Modern Tests of Lorentz Invariance

In the paper

“Equation (90) has two positive real roots, at , corresponding to a lower and upper threshold at 14TeV and 82TeV, respectively.”

In the paper

“Most frameworks explicitly break Lorentz invariance, in that there is a preferred set of observers or background field other than the metric [90, 34].”

What the sources say

• Not checked yetcites [90] Colladay, D., and Kostelecký, V.A., “Lorentz-violating extension of the standard model”, Phys. Rev. D, 58, 116002, (1998). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/9809521. 1, 2, 4.1.1, 5 source
• Not checked yetcites [34] Arkani-Hamed, N., Cheng, H.-C., Luty, M.A., and Mukohyama, S., “Ghost condensation and a consistent infrared modification of gravity”, J. High Energy Phys., 2004(05), 074, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0312099. 1, 4.4, 4.4 source

In the paper

“In this work, the authors find that microcausality is violated if the group velocity of any field mode is superluminal.”

What the sources say

• Not checked yetcites [176] Kostelecký, V.A., and Lehnert, R., “Stability, causality, and Lorentz and CPT violation”, Phys. Rev. D, 63, 065008, (2001). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-th/0012060. 1, 2.7.1, 2.7.2 source

In the paper

“As a consequence one cannot preserve the equivalence principle with Lorentz violation unless one also modifies Hamiltonian dynamics.”

In the paper

“These latter frameworks lead to only “apparent” low energy Lorentz violation.”

In the paper

“If, for example, exact SUSY is imposed in the MSSM (minimal supersymmetric standard model), then the only Lorentz violating operators that can appear have mass dimension five or above [137].”

What the sources say

• Not checked yetcites [137] Groot Nibbelink, S., and Pospelov, M., “Lorentz violation in supersymmetric field theories”, (2004). URL (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0404271. 2.3.2, 11

In the paper

“Strictly enforced, this rule would preclude any use of an experiment that relies on particle interactions, as these interactions are determined by the dynamics of the theory.”

In the paper

“Energy/momentum conservation between initial and final particle states requires translation invariance of the underlying spacetime and the Lorentz violating physics.”

In the paper

“Hence a small amount of Lorentz violation should be present at all energies.”

In the paper

“SUSY, while related to Lorentz symmetry, can still be an exact symmetry even in the presence of Lorentz violation.”

In the paper

“Lorentz violation implies a violation of the equivalence principle.”

In the paper

“Other high energy models of spacetime structure, such as non-commutative field theory, do however explicitly contain Lorentz violation [98].”

What the sources say

• Not checked yetcites [98] Douglas, M.R., and Nekrasov, N.A., “Noncommutative field theory”, Rev. Mod. Phys., 73, 977–1029, (2001). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0106048. 1, 4.2 source

In the paper

“Due to this unusual (and useful) feature, DSR evades many of the constraints on effective field theory formulations of Lorentz violation.”

In the paper

“While perhaps theoretically interesting, the large energy gap between the Planck scale and the highest known energy particles, the trans-GZK cosmic rays of 1011 GeV (not to mention accelerator energies of ∼ 1 TeV), precludes any direct observation of Planck scale Lorentz violation.”

In the paper

“The fundamental status of Lorentz symmetry, broken or deformed, as well as the additional symmetries makes a dramatic difference as to which experiments and observations are sensitive.”

In the paper

“Hence until these models become more mature, only kinematic tests of Lorentz invariance are truly applicable.”

In the paper

“Only a select few observations, such as interferometry, birefringence, Doppler shifts, or time of flight are by construction insensitive to dynamics.”

In the paper

“Conversely, however, CPT violation implies Lorentz violation for local field theories [134].”

What the sources say

• Not checked yetcites [134] Greenberg, O.W., “CPT violation implies violation of Lorentz invariance”, Phys. Rev. Lett., 89, 231602, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0201258. 2.3.1 source

In the paper

“Experiments carried out at low energies would therefore see Lorentz violation, even though it is a good symmetry of the theory at the Planck scale.”

In the paper

“The solution is to make all Lorentz violating tensors dynamical [173, 157], thereby removing prior geometry.”

What the sources say

• Not checked yetcites [173] Kostelecký, V.A., “Gravity, Lorentz violation, and the standard model”, Phys. Rev. D, 69, 105009, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0312310. 2.4, 4.4 source
• Not checked yetcites [157] Jacobson, T.A., and Mattingly, D., “Gravity with a dynamical preferred frame”, Phys. Rev. D, 64, 024028, (2001). 2.4, 4.4, 4.4 source

In the paper

“We now give a pedagogical example to show that the equivalence principle is violated even in this case.”

In the paper

“This is the situation in DSR: All reactions that are forbidden by conservation in ordinary Lorentz invariant physics are also forbidden in DSR [146], even though particle dispersion relations in DSR would naively allow new reactions.”

What the sources say

• Not checked yetcites [146] Heyman, D., Hinteleitner, F., and Major, S., “On reaction thresholds in doubly special relativity”, Phys. Rev. D, 69, 105016, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/gr-qc/0312089. 2.3.3, 6.6.1 source

In the paper

“Lorentz symmetry is intimately tied up with CPT symmetry in that the assumption of Lorentz invariance is required for the CPT theorem [162].”

What the sources say

• Not checked yetcites [162] Jost, R., “Eine Bemerkung zum CPT”, Helv. Phys. Acta, 30, 409, (1957). 2.3.1

In the paper

“Lorentz violation therefore allows for (but does not require) CPT violation, even if the other properties of standard quantum field theory are assumed.”

In the paper

“However others try to deform the Poincaré algebra, which would lead to modified transformations between frames but no preferred frame (for a review see [186]).”

