Modern searches for Lorentz violation

Important motivations for modern searches for Lorentz violation are deviations from Lorentz invariance (and thus special relativity

Special relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

) predicted by some variations of quantum gravity

Quantum gravity

Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

, string theory

String theory

String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, and some alternatives to general relativity

Alternatives to general relativity

Alternatives to general relativity are physical theories that attempt to describe the phenomena of gravitation in competition to Einstein's theory of general relativity.There have been many different attempts at constructing an ideal theory of gravity...

. Besides the fundamental predictions of special relativity, such as the principle of relativity

Principle of relativity

In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....

, the constancy of the speed of light

Speed of light

The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

in all inertial frames of reference, and time dilation

Time dilation

In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...

, also the predictions of the standard model

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

of particle physics

Particle physics

Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

are considered to be modified by possible Lorentz violations.

To assess and predict possible violations, test theories of special relativity

Test theories of special relativity

Test theories of special relativity give a mathematical framework for analyzing results of experiments to verify special relativity.An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of...

and effective field theories

Effective field theory

In physics, an effective field theory is, as any effective theory, an approximate theory, that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization...

(EFT) such as the Standard-Model Extension

Standard-Model Extension

Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...

(SME), have been invented. These models operate by introducing preferred frame

Preferred frame

In theoretical physics, a preferred or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different from those in other frames....

effects. For example, modifications of the dispersion relation

Dispersion relation

In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....

should lead to differences between the limiting velocity of matter and the speed of light. Also the parameterized post-Newtonian formalism

Parameterized post-Newtonian formalism

Post-Newtonian formalism is a calculational tool that expresses Einstein's equations of gravity in terms of the lowest-order deviations from Newton's theory. This allows approximations to Einstein's equations to be made in the case of weak fields...

as a test theory for general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

can be used to describe preferred frame effects. Another model including different Lorentz violations is doubly special relativity (DSR), which preserves the Planck energy as an invariant maximum energy-scale, yet without having a preferred reference frame.

Both terrestrial as well as astronomical experiments have been carried out, and new experimental techniques have been introduced. No Lorentz violations could be 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 Alan Kostelecký

Alan Kostelecký

Alan Kostelecký is a theoretical physicist who is currently a distinguished professor of physics at Indiana University, Bloomington. He is noted for his work on Lorentz symmetry breaking in particle physics...

and Russell (2011). See also the main article Tests of special relativity.

Isotropy of the speed of light

Experiments with optical resonators, by which deviations from the isotropy

Isotropy

Isotropy is uniformity in all orientations; it is derived from the Greek iso and tropos . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary...

of the speed of light

Speed of light

are tested, can be seen as modern variants of the Michelson–Morley experiment to test orientation dependence of the speed of light, and the Kennedy–Thorndike experiment to test velocity dependence. The anisotropy

Anisotropy

Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...

parameters are given using the Robertson-Mansouri-Sexl test theory

Test theories of special relativity

(RMS), which allows to distinguish between the relevant orientation- and velocity dependent values. The current precision, by which an anisotropy of the speed of light can be excluded, is at the

level. This is related to the relative velocity between the solar system

Solar System

The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

and the rest frame of the cosmic microwave background radiation

Cosmic microwave background radiation

In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

of ∼368 km/s (see also Resonator Michelson–Morley experiments)

Orientation dependence
Author	Year	RMS bounds	Anisotropy of c
Herrmann et al.	2009
Eisele et al.	2009
Müller et al.	2007
Stanwix et al.	2006
Herrmann et al.	2005
Stanwix et al.	2005
Antonini et al.	2005
Wolf et al.	2004
Wolf et al.	2004
Müller et al.	2003
Wolf et al.	2003
Brillet & Hall	1979

Velocity dependence
Author	Year	RMS bounds
Tobar et al.	2009
Wolf et al.	2004
Braxmeier et al.	2002
Hils and Hall	1990

Time dilation

The classic time dilation

Time dilation

experiments such as the Ives–Stilwell experiment, the Moessbauer rotor experiments, and the Time dilation of moving particles, have been enhanced by modernized equipment. For example, the Doppler shift of lithium

Lithium

Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

ion

Ion

An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

s traveling at high speeds is evaluated by using saturated spectroscopy

Saturated spectroscopy

Saturated spectroscopy is the method by which the exact energy of the hyperfine transitions within an atom can be found. When a monochromatic light is shone through an atom, the Absorption cross section is broadened due to Doppler broadening...

in heavy ion

Heavy ion

Heavy ion refers to an ionized atom which is usually heavier than helium. Heavy-ion physics is devoted to the study of extremely hot nuclear matter and the collective effects appearing in such systems, differing from particle physics, which studies the interactions between elementary particles...

storage ring

Storage ring

A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating for a long period of time, up to many hours. Storage of a particular particle depends upon the mass, energy and usually charge of the particle being stored...

s. The current precision, with which time dilation is measured, is at the

level. Chou et al. (2010) even managed to measure a frequency shift of

due to time dilation, namely at every day's speeds such as 36 km/h. For more information, see Modern Ives–Stilwell experiments.

