Modern searches for Lorentz violation are scientific studies that look for deviations from Lorentz invariance or symmetry, a set of fundamental frameworks that underpin modern science and fundamental physics in particular. These studies try to determine whether violations or exceptions might exist for well-known physical laws such as special relativity and CPT symmetry, as predicted by some variations of quantum gravity, string theory, and some alternatives to general relativity.
Lorentz violations concern the fundamental predictions of special relativity, such as the principle of relativity, the constancy of the speed of light in all inertial frames of reference, and time dilation, as well as the predictions of the Standard Model of particle physics. To assess and predict possible violations, test theories of special relativity and effective field theories (EFT) such as the Standard-Model Extension (SME) have been invented. These models introduce Lorentz and CPT violations through spontaneous symmetry breaking caused by hypothetical background fields, resulting in some sort of preferred frame effects. This could lead, for instance, to modifications of the dispersion relation, causing differences between the maximal attainable speed of matter and the speed of light.
Both terrestrial and astronomical experiments have been carried out, and new experimental techniques have been introduced. No Lorentz violations have been measured thus far, and exceptions in which positive results were reported have been refuted or lack further confirmations. For discussions of many experiments, see Mattingly (2005). For a detailed list of results of recent experimental searches, see Kostelecký and Russell (2008–2013). For a recent overview and history of Lorentz violating models, see Liberati (2013).
Assessing Lorentz invariance violations Early models assessing the possibility of slight deviations from Lorentz invariance have been published between the 1960s and the 1990s. In addition, a series of test theories of special relativity and effective field theories (EFT) for the evaluation and assessment of many experiments have been developed, including: The parameterized post-Newtonian formalism is widely used as a test theory for general relativity and alternatives to general relativity, and can also be used to describe Lorentz violating preferred frame effects. The Robertson-Mansouri-Sexl framework (RMS) contains three parameters, indicating deviations in the speed of light with respect to a preferred frame of reference. The c2 framework (a special case of the more general THεμ framework) introduces a modified dispersion relation and describes Lorentz violations in terms of a discrepancy between the speed of light and the maximal attainable speed of matter, in presence of a preferred frame. Doubly special relativity (DSR) preserves the Planck length as an invariant minimum length-scale, yet without having a preferred reference frame. Very special relativity describes space-time symmetries that are certain proper subgroups of the Poincaré group. It was shown that special relativity is only consistent with this scheme in the context of quantum field theory or CP conservation. Noncommutative geometry (in connection with noncommutative quantum field theory or the noncommutative standard model) might lead to Lorentz violations. Lorentz violations are also discussed in relation to alternatives to general relativity such as loop quantum gravity, emergent gravity, Einstein aether theory, and Hořava–Lifshitz gravity.
However, the Standard-Model Extension (SME) in which Lorentz violating effects are introduced by spontaneous symmetry breaking, is used for most modern analyses of experimental results. It was introduced by Kostelecký and colleagues in 1997 and the following years, containing all possible Lorentz and CPT violating coefficients not violating gauge symmetry. It includes not only special relativity, but the Standard Model and general relativity as well. Models whose parameters can be related to SME and thus can be seen as special cases of it, include the older RMS and c2 models, the Coleman-Glashow model confining the SME coefficients to dimension 4 operators and rotation invariance, and the Gambini–Pullin model or the Myers–Pospelov model corresponding to dimension 5 or higher operators of SME.
Speed of light
Terrestrial Many terrestrial experiments have been conducted, mostly with optical resonators or in particle accelerators, by which deviations from the isotropy of the speed of light are tested. Anisotropy parameters are given, for instance, by the Robertson–Mansouri–Sexl test theory (RMS). This allows for distinction between the relevant orientation and velocity dependent parameters. In modern variants of the Michelson–Morley experiment, the dependence of light speed on the orientation of the apparatus and the relation of longitudinal and transverse lengths of bodies in motion is analyzed. Also modern variants of the Kennedy–Thorndike experiment, by which the dependence of light speed on the velocity of the apparatus and the relation of time dilation and length contraction is analyzed, have been conducted; the recently reached limit for Kennedy–Thorndike test yields 7 × 10−12. The current precision, by which an anisotropy of the speed of light can be excluded, is at the 10−17 level. This is related to the relative velocity between the Solar System and the rest frame of the cosmic microwave background radiation of ~368 km/s (see also Resonator Michelson–Morley experiments).
In addition, the Standard-Model Extension (SME) can be used to obtain a larger number of isotropy coefficients in the photon sector. It uses the even- and odd-parity coefficients (3×3 matrices) , and . They can be interpreted as follows: represent anisotropic shifts in the two-way (forward and backwards) speed of light, represent anisotropic differences in the one-way speed of counterpropagating beams along an axis,; Standalone version of work included in the Ph.D. Thesis of M.A. Hohensee. and represent isotropic (orientation-independent) shifts in the one-way phase velocity of light. It was shown that such variations in the speed of light can be removed by suitable coordinate transformations and field redefinitions, though the corresponding Lorentz violations cannot be removed, because such redefinitions only transfer those violations from the photon sector to the matter sector of SME. While ordinary symmetric optical resonators are suitable for testing even-parity effects and provide only tiny constraints on odd-parity effects, also asymmetric resonators have been built for the detection of odd-parity effects. For additional coefficients in the photon sector leading to birefringence of light in vacuum, which cannot be redefined as the other photon effects, see .
