Editing Michelson–Morley experiment (section)

== Recent experiments ==

===Optical tests===
Optical tests of the isotropy of the speed of light became commonplace.<ref group=A >Relativity FAQ (2007): [http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html What is the experimental basis of Special Relativity?]</ref> New technologies, including the use of  [[laser]]s and [[maser]]s, have significantly improved measurement precision. (In the following table, only Essen (1955), Jaseja (1964), and Shamir/Fox (1969) are experiments of Michelson–Morley type, ''i.e.,'' comparing two perpendicular beams. The other optical experiments employed different methods.)

{| class=wikitable
|-
! Author !! Year !! Description !! Upper bounds
|-
| [[Louis Essen]]<ref name=essen />|| 1955 || The frequency of a rotating microwave [[optical cavity|cavity resonator]] is compared with that of a [[quartz clock]] || ~3&nbsp;km/s
|-
| Cedarholm ''et al''.<ref name=cedarholm /><ref name=cedarholm2 />|| 1958 || Two [[ammonia]] masers were mounted on a rotating table, and their beams were directed in opposite directions. || ~30&nbsp;m/s
|-
| [[Ives–Stilwell experiment#Mössbauer rotor experiments|Mössbauer rotor experiments]] || 1960–68 || In a series of experiments by different researchers, the frequencies of [[gamma rays]] were observed using the [[Mössbauer effect]]. || ~2.0&nbsp;cm/s
|-
| Jaseja ''et al''.<ref name=Jaseja />|| 1964 || The frequencies of two [[Helium–neon laser|He–Ne masers]], mounted on a rotating table, were compared. Unlike Cedarholm ''et al.'', the masers were placed perpendicular to each other. || ~30&nbsp;m/s
|-
| nowrap=nowrap| Shamir and Fox<ref name=shamir />|| 1969 || Both arms of the interferometer were contained in a transparent solid ([[Poly(methyl methacrylate)|plexiglass]]). The light source was a [[Helium–neon laser]]. || ~7&nbsp;km/s
|-
| Trimmer ''et al''.<ref name=trimmer /><ref name=trimmer2 />|| 1973 || They searched for anisotropies of the speed of light behaving as the first and third of the [[Legendre polynomials]]. They used a triangle interferometer, with one portion of the path in glass. (In comparison, the Michelson–Morley type experiments test the second Legendre polynomial)<ref name=sexl group=A />|| ~2.5&nbsp;cm/s
|}

[[File:MMX with optical resonators.svg|thumb|250px |Michelson–Morley experiment with cryogenic [[optical resonators]] of a form such as was used by Müller ''et al.'' (2003).<ref name=Muller2003/>]]

=== Recent optical resonator experiments ===
During the early 21st century, there has been a resurgence in interest in performing precise Michelson–Morley type experiments using lasers, masers, cryogenic [[optical resonator]]s, etc. This is in large part due to predictions of quantum gravity that suggest that special relativity may be violated at scales accessible to experimental study. The first of these highly accurate experiments was conducted by Brillet & Hall (1979), in which they analyzed a laser frequency stabilized to a resonance of a rotating optical [[Fabry–Pérot interferometer|Fabry–Pérot]] cavity. They set a limit on the anisotropy of the speed of light resulting from the Earth's motions of Δ''c''/''c''&nbsp;≈&nbsp;10<sup>−15</sup>, where Δ''c'' is the difference between the speed of light in the ''x''- and ''y''-directions.<ref name=brillet />

As of 2015, optical and microwave resonator experiments have improved this limit to Δ''c''/''c''&nbsp;≈&nbsp;10<sup>−18</sup>. In some of them, the devices were rotated or remained stationary, and some were combined with the [[Kennedy–Thorndike experiment]]. In particular, Earth's direction and velocity (ca.&nbsp;{{Convert|368|km/s|abbr = on}}) relative to the [[Cosmic microwave background radiation#CMBR dipole anisotropy|CMB rest frame]] are ordinarily used as references in these searches for anisotropies.
{{Clear}}