Author	Year	Velocity	Maximum deviation from time dilation
Novotny et al.	2009	0,34c
Reinhardt et al.	2007	0,064c
Saathoff et al.	2003	0,064c
Grieser et al.	1994	0,064c

Clock anisotropy

By this kind of spectroscopy

Spectroscopy

Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

experiments – called Hughes–Drever experiment

Hughes–Drever experiment

Hughes–Drever experiments are testing the isotropy of mass and space. As in Michelson–Morley experiments, the existence of a preferred frame of reference, or deviations from Lorentz invariance can be tested, which also affects the validity of the equivalence principle...

s as well – violations of Lorentz invariance in the interactions of proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s and neutron

Neutron

The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s are investigated, caused by a possible existence of a preferred frame. The energy level

Energy level

A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...

s of those nucleon

Nucleon

In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

s are studied in order to find anisotropies in their frequencies ("clocks"). Clock anisotropy experiments are currently the most sensitive terrestrial ones, because the current precision by which Lorentz violations can be excluded, lies at the

GeV level. Using spin-polarized

Spin polarization

Spin polarization is the degree to which the spin, i.e., the intrinsic angular momentum of elementary particles, is aligned with a given direction. This property may pertain to the spin, hence to the magnetic moment, of conduction electrons in ferromagnetic metals, such as iron, giving rise to...

torsion balances, also anisotropies with respect to electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s can be examined.

Author	Year	SME-Anisotropy in GeV
Author	Year	Proton	Neutron
Smiciklas et al.	2011		10⁻²⁹
Gemmel et al.	2010		10⁻³²
Brown et al.	2010	10⁻³²	10⁻³³
Altarev et al.	2009		10⁻²⁰
Wolf et al.	2006	10⁻²⁵
Canè et al.	2004		10⁻³²
Humphrey et al.	2003	10⁻²⁷
Walsworth et al.	2000	10⁻²⁷	10⁻³¹
Bear et al.	2000		10⁻³¹
Berglund et al.	1995	10⁻²⁷	10⁻³⁰
Chupp et al.	1989		10⁻²⁷
Lamoreaux et al.	1989		10⁻²⁹
Prestage et al.	1985		10⁻²⁷

Electron
Author	Year	SME-Anisotropy in GeV
Heckel et al.	2008	10⁻³¹
Heckel et al.	2006	10⁻³⁰
Hou et al.	2003	10⁻²⁹
Humphrey et al.	2003	10⁻²⁷
Phillips et al.	2000	10⁻²⁷
Berglund et al.	1995	10⁻²⁷
Wang et al.	1993	10⁻²⁷
Wineland David J. Wineland David J. Wineland is an American physicist at the National Institute of Standards and Technology physics laboratory in Boulder... et al.	1991	10⁻²⁵
Phillips	1987	10⁻²⁷

Antimatter tests

Lorentz symmetry is closely connected to CPT symmetry

CPT symmetry

CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...

, from which a symmetry between matter and antimatter

Antimatter

In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

follows. This can be tested by using Penning trap

Penning trap

Penning traps are devices for the storage of charged particles using a homogeneous static magnetic field and a spatially inhomogeneous static electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have...

s, by which individual charged particles and there counterparts are trapped. Gabrielse et al. (1999) examined cyclotron frequencies in proton-antiproton

Antiproton

The antiproton is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy....

measurements, and couldn't find any deviation down to

.

Hans Dehmelt et al. tested the anomaly frequency, which plays a fundamental role in the measurement of the electron's gyromagnetic ratio. They searched for sidereal variations, and differences between electrons and positrons as well. Eventually they found no deviations, thereby establishing bounds of

GeV.