What the sources say

• Not checked yetcites [186] Kowalski-Glikman, J., “Introduction to Doubly Special Relativity”, (2004). URL (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0405273. 1, 2.1.2, 2.2, 3.4, 3, 3, 15, 17

In the paper

“However, the observational situation is often such that tests that use particle interactions can be applied to theories where only the kinematics is understood.”

In the paper

“Lorentz violation can induce a breakdown of microcausality, as shown in [176].”

What the sources say

• Not checked yetcites [176] Kostelecký, V.A., and Lehnert, R., “Stability, causality, and Lorentz and CPT violation”, Phys. Rev. D, 63, 065008, (2001). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-th/0012060. 1, 2.7.1, 2.7.2 source

In the paper

“If Lorentz invariance is violated at the Planck scale, there must be an interpolation to the low energy, (at least nearly) Lorentz invariant world we live in.”

In the paper

“DSR, if it can eventually be made mathematically consistent in its current incarnation, has one phenomenological advantage — it does not have a preferred frame.”

In the paper

“With the introduction of Lorentz violation, one must still have some ground state.”

In the paper

“For example, rotationally invariant n = 1, 3 type dispersion cannot be imposed universally on photons [90, 230].”

What the sources say

• Not checked yetcites [90] Colladay, D., and Kostelecký, V.A., “Lorentz-violating extension of the standard model”, Phys. Rev. D, 58, 116002, (1998). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/9809521. 1, 2, 4.1.1, 5 source
• Not checked yetcites [230] Myers, R.C., and Pospelov, M., “Experimental challenges for quantum gravity”, Phys. Rev. Lett., 90, 211601, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0301124. 2, 4.1.4, 5.4, 8 source

In the paper

“In other words, the vacuum Čerenkov effect (discussed in more detail in Section 6.5) can be understood as an effect of inequivalent vacua.”

In the paper

“Many experiments, such as those that measure the isotropy of the one way speed of light [275] or propagation of light around closed loops, have observables that depend on a, b, d but not on the synchronization procedure.”

What the sources say

• Not checked yetcites [275] Will, C.M., “Clock synchronization and isotropy of the one-way speed of light”, Phys. Rev. D, 45, 403–411, (1992). 3.2 source

In the paper

“For example in an aether theory, where Lorentz violation is described by a timelike four-vector, the four-vector can twist in such a way that local superluminal propagation can lead to energy-momentum flowing around closed paths [206].”

What the sources say

• Not checked yetcites [206] Lim, E.A., “Can we see Lorentz-violating vector fields in the CMB?”, Phys. Rev. D, 71, 063504-1–16, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/astro-ph/0407437. 2.7.1, 33 source

In the paper

“Furthermore, it is not fully settled yet if DSR is mathematically consistent or physically meaningful.”

In the paper

“The c2 framework [277] is the flat space limit of the THϵμ [205] framework.”

What the sources say

• Not checked yetcites [277] Will, C.M., “The Confrontation between General Relativity and Experiment”, Living Rev. Relativity, 4(4), lrr-2001-4, (2001). URL (cited on 22 February 2005): http://www.livingreviews.org/lrr-2001-4. 3.2, 3.3, 4.4, 31, 7.3, 7.3
• Not checked yetcites [205] Lightman, A.P., and Lee, D.L., “Restricted proof that the Weak Equivalence Principle implies the Einstein Equivalence Principle”, Phys. Rev. D, 8, 364–376, (1973). 2.2, 3.3 source

In the paper

“For the models in Section 3.1 with higher order dispersion relations ( with n > 2) there is a stability problem for particles with momentum near the Planck energy if f(n) < 0 as modes do not have positive energy at these high momenta.”

In the paper

“In fact, it was shown in [179] that the RMS framework can be incorporated into the standard model extension.”

What the sources say

• Not checked yetcites [179] Kostelecký, V.A., and Mewes, M., “Signals for Lorentz violation in electrodynamics”, Phys. Rev. D, 66, 056005, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0205211. 3.2, 3.3, 4.1.4, 4.1.4, 5.3, 5.3, 18 source

In the paper

“If we happened to be in such a concordant frame then physics would be perfectly local and causal even though microcausality does not hold.”

In the paper

“As will be shown in detail in Section 4.1, universal dispersion relations cannot be imposed for all n from an EFT standpoint.”

In the paper

“Hence it is not possible to compare the RMS parameters of two experiments that use physically different clocks and rods (for example, an experiment that uses a cesium atomic clock versus an experiment that uses a hydrogen one).”

In the paper

“With Lorentz violation even inertial observers do not necessarily agree on the vacuum.”

In the paper

“The THϵμ and c2 constructions can also be expressed in terms on the standard model extension [179].”

What the sources say

• Not checked yetcites [179] Kostelecký, V.A., and Mewes, M., “Signals for Lorentz violation in electrodynamics”, Phys. Rev. D, 66, 056005, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0205211. 3.2, 3.3, 4.1.4, 4.1.4, 5.3, 5.3, 18 source

In the paper

“If the energy for every mode is positive, then the vacuum state |0S〉 is stable.”

In the paper

“Dynamical Lorentz violating tensors introduce further possible instabilities.”

In the paper

“Either way, the boost subgroup must be broken.”

In the paper

“In particular, the coordinate transformation of Equation (16) only has meaning if we identify the coordinates with the measurements made by a particular set of clocks and rods.”

In the paper

“The only existing constraints on non-systematic dispersion come from threshold reactions (see Section 6.6.2) and the phase coherence of light (see Section 6.9).”

In the paper

“For aether theories, the total energy is proportional to the usual ADM energy of general relativity [104].”

What the sources say

• Not checked yetcites [104] Eling, C., Jacobson, T.A., and Mattingly, D., “Einstein-aether theory”, (2004). URL (cited on 08 June 2005): http://arXiv.org/abs/gr-qc/0410001. 2.7.2, 4.4

In the paper

“However, it is possible to have a broken boost symmetry and unbroken rotation symmetry.”