Another type of test of the related one-way light speed isotropy in combination with the electron sector of the SME was conducted by Bocquet et al. (2010). They searched for fluctuations in the 3-momentum of photons during Earth's rotation, by measuring the Compton scattering of ultrarelativistic electrons on monochromatic laser photons in the frame of the cosmic microwave background radiation, as originally suggested by Vahe Gurzadyan and Amur Margarian (for details on that 'Compton Edge' method and analysis see, discussion e.g.).
Author Year RMS SME Orientation Velocity Michimura et al. 2013 (0.7±1) (−0.4±0.9) Baynes et al. 2012 (3±11) Baynes et al. 2011 (0.7±1.4) (3.4±6.2) Hohensee et al. 2010 (0.8±0.6) (−1.5±1.2) (−1.50±0.74) Bocquet et al. 2010 ≤1.6 combined with electron coefficients Herrmann et al. 2009 (4±8) (−0.31±0.73) (−0.14±0.78) Eisele et al. 2009 (−1.6±6±1.2) (0.0±1.0±0.3) (1.5±1.5±0.2) Tobar et al. 2009 (−4.8±3.7) Tobar et al. 2009 (−0.3±3) Müller et al. 2007 (7.7±4.0) (1.7±2.0) Carone et al. 2006 ≲3Measured by examining the anomalous magnetic moment of the electron. Stanwix et al. 2006 (9.4±8.1) (−6.9±2.2) (−0.9±2.6) Herrmann et al. 2005 (−2.1±1.9) (−3.1±2.5) (−2.5±5.1) Stanwix et al. 2005 (−0.9±2.0) (−0.63±0.43) (0.20±0.21) Antonini et al. 2005 (+0.5±3±0.7) (−2.0±0.2) Wolf et al. 2004 (−5.7±2.3) (−1.8±1.5) Wolf et al. 2004 (+1.2±2.2) (3.7±3.0) Müller et al. 2003 (+2.2±1.5) (1.7±2.6) (14±14) Lipa et al. 2003 (1.4±1.4) ≤ Wolf et al. 2003 (+1.5±4.2) Braxmaier et al. 2002 (1.9±2.1) Hils and Hall 1990 6.6 Brillet and Hall 1979 ≲5 ≲
Solar System Besides terrestrial tests also astrometric tests using Lunar Laser Ranging (LLR), i.e. sending laser signals from Earth to Moon and back, have been conducted. They are ordinarily used to test general relativity and are evaluated using the Parameterized post-Newtonian formalism. However, since these measurements are based on the assumption that the speed of light is constant, they can also be used as tests of special relativity by analyzing potential distance and orbit oscillations. For instance, Zoltán Lajos Bay and White (1981) demonstrated the empirical foundations of the Lorentz group and thus special relativity by analyzing the planetary radar and LLR data.
In addition to the terrestrial Kennedy–Thorndike experiments mentioned above, Müller & Soffel (1995) and Müller et al. (1999) tested the RMS velocity dependence parameter by searching for anomalous distance oscillations using LLR. Since time dilation is already confirmed to high precision, a positive result would prove that light speed depends on the observer's velocity and length contraction is direction dependent (like in the other Kennedy–Thorndike experiments). However, no anomalous distance oscillations have been observed, with a RMS velocity dependence limit of , comparable to that of Hils and Hall (1990, see table above on the right).
Vacuum dispersion Another effect often discussed in connection with quantum gravity (QG) is the possibility of dispersion of light in vacuum (i.e. the dependence of light speed on photon energy), due to Lorentz-violating dispersion relations. This effect should be strong at energy levels comparable to, or beyond the Planck energy , while being extraordinarily weak at energies accessible in the laboratory or observed in astrophysical objects. In an attempt to observe a weak dependence of speed on energy, light from distant astrophysical sources such as gamma ray bursts and distant galaxies has been examined in many experiments. Especially the Fermi-LAT group was able show that no energy dependence and thus no observable Lorentz violation occurs in the photon sector even beyond the Planck energy, which excludes a large class of Lorentz-violating quantum gravity models.
Name Year QG Bounds (GeV) 95% C.L. 99% C.L. Vasileiou et al. 2013 > 7.6 × Nemiroff et al. 2012 > 525 × Fermi-LAT-GBM 2009 > 3.42 × > 1.19 × H.E.S.S. 2008 ≥ 7.2 MAGIC 2007 ≥ 0.21 Ellis et al. 2007 ≥ 1.4 Lamon et al. 2007 ≥ 3.2 Martinez et al. 2006 ≥ 0.66 Boggs et al. 2004 ≥ 1.8 Ellis et al. 2003 ≥ 6.9 Ellis et al. 2000 ≥ Kaaret 1999 > 1.8 Schaefer 1999 ≥ 2.7 Biller 1999 > 4
Vacuum birefringence Lorentz violating dispersion relations due to the presence of an anisotropic space might also lead to vacuum birefringence and parity violations. For instance, the polarization plane of photons might rotate due to velocity differences between left- and right-handed photons. In particular, gamma ray bursts, galactic radiation, and the cosmic microwave background radiation are examined. The SME coefficients and for Lorentz violation are given, 3 and 5 denote the mass dimensions employed. The latter corresponds to in the EFT of Meyers and Pospelov by , being the Planck mass.