Hughes et al. (2001) examined muon

Muon

The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...

s for sidereal

Sidereal time

Sidereal time is a time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky...

signals in the spectrum of muons, and found no Lorentz violation down to

GeV.
The "Muon g-2" collaboration of the Brookhaven National Laboratory

Brookhaven National Laboratory

Brookhaven National Laboratory , is a United States national laboratory located in Upton, New York on Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base...

searched for deviations in the anomaly frequency of muons and anti-muons, and for sidereal variations under consideration of Earth's orientation. Also here, no Lorentz violations could be found, with a precision of

GeV.

Dispersion

Dispersion may refer to:In physics:*The dependence of wave velocity on frequency or wavelength:**Dispersion , for light waves**Dispersion **Acoustic dispersion, for sound waves...

of light (i.e. the dependence of light speed on its energy) from distant astronomic sources as a possible consequence of Lorentz violation has been tested in many experiments. In the context of some models of quantum gravity

Quantum gravity

Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

(QG), it was assumed that such violations should occur at energy levels similar to, or beyond the Planck energy of

GeV. In the following papers, light from gamma ray bursts and from distant galaxies etc. are used to measure such relations. Especially the Fermi-LAT group was able show, that no energy dependence and thus no Lorentz violation occurs in the photon sector even beyond the Planck energy limit, since they observed photon energies up to 31 GeV. So a large class of Lorentz violating quantum gravity models is excluded by that.

Name	Year	QG-Bounds in GeV
Fermi-LAT-GBM-Collaboration	2009
H.E.S.S.-Collaboration	2008
MAGIC MAGIC (telescope) MAGIC is a system of two Imaging Atmospheric Cherenkov telescopes situated at the Roque de los Muchachos Observatory on La Palma, one of the Canary Islands, at about 2200 m above sea level... -Collaboration	2007
Lamon et al.	2008
Martinez et al.	2006
Ellis et al.	2006/8
Boggs et al.	2004
Ellis et al.	2003
Ellis et al.	2000
Schaefer	1999
Biller	1999
Kaaret	1999

Birefringence

Due to Lorentz violations, such as the presence of an anisotropic space, also vacuum birefringence

Birefringence

Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...

and parity violations could occur. Researches have been undertaken to detect deviations in the polarization

Polarization

Polarization is a property of certain types of waves that describes the orientation of their oscillations. Electromagnetic waves, such as light, and gravitational waves exhibit polarization; acoustic waves in a gas or liquid do not have polarization because the direction of vibration and...

of photons, for instance the rotation of the polarization plane due to velocity differences between left- and right photons. In the following publications, gamma ray bursts, galactic radiation, and the Cosmic microwave background radiation

Cosmic microwave background radiation

In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

are examined. The SME

Standard-Model Extension

coefficients

and

(the latter corresponds to

in another EFT

Effective field theory

) for Lorentz violation are given, where 3 and 5 denote the mass dimensions used. No significant Lorentz violations could be measured up to now.

Name	Year	SME bounds	EFT bounds
Laurent et al.	2011	GeV^-1
Stecker	2011	GeV^-1
Kostelecký et al.	2009	GeV^-1
QUaD Collaboration	2008	GeV
Kostelecký et al.	2008	GeV
Maccione et al.	2008	GeV^-1
Komatsu et al.	2008	GeV
Kahniashvili et al.	2008	GeV
Xia et al.	2008	GeV
Cabella et al.	2007	GeV
Fan et al.	2007	GeV^-1
Feng et al.	2006	GeV
Gleiser et al.	2001	GeV^-1
Carroll et al.	1990	GeV

Vacuum Cherenkov radiation

Exceedance of the threshold energy

Threshold energy

In particle physics, the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide. The threshold energy is always greater than or equal to the rest energy of the desired particle...

could lead to a difference between the speed of photons, and the limiting velocity of any particle having a charge structure (protons, electrons, neutrinos), since the dispersion relation

Dispersion relation

is assumed to be modified in Lorentz violating EFT

Effective field theory

models such as SME

Standard-Model Extension

. Depending on which of these particles travels faster or slower than the speed of light, otherwise forbidden processes can occur:

Decay at superluminal speed of photons. These photons quickly decay into other particles, which means that high energy light cannot propagate over long distances. So the mere existence of high energy light from astronomic sources constrains possible deviations from the limiting velocity.
Vacuum Cherenkov radiation
Cherenkov radiation
Cherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium...

at superluminal speed of any particle (protons, electrons, neutrinos) having a charge structure. In this case, emission of Bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

can occur, until the particle falls below threshold and subluminal speed is reached again. This is similar to the known Cherenkov radiation in media, in which particles are traveling faster than the phase velocity of light in that medium. Deviations from the limiting velocity can be constrained, by observing high energy particles of distant astronomic sources that reach Earth.
The rate of synchrotron radiation
Synchrotron radiation
The electromagnetic radiation emitted when charged particles are accelerated radially is called synchrotron radiation. It is produced in synchrotrons using bending magnets, undulators and/or wigglers...

could be modified, if the limiting velocity between charged particles and photons is different.