In the paper

“However, the breakdown of microcausality does not lead to a breakdown of cluster decomposition in a Lorentz violating theory, in contrast to a Lorentz invariant theory.”

In the paper

“Supersymmetry is currently the only known symmetry (other than Lorentz symmetry itself) that can protect Lorentz violating operators of dimension four or less [137, 159, 65], much as SUSY protects some lower dimension operators in non-commutative field theory [216].”

What the sources say

• Not checked yetcites [137] Groot Nibbelink, S., and Pospelov, M., “Lorentz violation in supersymmetric field theories”, (2004). URL (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0404271. 2.3.2, 11
• Not checked yetcites [159] Jain, P., and Ralston, J.P., “Supersymmetry and the Lorentz fine tuning problem”, Phys. Lett. B, 621, 213–218, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0502106. 11 source
• Not checked yetcites [65] Bolokhov, P.A., Groot Nibbelink, S., and Pospelov, M., “Lorentz violating supersymmetric quantum electrodynamics”, (2005). URL (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0505029. 2.3.2, 11, 11
• Not checked yetcites [216] Matusis, A., Susskind, L., and Toumbas, N., “The IR/UV connection in the non-commutative gauge theories”, J. High Energy Phys., 2000(12), 002, (2000). Related online version (cited on 22 February 2005): http://arxiv.org/abs/hep-th/0002075. 4.2, 11 source

In the paper

“One should note that these operators violate CPT.”

In the paper

“For electrons and positrons, where g ≈ 2, the state n, s = −1/2 is almost degenerate with the state n − 1, s = +1/2.”

In the paper

“A continuation of this experiment has recently been able to directly constrain boost violation at the level of 10−27 GeV [71] (sidereal variations look at rotation invariance).”

What the sources say

• Not checked yetcites [71] Canè, F., Bear, D., Phillips, D.F., Rosen, M.S., Smallwood, C.L., Stoner, R.E., and Walsworth, R.L., “Bound on Lorentz- and CPT-Violating Boost Effects for the Neutron”, Phys. Rev. Lett., 93, 230801, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/physics/0309070. 13 source

In the paper

“However, one can always eliminate one of the aμ, i.e. only the differences between aμ for various particles are actually observable.”

In the paper

“However, without some custodial symmetry protecting the theory from Lorentz violating dimension ≤ 4 operators, the lower dimension operators will be more important than irrelevant higher mass dimension operators (see Section 4.3 for details).”

In the paper

“However, no evidence for such violation has been found.”

In the paper

“Assuming these conditions, aether theories possess a set of coupled aether-metric modes which act as new gravitational degrees of freedom that can be searched for with gravitational wave interferometers or by determining energy loss rates from inspiral systems like the binary pulsar.”

In the paper

“Other strong constraints can be derived by noting that without a custodial symmetry loop effects with the dimension six operators will induce lower dimension operators.”

In the paper

“The best overall limit is in the neutron sector of the mSME and comes from a 3He/129Xe maser system [44, 45].”

What the sources say

• Not checked yetcites [44] Bear, D., Stoner, R.E., Walsworth, R.L., Kostelecký, V.A., and Lane, C.D., “Limit on Lorentz and CPT violation of the neutron using a two-species noble-gas maser”, Phys. Rev. Lett., 85, 5038–5041, (2000). Related online version (cited on 22 February 2005): http://arXiv.org/abs/physics/0007049. 13 source
• Not checked yetcites [45] Bear, D., Stoner, R.E., Walsworth, R.L., Kostelecký, V.A., and Lane, C.D., “Erratum: Limit on Lorentz and CPT Violation of the Neutron Using a Two-Species Noble-Gas Maser”, Phys. Rev. Lett., 89, 209902, (2002). 13 source

In the paper

“Strong limits can be placed on this birefringent effect from astrophysical sources [179], as detailed in Section 6.3.”

What the sources say

• Not checked yetcites [179] Kostelecký, V.A., and Mewes, M., “Signals for Lorentz violation in electrodynamics”, Phys. Rev. D, 66, 056005, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0205211. 3.2, 3.3, 4.1.4, 4.1.4, 5.3, 5.3, 18 source

In the paper

“However, dimension five SUSY operators are CPT violating, so a combination of CPT invariance and SUSY would forbid Lorentz violating operators below dimension six.”

In the paper

“We note that since the dimension five operators violate CPT, they give rise to different dispersions for positrons than electrons.”

In the paper

“The difficulty with this formulation is that it constitutes prior geometry and generically leads to energy-momentum non-conservation, similar to the bimetric model in Section 2.4.”

In the paper

“In [90] Colladay and Kostelecky derived just such a theory in flat space — the so-called (minimal) Standard Model Extension (mSME).”

What the sources say

• Not checked yetcites [90] Colladay, D., and Kostelecký, V.A., “Lorentz-violating extension of the standard model”, Phys. Rev. D, 58, 116002, (1998). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/9809521. 1, 2, 4.1.1, 5 source

In the paper

“In this scenario, the matter stress tensor is automatically conserved if all the fields are on-shell.”

In the paper

“However, in order to match a non-commutative theory to low energy observations, we must have the appropriate low energy theory, which implies that the infamous UV/IR mixing problem of non-commutative field theory must be tamed enough to create a well-defined low energy expansion.”

In the paper

“The observational bound on the difference between ωa for electrons and positrons is [97]. This leads to a bound on bZ of order bZ ≤ 10−21me.”

What the sources say

• Not checked yetcites [97] Dehmelt, H.G., Mittleman, R.K., van Dyck Jr, R.S., and Schwinberg, P., “Past electron positron g-2 experiments yielded sharpest bound on CPT violation”, Phys. Rev. Lett., 83, 4694–4696, (1999). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/9906262. 5.1 source

In the paper

“However, in multi-particle theories involving fermion interactions one cannot remove aμ for all fermions [89].”