{| class=wikitable
|-
! Author !! Year !! Description !! Δ''c''/''c''
|-
| Wolf ''et al.''<ref name=wolf1 />||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 and 2002 was analyzed.||rowspan=4 style="text-align:center;" |<math>\lesssim10^{-15}</math>
|-
| Müller ''et al.''<ref name=Muller2003 />||2003 ||Two optical resonators constructed from crystalline sapphire, controlling the frequencies of two [[Nd:YAG laser]]s, are set at right angles within a helium cryostat. A frequency comparator measures the beat frequency of the combined outputs of the two resonators.
|-
| Wolf ''et al.''<ref name=wolf2 />||2004 || See Wolf ''et al.'' (2003). An active temperature control was implemented. Data between 2002 and 2003 was analyzed.
|-
| Wolf ''et al.''<ref name=wolf3 />||2004 || See Wolf ''et al.'' (2003). Data between 2002 and 2004 was analyzed.
|-
| Antonini ''et al.''<ref name=antonini />||2005|| Similar to Müller ''et al.'' (2003), though the apparatus itself was set into rotation. Data between 2002 and 2004 was analyzed.||rowspan=5 style="text-align:center;" |<math>\lesssim10^{-16}</math>
|-
| Stanwix ''et al.''<ref name=stanwix />||2005 || Similar to Wolf ''et al.'' (2003). The frequency of two cryogenic oscillators was compared. In addition, the apparatus was set into rotation. Data between 2004 and 2005 was analyzed.
|-
| Herrmann ''et al.''<ref name=Herrmann1 />||2005 || Similar to Müller ''et al.'' (2003). The frequencies of two optical [[Fabry–Pérot interferometer|Fabry–Pérot resonators]] cavities are compared – one cavity was continuously rotating while the other one was stationary oriented north–south. Data between 2004 and 2005 was analyzed.
|-
| Stanwix ''et al.''<ref name=stanwix2 />||2006 || See Stanwix ''et al.'' (2005). Data between 2004 and 2006 was analyzed.
|-
| Müller ''et al.''<ref name=Muller2007 />||2007 || See Herrmann ''et al.'' (2005) and Stanwix ''et al.'' (2006). Data of both groups collected between 2004 and 2006 are combined and further analyzed. Since the experiments are located at difference continents, at [[Berlin]] and [[Perth]] respectively, the effects of both the rotation of the devices themselves and the rotation of Earth could be studied.
|-
| Eisele ''et al.''<ref name=Eisele />||2009|| The frequencies of a pair of orthogonal oriented optical standing wave cavities are compared. The cavities were interrogated by a [[Nd:YAG laser]]. Data between 2007 and 2008 was analyzed. ||rowspan=2 style="text-align:center;" |<math>\lesssim10^{-17}</math>
|-
| style="white-space:nowrap;"| Herrmann ''et al.''<ref name=Herrmann2 />||2009 || The frequencies of a pair of rotating, orthogonal optical [[Fabry–Pérot interferometer|Fabry–Pérot resonators]] are compared. The frequencies of two [[Nd:YAG laser]]s are stabilized to resonances of these resonators.
|-
| style="white-space:nowrap;"| Nagel ''et al.''<ref name=Nagel />||2015 || The frequencies of a pair of rotating, orthogonal microwave resonators are compared.
|<math>\lesssim10^{-18}</math>
|}

===Other tests of Lorentz invariance===
{{Further|Modern searches for Lorentz violation}}
[[File:Lithium-7-NMR spectrum of LiCl (1M) in D2O.gif|thumb|225px|<sup>7</sup>Li-[[NMR]] spectrum of [[LiCl]] (1M) in D<sub>2</sub>O. The sharp, unsplit NMR line of this [[isotope]] of [[lithium]] is evidence for the isotropy of mass and space.]]
Examples of other experiments not based on the Michelson–Morley principle, i.e., non-optical isotropy tests achieving an even higher level of precision, are [[Hughes–Drever experiment|Clock comparison or Hughes–Drever experiments]]. In Drever's 1961 experiment, <sup>7</sup>Li nuclei in the ground state, which has total angular momentum ''J''&nbsp;=&nbsp;3/2, were split into four equally spaced levels by a magnetic field. Each transition between a pair of adjacent levels should emit a photon of equal frequency, resulting in a single, sharp spectral line. However, since the nuclear wave functions for different ''M<sub>J</sub>'' have different orientations in space relative to the magnetic field, any orientation dependence, whether from an aether wind or from a dependence on the large-scale distribution of mass in space (see [[Mach's principle]]), would perturb the energy spacings between the four levels, resulting in an anomalous broadening or splitting of the line. No such broadening was observed. Modern repeats of this kind of experiment have provided some of the most accurate confirmations of the principle of [[Lorentz covariance|Lorentz invariance]].<ref group=A name=haugan/>