However, since astronomic measurements also contain additional assumptions – like the unknown conditions at the emission or along the path traversed by the particles, or the nature of the particles –, terrestrial measurements provide results of higher significance, even though the bounds are lower (the following bounds describe maximal deviations between the speed of light and the limiting velocity of matter):

Name	Year	SME bounds !! Particle			Astr./Terr.
		Photon decay	Cherenkov	Synchrotron
Altschul	2009				Electron	Terr.
Hohensee et al.	2009				Electron	Terr.
Klinkhamer & Schreck	2008				UHECR Ultra-high-energy cosmic ray In astroparticle physics, an ultra-high-energy cosmic ray or extreme-energy cosmic ray is a cosmic ray with an extreme kinetic energy, far beyond both its rest mass and energies typical of other cosmic rays....	Astr.
Klinkhamer & Risse	2007				UHECR	Astr.
Kaufhold et al.	2007				UHECR	Astr.
Altschul	2005				Electron	Astr.
Gagnon et al.	2004				UHECR	Astr.
Jacobson et al.	2003				Electron	Astr.
Coleman & Glashow	1997				UHECR	Astr.

Neutrino oscillations

Although neutrino oscillation

Neutrino oscillation

Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...

s have been experimentally confirmed, the theoretical foundations are still controversial, as it can be seen in the discussion related to sterile neutrino

Sterile neutrino

Sterile neutrinosIn scientific literature, these particles are also variously referred to as right-handed neutrinos, inert neutrinos, heavy neutrinos, or neutral heavy leptons . are a hypothetical type of neutrino that do not interact via any of the fundamental interactions of the Standard Model...

s. This makes predictions of possible Lorentz violations very complicated. However, some succeeded in deriving a possible scenario for neutrino

Neutrino

A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

Lorentz violations, such as the EFT

Effective field theory

of Sidney Coleman

Sidney Coleman

Sidney Richard Coleman was an American theoretical physicist who studied under Murray Gell-Mann.- Life and work :Sidney Coleman grew up on the Far North Side of Chicago...

& Sheldon Lee Glashow

Sheldon Lee Glashow

Sheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.-Birth and education:...

, or SME

Standard-Model Extension

. It is generally assumed that Neutrino oscillations require a certain finite mass. However, oscillations could also occur as a consequence of Lorentz violations, so there are speculations as to how much those violations contribute to the mass of the neutrinos.

Additionally, a series of investigations was published, in which a sidereal dependence of the occurrence of neutrino oscillations was tested, which could arise when there were a preferred background field. This, possible CPT violations, and other coefficients of Lorentz violations in the framework of SME, have been tested. Here, some of the achieved GeV bounds for the validity of Lorentz invariance are stated:

Name	Year	SME bounds in GeV
MiniBooNE MiniBooNE MiniBooNE is an experiment at Fermilab designed to observe neutrino oscillations . A neutrino beam consisting primarily of muon neutrinos is directed at a detector filled with 800 tons of mineral oil and lined with 1,280 photomultiplier tubes...	2011
IceCube	2010
MINOS MINOS MINOS is a particle physics experiment designed to study the phenomena of neutrino oscillations, first discovered by a Super-Kamiokande experiment in 1998...	2010
MINOS MINOS MINOS is a particle physics experiment designed to study the phenomena of neutrino oscillations, first discovered by a Super-Kamiokande experiment in 1998...	2008
LSND LSND The Liquid Scintillator Neutrino Detector was a scintillation counter at Los Alamos National Laboratory that measured the number of neutrinos being produced by an accelerator neutrino source...	2005

Neutrino speed

It was thought for a long time in accordance with the standard model

Standard Model

, that neutrino

Neutrino

s are massless and thus traveling at the speed of light. However, since the discovery of neutrino oscillations, neutrinos are considered as having a certain mass, and thus their speed should be less than the speed of light. Some non-standard models also predict faster than light speeds, for instance, in models where the neutrinos are assumed to be tachyon

Tachyon

A tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...

s, or in Lorentz violating models with modified dispersion

Dispersion

Dispersion may refer to:In physics:*The dependence of wave velocity on frequency or wavelength:**Dispersion , for light waves**Dispersion **Acoustic dispersion, for sound waves...

relations, or models in which neutrinos take "shortcuts" through extra dimensions.