What the sources say

• Not checked yetcites [89] Colladay, D., and Kostelecký, V.A., “CPT violation and the standard model”, Phys. Rev. D, 55, 6760–6774, (1997). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/9703464. 4.1.3 source

In the paper

“These dimension five operators do not induce n = 3 type dispersion like the operators (40).”

In the paper

“However, the frequencies ωa and ωc both receive corrections [60].”

What the sources say

• Not checked yetcites [60] Bluhm, R., Kostelecký, V.A., and Russell, N., “CPT and Lorentz tests in Penning traps”, Phys. Rev. D, 57, 3932–3943, (1998). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/9809543. 5.1 source

In the paper

“If one imposes exact SUSY on a Lorentz violating theory, the first allowed operators are of dimension five [137].”

What the sources say

• Not checked yetcites [137] Groot Nibbelink, S., and Pospelov, M., “Lorentz violation in supersymmetric field theories”, (2004). URL (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0404271. 2.3.2, 11

In the paper

“A stronger bound of ΛNC > 5 × 1014 GeV [218] on the non-commutativity scale can be derived from clock comparison experiments with Cs/Hg magnetometers [46] (see Section 5.2).”

What the sources say

• Not checked yetcites [218] Mocioiu, I., Pospelov, M., and Roiban, R., “Low-energy limits on the antisymmetric tensor field background on the brane and on the non-commutative scale”, Phys. Lett. B, 489, 390–396, (2000). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0005191. 9 source
• Not checked yetcites [46] Berglund, C.J. et. al., “New Limits on Local Lorentz Invariance from Hg and Cs Magnetometers”, Phys. Rev. Lett., 75, 1879, (1995). 9, 13 source

In the paper

“Other clock comparison experiments have been performed that yield constraints on the proton sector [84, 243, 196, 46, 241] in the mSME.”

What the sources say

• Not checked yetcites [84] Chupp, T.E., Hoare, R.J., Loveman, R.A., Oteiza, E.R., Richardson, J.M., Wagshul, M.E., and Thompson, A.K., “Results of a new test of local Lorentz invariance: A search for mass anisotropy in 21Ne”, Phys. Rev. Lett., 63, 1541–1545, (1989). 13 source
• Not checked yetcites [243] Prestage, J.D., Bollinger, J.J., Itano, W.M., and Wineland, D.J., “Limits for spatial anisotrophy by use of nuclear spin polarized Be-9+ ions”, Phys. Rev. Lett., 54, 2387–2390, (1985). 13 source
• Not checked yetcites [196] Lamoreaux, S.K., Jacobs, J.P., Heckel, B.R., Raab, F.J., and Fortson, E.N., “New limits on spatial anisotrophy from optically pumped He-201 and Hg-199”, Phys. Rev. Lett., 57, 3125–3128, (1986). 13 source

In the paper

“The best limits on (where i is the spatial direction, including that parallel to the earth’s rotation axis) for the electron come from two balances, one in Washington [170, 141] and one in Taiwan [148].”

What the sources say

• Not checked yetcites [170] Kostelecký, V.A., ed., CPT and Lorentz Symmetry, Proceedings of the Meeting held at Indiana University, Bloomington, USA, November 6–8, 1998, (World Scientific, Singapore, 1999). 5.4
• Not checked yetcites [141] Heckel, B.R. (for the Eöt-Wash Group), “Torsion Balance Tests of Spin Coupled Forces”, project homepage, University of Washington. URL (cited on 22 February 2005): http://www.npl.washington.edu/eotwash/publications/cpt01.pdf. 5.4
• Not checked yetcites [148] Hou, L.-S., Ni, W.-T., and Li, Y.-C.M., “Test of Cosmic Spatial Isotropy for Polarized Electrons Using a Rotatable Torsion Balance”, Phys. Rev. Lett., 90, 201101, (2003). 5.4, 5.4 source

In the paper

“A constraint of the dimension five operators of Equation (40) for neutrons was recently derived in [52] using limits on the spatial variation of the hyperfine nuclear spin transition in Be+ as a function of the angle between the spin axis and an external magnetic field [64].”

What the sources say

• Not checked yetcites [52] Bertolami, O., and Rosa, J.G., “New bounds on cubic Lorentz-violating terms in the fermionic dispersion relation”, Phys. Rev. D, 71, 097901, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0412289. 13 source
• Not checked yetcites [64] Bollinger, J., Heinzen, D.J., Itano, W.M., Gilbert, S.L., and Wineland, D.J., “Test of the linearity of quantum mechanics by rf spectroscopy of the 9Be+ ground state”, Phys. Rev. Lett., 63, 1031–1034, (1989). 13 source

In the paper

“The magnets give an estimated net spin polarization equivalent to approximately 1023 aligned electron spins.”

In the paper

“In the framework of the mSME, CPT violation also implies Lorentz violation.”

In the paper

“Spin polarized torsion balances are able to place comparable limits on the electron sector of the mSME [56].”

What the sources say

• Not checked yetcites [56] Bluhm, R., and Kostelecký, V.A., “Lorentz and CPT tests with spin-polarized solids”, Phys. Rev. Lett., 84, 1381–1384, (2000). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/9912542. 5.4 source

In the paper

“Furthermore, by using a cavity with a medium, the dependence of fr on n gives additional electron sensitivity [226].”

What the sources say

• Not checked yetcites [226] Müller, H., “Testing Lorentz invariance by use of vacuum and matter filled cavity resonators”, (2004). URL (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0412385. 5.3, 1

In the paper

“Hence the relevant observable for this type of CPT violation in the kaon system is the K0 and mass difference, .14”

In the paper

“In contrast to sapphire, for certain materials the strain induced on the cavity by Lorentz violation is large. This allows sensitivity to the electron parameters cμν at a level equivalent to the photon parameters.”

