrate dependence of the speed of light on the observer’s velocity, as well as direction dependence of length contraction. However, no such oscillations were observed in either study, with a RMS velocity bound of ~10<sup>−5</sup>,<ref name=muell99 /> comparable to the bounds set by Hils and Hall (1990). Hence both length contraction and time dilation must have the values predicted by relativity.