First time of flight measurements were made in the 1970s, and the observed interactions of 25-GeV muon neutrino gave

as maximal deviation from the speed of light.
A much higher agreement with the speed of light was achieved in the course of observations of 10-MeV neutrinos coming from SN 1987A

SN 1987A

SN 1987A was a supernova in the outskirts of the Tarantula Nebula in the Large Magellanic Cloud, a nearby dwarf galaxy. It occurred approximately 51.4 kiloparsecs from Earth, approximately 168,000 light-years, close enough that it was visible to the naked eye. It could be seen from the Southern...

, giving bounds of

.
A measurement of the absolute transit time over a distance of 734 km was carried out by MINOS

MINOS

MINOS is a particle physics experiment designed to study the phenomena of neutrino oscillations, first discovered by a Super-Kamiokande experiment in 1998...

(2007). They determined the speed of 3-GeV neutrinos as being 1,000051(29) c, so they apparently traveled with superluminal speeds, with a deviation from the speed of light of

. However, the standard deviation

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

was only 1.8

, clearly below the 5σ-limit necessary for a significant result. Thus, as argued by the MINOS-group,
the deviation is not significant and is also consistent with the speed of light. For the alleged measurement of superluminal neutrinos, see section OPERA below.

Another possible consequence of Lorentz violation could be the occurrence of velocity differences between neutrino flavor

Flavour (particle physics)

In particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry...

s. A comparison between muon- and electron-neutrinos by Coleman & Glashow (1998) gave a negative result, with bounds

OPERA

In 2011, the OPERA Collaboration

OPERA Experiment

The Oscillation Project with Emulsion-tRacking Apparatus is a scientific experiment for detecting tau neutrinos from muon neutrino oscillations. It is a collaboration between CERN in Geneva, Switzerland, and the Laboratori Nazionali del Gran Sasso in Gran Sasso, Italy and uses the CERN Neutrinos...

published (in a non-peer reviewed

Peer review

Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...

arXiv

ArXiv

The arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...

preprint) the results of neutrino measurements, according to which neutrinos are traveling faster than light. Traversing a distance of 730 km, the neutrinos arrived early by

ns. The relative difference to the speed of light was

, corresponding to ∼7.44 km/s. The standard deviation

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

was 6σ, so unlike the MINOS experiment the result is clearly beyond the 5σ limit necessary for a significant result. They also reported that no significant energy dependence (between 13.9 and 42.9 GeV) of neutrino speeds was measured. They argued that earlier experiments were executed with much lower neutrino energies (see Neutrino speed above). Eventually, they stress that they don't want to draw far reaching conclusions from their experiment, and await further research by the scientific community. Fermilab

Fermilab

Fermi National Accelerator Laboratory , located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in high-energy particle physics...

has announced to repeat the MINOS experiment in the next months to check the OPERA result. Also a series of arXiv preprints concerning this subject have been published.

MAGIC

In 2007, the MAGIC Collaboration

MAGIC (telescope)

MAGIC is a system of two Imaging Atmospheric Cherenkov telescopes situated at the Roque de los Muchachos Observatory on La Palma, one of the Canary Islands, at about 2200 m above sea level...

published a paper, in which they claimed a possible energy dependence of the speed of photons from the galaxy Markarian 501. They admitted, that also a possible energy dependent emission effect could have cause this result as well.
However, the MAGIC result was superseded by the substantially more precise measurements of the Fermi-LAT group, which couldn't find any effect even beyond the Planck energy. For details, see section Dispersion.

Nodland & Ralston

In 1997, Nodland & Ralston claimed to have found a rotation of the polarization plane of light coming from distant radio galaxies

Radio galaxy

Radio galaxies and their relatives, radio-loud quasars and blazars, are types of active galaxy that are very luminous at radio wavelengths, with luminosities up to 1039 W between 10 MHz and 100 GHz. The radio emission is due to the synchrotron process...

. This would indicate an anisotropy of space.
This attracted some interest in the media. However, some criticisms immediately appeared, which disputed the interpretation of the data, and who alluded to errors in the publication.
More recent researches also haven't found any evidence for this effect, see section Birefringence.

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