In the paper

“Similar bounds have been estimated [175] from the experiment of Berglund et al. [46] using the Schmidt model [251] for nuclear structure, where an individual nucleon is assumed to carry the entire nuclear angular momentum.”

What the sources say

• Not checked yetcites [175] Kostelecký, V.A., and Lane, C.D., “Constraints on Lorentz violation from clock-comparison experiments”, Phys. Rev. D, 60, 116010, (1999). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/9908504. 13, 13, 13 source
• Not checked yetcites [46] Berglund, C.J. et. al., “New Limits on Local Lorentz Invariance from Hg and Cs Magnetometers”, Phys. Rev. Lett., 75, 1879, (1995). 9, 13 source
• Not checked yetcites [251] Schmidt, T., Z. Phys., 106, 358, (1937). 13 source

In the paper

“In general, all cavities are sensitive to the photon κ parameters.”

In the paper

“If uα is spacelike one has |η1| < 2 × 10−8 and |η2| < 10−8.”

What the sources say

• Not checked yetcites [52] Bertolami, O., and Rosa, J.G., “New bounds on cubic Lorentz-violating terms in the fermionic dispersion relation”, Phys. Rev. D, 71, 097901, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0412289. 13 source

In the paper

“If uα is lightlike both coefficients are bounded at the 10−8 level.”

What the sources say

• Not checked yetcites [52] Bertolami, O., and Rosa, J.G., “New bounds on cubic Lorentz-violating terms in the fermionic dispersion relation”, Phys. Rev. D, 71, 097901, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0412289. 13 source

In the paper

“Constraints from cavity experiments are not on the κ parameters themselves, but rather on the linear combinations”

In the paper

“This redefinition shows that the Lorentz violating background tensor (kF)μναβ can be thought of as a dielectric medium with no charge or current density.”

What the sources say

• Not checked yetcites [179] Kostelecký, V.A., and Mewes, M., “Signals for Lorentz violation in electrodynamics”, Phys. Rev. D, 66, 056005, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0205211. 3.2, 3.3, 4.1.4, 4.1.4, 5.3, 5.3, 18 source

In the paper

“CPT violation only occurs when the diagonal components of H are not equal [198].”

What the sources say

• Not checked yetcites [198] Lee, T.D., and Wu, C.S., “Weak Interactions (Second section) Chapter 9: Decays of Neutral K Mesons”, Annu. Rev. Nucl. Sci., 16, 511–590, (1966). 5.5 source

In the paper

“The limits are roughly |η1| < 6 × 10−3 and |η2| < 3 if uα is timelike and coincides with the rest frame of the CMBR.”

What the sources say

• Not checked yetcites [52] Bertolami, O., and Rosa, J.G., “New bounds on cubic Lorentz-violating terms in the fermionic dispersion relation”, Phys. Rev. D, 71, 097901, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0412289. 13 source

In the paper

“Assuming that all lower dimension operators are absent, the constraint on the dimension five operators is |ηR − ηL| < 4 [230].”

What the sources say

• Not checked yetcites [230] Myers, R.C., and Pospelov, M., “Experimental challenges for quantum gravity”, Phys. Rev. Lett., 90, 211601, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0301124. 2, 4.1.4, 5.4, 8 source

In the paper

“Note that since and depend on the components of (kF)μναβ, the properties of the dielectric are orientation dependent.”

In the paper

“The absence of any extra twist limits all components of for the electron to be less than 10−28 GeV.”

What the sources say

• Not checked yetcites [170] Kostelecký, V.A., ed., CPT and Lorentz Symmetry, Proceedings of the Meeting held at Indiana University, Bloomington, USA, November 6–8, 1998, (World Scientific, Singapore, 1999). 5.4
• Not checked yetcites [141] Heckel, B.R. (for the Eöt-Wash Group), “Torsion Balance Tests of Spin Coupled Forces”, project homepage, University of Washington. URL (cited on 22 February 2005): http://www.npl.washington.edu/eotwash/publications/cpt01.pdf. 5.4

In the paper

“However, since one of the clocks involves photons, cavity experiments constrain the electromagnetic sector of the mSME as well.”

In the paper

“To conclude this section, we note that the torsion balance experiments are actually sensitive enough to also constrain the dimension 5 operators in Equation (40).”

In the paper

“The best test to date comes from spectroscopy of lithium ions in a storage ring [249]. In this experiment, 7Li+ ions are trapped in a storage ring at a velocity of 0.064 c. The transition frequencies of the boosted ions are then measured and compared to the transition frequencies at rest, providing a bound on the deviation from the special relativistic Doppler shift of |αRMS| < 2 × 10−7 in the RMS”

What the sources say

• Not checked yetcites [249] Saathoff, G., Karpuk, S., Eisenbarth, U., Huber, G., Krohn, S., Horta, R.M., Reinhardt, S., Schwalm, D., Wolf, A., and Gwinner, G., “Improved Test of Time Dilation in Special Relativity”, Phys. Rev. Lett., 91, 190403, (2003). 5.6 source

In the paper

“If we assume that the flare was emitted from the same event at the source, the time of arrival delay between 1TeV and 2TeV photons must be less than 280 s. Combining all these factors yields the limit |f(3)| < 128.”

What the sources say

• Not checked yetcites [53] Biller, S.D., Breslin, A.C., Buckley, J., Catanese, M., Carson, M., Carter-Lewis, D.A., Cawley, M.F., Fegan, D.J., Finley, J.P., Gaidos, J.A., Hillas, A.M., Krennrich, F., Lamb, R.C., Lessard, R., Masterson, C., McEnery, J.E., McKernan, B., Moriarty, P., Quinn, J., Rose, H.J., Samuelson, F., Sembroski, G., Skelton, P., and Weekes, T.C., “Limits to quantum gravity effects from observations of TeV flares in active galaxies”, Phys. Rev. Lett., 83, 2108–2111, (1999). Related online version (cited on 22 February 2005): http://arXiv.org/abs/gr-qc/9810044. 16 source

In the paper

“This fact alone has been used to constrain the kAF term in the mSME to the level of 10−42 GeV by analyzing the plane of polarization of distant galaxies [74].”

What the sources say

• Not checked yetcites [74] Carroll, S.M., Field, G.B., and Jackiw, R., “Limits on a Lorentz and parity violating modification of electrodynamics”, Phys. Rev. D, 41, 1231, (1990). 18 source

In the paper

“Furthermore, an analysis of sidereal variations involving only one of the μ−/μ+ at the current sensitivity in [72] could bound the coefficient at the level of 10−25 GeV [58].”

What the sources say

• Not checked yetcites [72] Carey, R.M. et al., “New Measurement of the Anomalous Magnetic Moment of the Positive Muon”, Phys. Rev. Lett., 82, 1632–1635, (1999). 5.7 source
• Not checked yetcites [58] Bluhm, R., Kostelecký, V.A., and Lane, C.D., “CPT and Lorentz tests with muons”, Phys. Rev. Lett., 84, 1098–1101, (2000). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/9912451. 5.7 source

In the paper

“The first is a direct comparison between the g − 2 factors for μ− and μ+, which limits the CPT violating coefficient bZ < 10−22 GeV.”

What the sources say

• Not checked yetcites [58] Bluhm, R., Kostelecký, V.A., and Lane, C.D., “CPT and Lorentz tests with muons”, Phys. Rev. Lett., 84, 1098–1101, (2000). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/9912451. 5.7 source
• Not checked yetcites [39] Bailey, J., Borer, K., Combley, F., Drumm, H., Eck, C., Farley, F.J.M., Field, J.H., Flegel, W., Hattersley, P.M., Krienen, F., Lange, F., Lebée, G., McMillan, E., Petrucci, G., Picasso, E., Rúnolfsson, O., von Rüden, W., Williams, R.W., and Wojcicki, S., “Final report on the CERN muon storage ring including the anomalous magnetic moment and the electric dipole moment of the muon, and a direct test of relativistic time dilation”, Nucl. Phys. B, 150, 1–75, (1979). 5.7 source
• Not checked yetcites [72] Carey, R.M. et al., “New Measurement of the Anomalous Magnetic Moment of the Positive Muon”, Phys. Rev. Lett., 82, 1632–1635, (1999). 5.7 source

In the paper

“However, the main point remains valid with more complicated forms of Lorentz violation: Constraints can be derived with current data that are much less than even for n = 4 Lorentz violation.”

In the paper

“Upper thresholds do not occur in Lorentz invariant physics.”

In the paper

“Hence in the presence of birefringence a linearly polarized wave rotates its direction of polarization during propagation.”

In the paper

“Hence unless f(n) ≫ 1, pTO is much higher than any relevant observational energy, and we can make the assumption of monotonicity without loss of generality.”

In the paper

“This cannot occur in Lorentz invariant reactions.”

In the paper

“In summary there is currently no “natural” and complete way that astrophysics might observe Lorentz violation, but terrestrial experiments confirm Lorentz invariance.”

In the paper

“If, however, we break Lorentz invariance and assume a photon obeys a dispersion relation of the form 79 while electrons/positrons have their usual Lorentz invariant dispersion, then it is possible to satisfy energy conservation equation if (to see this intuitively, note that the extra term at high energies acts as a large effective mass for a photon). Therefore a photon can decay to an electron”

In the paper

“Hard photon emission can occur even when the velocity condition is never satisfied, if the photon energy-momentum vector is spacelike with n > 2 dispersion.”

In the paper

“First, spin transitions in muonium (μ+e−) have been used to place a bound on for the muon (see Equation (52) for the definition of ) [149].”

What the sources say

• Not checked yetcites [149] Hughes, V.W., Grosse Perdekamp, M., Kawall, D., Liu, W., Jungmann, K., and zu Pulitz, G., “Test of CPT and Lorentz Invariance from Muonium Spectroscopy”, Phys. Rev. Lett., 87, 111804-1–4, (2001). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ex/0106103. 5.7

In the paper

“Constraints on the antisymmetric part of (kϕϕ)μν, which we denote , and (kϕB)μν, (kϕW)μν come from the birefringence constraints on photon propagation (see Section 6.3). Here the loop corrections to the photon propagator induce a non-zero (kF)αβμν, which can be directly constrained. This yields a constraint on all three coefficients of order 10−16.”

In the paper

“Recently, the results of [249] have been reinterpreted in the context of the mSME. For the electron/proton sector the approximate bounds are [197] 69 70 71 72”

What the sources say

• Not checked yetcites [249] Saathoff, G., Karpuk, S., Eisenbarth, U., Huber, G., Krohn, S., Horta, R.M., Reinhardt, S., Schwalm, D., Wolf, A., and Gwinner, G., “Improved Test of Time Dilation in Special Relativity”, Phys. Rev. Lett., 91, 190403, (2003). 5.6 source
• Not checked yetcites [197] Lane, C.D., “Probing Lorentz violation with Doppler-shift experiments”, (2005). URL (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0505130. 5.6

In the paper

“Asymmetric thresholds occur because the minimum energy configuration is not necessarily the symmetric configuration.”

In the paper

“As mentioned in Section 4.3, the existence of Lorentz violating higher dimensional operators would generically generate lower dimension ones.”

In the paper

“Such a threshold structure would produce a deficit in the observed photon spectrum in this energy band.”

In the paper

“Such an approach has been recently taken in [28], where loop corrections to mSME coefficients from Lorentz violation in the Higgs sector are considered.”

What the sources say

• Not checked yetcites [28] Anderson, D.L., Sher, M., and Turan, I., “Lorentz and CPT violation in the Higgs sector”, Phys. Rev. D, 70, 016001, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0403116. 5.8 source

In the paper

“In general, under the assumption that the dynamics is not drastically different from that of Lorentz invariant effective field theory, one can effectively apply particle reaction constraints to kinematic theories since the decay times are extremely short above threshold.”

In the paper

“It is easy to see that they are possible with Lorentz violation, however.”

In the paper

“Theorem 1: The configuration at a threshold for a particle with momentum p1 is the minimum energy configuration of all other particles that conserves momentum.”

What the sources say

• Not checked yetcites [88] Coleman, S.R., and Glashow, S.L., “High-energy tests of Lorentz invariance”, Phys. Rev. D, 59, 116008, (1999). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/9812418. 6.5.3, 6.5.6, 6.5.6, 30 source
• Not checked yetcites [215] Mattingly, D., Jacobson, T.A., and Liberati, S., “Threshold configurations in the presence of Lorentz violating dispersion relations”, Phys. Rev. D, 67, 124012, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0211466. 6.5.3 source

In the paper

“The He/Xe maser system gives a better, although less clean, bound on the transverse components of order 10−31 GeV.”

In the paper

“The parton approach yields two-sided bounds on dimension six operators of order for all constituent particles, depending on the assumptions made about equal parton dispersion corrections.”

What the sources say

• Not checked yetcites [119] Gagnon, O., and Moore, G.D., “Limits on Lorentz violation from the highest energy cosmic rays”, Phys. Rev. D, 70, 065002, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0404196. 6.5.6, 25, 27, 26 source

In the paper

“AGASA found trans-GZK events inconsistent with the GZK cutoff at 2.5σ [96]”

What the sources say

• Not checked yetcites [96] De Marco, D., Blasi, P., and Olinto, A.V., “On the statistical significance of the GZK feature in the spectrum of ultra high energy cosmic rays”, Astropart. Phys., 20, 53–65, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/astro-ph/0301497. 6.5.6 source

In the paper

“However, for higher dimension operators that yield energy dependent dispersion, simply assigning electrons and protons equal coefficients f(n) does yield comparable constraints.”

In the paper

“From this heuristic threshold analysis, however, it is clear that Lorentz violation can become important when the modification to the dispersion relation is of the same order of magnitude as the proton mass.”

In the paper

“For n = 2 the constraint is [154], where is the coefficient for one of the electron helicities. In terms of the mSME parameters this condition can be written as c − |d| − kF/2 ≤ 10−16.”

What the sources say

• Not checked yetcites [154] Jacobson, T.A., Liberati, S., and Mattingly, D., “Threshold effects and Planck scale Lorentz violation: Combined constraints from high energy astrophysics”, Phys. Rev. D, 67, 124011, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0209264. 6.4, 6.5, 6.5.1, 6.5.1, 20, 21, 6.5.5, 22, 23, 22, 6.5.6, 6.5.6, 25, 6.6.2, 6.8.2 source

In the paper

“Note that if one treated electrons, positrons, and protons as the fundamental constituents with only n = 2 dispersion and assigned each a common speed 1 − ϵ, one would obtain no constraints.”

In the paper

“The high energy photon spectrum (above 10TeV) from astrophysical sources such as Markarian 501 and 421 has been observed to show signs of absorption due to scattering off the IR background.”

In the paper

“For n = 2 with CPT preserved we have [154]. If we set d = 0 in Equation (39) so that there is no helicity dependence, this translates to the constraint kF/2 + c ≤ 4 × 10−16.”

What the sources say

• Not checked yetcites [154] Jacobson, T.A., Liberati, S., and Mattingly, D., “Threshold effects and Planck scale Lorentz violation: Combined constraints from high energy astrophysics”, Phys. Rev. D, 67, 124011, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0209264. 6.4, 6.5, 6.5.1, 6.5.1, 20, 21, 6.5.5, 22, 23, 22, 6.5.6, 6.5.6, 25, 6.6.2, 6.8.2 source

In the paper

“while Hi-Res has found evidence for the GZK cutoff (although at a lower confidence level; for a discussion see [263]).”

What the sources say

• Not checked yetcites [263] Stecker, F.W., “Cosmic physics: The high energy frontier”, J. Phys. G, G29, R47–R88, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/astro-ph/0309027. 22, 6.5.6 source

In the paper

“although current data from blazars suggest that both polarizations must be absorbed to some degree [263].”

What the sources say

• Not checked yetcites [263] Stecker, F.W., “Cosmic physics: The high energy frontier”, J. Phys. G, G29, R47–R88, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/astro-ph/0309027. 22, 6.5.6 source

In the paper

“If d ≠ 0 then both helicities of electrons/positrons must satisfy this bound since the photon has a decay channel into every possible combination of electron/positron helicity. The corresponding limit is kF/2 + (c ± d) ≤ 4 · 10−16.”

What the sources say

• Not checked yetcites [154] Jacobson, T.A., Liberati, S., and Mattingly, D., “Threshold effects and Planck scale Lorentz violation: Combined constraints from high energy astrophysics”, Phys. Rev. D, 67, 124011, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0209264. 6.4, 6.5, 6.5.1, 6.5.1, 20, 21, 6.5.5, 22, 23, 22, 6.5.6, 6.5.6, 25, 6.6.2, 6.8.2 source

In the paper

“Hence the GZK cutoff could vanish or be shifted due to source effects as well.”

In the paper

“The level of constraints from threshold reactions at 50 TeV is around 10−2 [152, 167].”

What the sources say

• Not checked yetcites [152] Jacobson, T.A., Liberati, S., and Mattingly, D., “TeV astrophysics constraints on Planck scale Lorentz violation”, Phys. Rev. D, 66, 081302, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0112207. 6.4, 22 source
• Not checked yetcites [167] Konopka, T.J., and Major, S.A., “Observational limits on quantum geometry effects”, New J. Phys., 4, 57, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0201184. 20, 22, 6.5.6 source

In the paper

“The corresponding constraint from the observation of high energy cosmic rays is cp − 1 ≤ 2 × 10−15.”

What the sources say

• Not checked yetcites [224] Moore, G.D., and Nelson, A.E., “Lower bound on the propagation speed of gravity from gravitational Cherenkov radiation”, J. High Energy Phys., 2001(09), 023, (2001). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0106220. 6.5.5, 6.5.7 source

In the paper

“Ultra-high energy cosmic rays (UHECR), if they are protons, will interact strongly with the cosmic microwave background and produce pions, p + γ ⟶ p + π0, losing energy in the process.”

In the paper

“The region of parameter space where such a scenario might happen is extremely small, however.”

In the paper

“High energy particles travelling faster than the speed of graviton modes will emit graviton Čerenkov radiation.”

What the sources say

• Not checked yetcites [224] Moore, G.D., and Nelson, A.E., “Lower bound on the propagation speed of gravity from gravitational Cherenkov radiation”, J. High Energy Phys., 2001(09), 023, (2001). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0106220. 6.5.5, 6.5.7 source

In the paper

“When the fermion dispersion is helicity dependent, the phenomenon of helicity decay occurs. One of the helicities is unstable and will decay into the other as a particle propagates, emitting some sort of radiation depending on the exact process considered.”

In the paper

“The 50 TeV photons observed from the Crab nebula are believed to be produced via inverse Compton (IC) scattering of charged particles off the ambient soft photon background.”

In the paper

“Since Lorentz violation shifts the location of the GZK cutoff, significant information about Lorentz violation (even for n = 4 type dispersion) can be gleaned from the UHECR spectrum.”

In the paper

“We can simplify the problem dramatically by noting that the birefringence constraint on ξ in Equation (40) is |ξ| ≤ 10−4 [127].”

What the sources say

• Not checked yetcites [127] Gleiser, R.J., and Kozameh, C.N., “Astrophysical limits on quantum gravity motivated birefringence”, Phys. Rev. D, 64, 083007, (2001). Related online version (cited on 22 February 2005): http://arXiv.org/abs/gr-qc/0102093. 18, 19, 22 source

In the paper

“Lorentz violating terms can be chosen such that photons become unstable to decay into electron-positron pairs [152].”

What the sources say

• Not checked yetcites [152] Jacobson, T.A., Liberati, S., and Mattingly, D., “TeV astrophysics constraints on Planck scale Lorentz violation”, Phys. Rev. D, 66, 081302, (2002). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0112207. 6.4, 22 source

In the paper

“However, none of the analyses take into account the EFT requirement for n = 3 that opposite photon polarization have opposite Lorentz violating terms.”

In the paper

“Bounds on the coefficients of CPT violating dimension five operators are of the order 10−15.”

What the sources say

• Not checked yetcites [119] Gagnon, O., and Moore, G.D., “Limits on Lorentz violation from the highest energy cosmic rays”, Phys. Rev. D, 70, 065002, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0404196. 6.5.6, 25, 27, 26 source

In the paper

“The lifetime of a high energy particle in QED above threshold is therefore short enough that we can establish constraints simply by looking at threshold conditions.”

In the paper

“A complimentary constraint to the GZK analysis can be derived by recognizing that 1019 − 1020 eV protons reach us — a vacuum Čerenkov effect must be forbidden up to the highest observed UHECR energy [88, 154, 119].”

What the sources say

• Not checked yetcites [88] Coleman, S.R., and Glashow, S.L., “High-energy tests of Lorentz invariance”, Phys. Rev. D, 59, 116008, (1999). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/9812418. 6.5.3, 6.5.6, 6.5.6, 30 source
• Not checked yetcites [154] Jacobson, T.A., Liberati, S., and Mattingly, D., “Threshold effects and Planck scale Lorentz violation: Combined constraints from high energy astrophysics”, Phys. Rev. D, 67, 124011, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ph/0209264. 6.4, 6.5, 6.5.1, 6.5.1, 20, 21, 6.5.5, 22, 23, 22, 6.5.6, 6.5.6, 25, 6.6.2, 6.8.2 source
• Not checked yetcites [119] Gagnon, O., and Moore, G.D., “Limits on Lorentz violation from the highest energy cosmic rays”, Phys. Rev. D, 70, 065002, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0404196. 6.5.6, 25, 27, 26 source

In the paper

“In the aether theory (see Section 4.4) there are three new modes, corresponding to the three new degrees of freedom introduced by the constrained aether vector.”

In the paper

“While this process occurs in Lorentz invariant physics, the amount of absorption is affected by Lorentz violation.”

In the paper

“If, as the authors of [105] argue, no gravity-aether mode can be superluminal, then these bounds imply that every coefficient is generically bounded by |ci| < 10−15.”

What the sources say

• Not checked yetcites [105] Elliott, J.W., Moore, G.D., and Stoica, H., “Constraining the New Aether: Gravitational Cherenkov Radiation”, J. High Energy Phys., 2005(08), 066, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0505211. 12, 6.5.7, 6.5.7, 31 source

In the paper

“The possible importance of positrons in the Crab implies that the synchrotron constraint is always satisfied when considered by itself.”

In the paper

“Current data support neutrino oscillations that vary as a function of L/E [35, 125], so it seems unlikely that Lorentz violation could be the sole source of neutrino oscillations.”

What the sources say

• Not checked yetcites [35] Ashie, Y. et al. (Super-Kamiokande Collaboration), “Evidence for an Oscillatory Signature in Atmospheric Neutrino Oscillation”, Phys. Rev. Lett., 93, 101801, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ex/0404034. 6.8.1 source
• Not checked yetcites [125] Giacomelli, G., and Margiotta, A., “MACRO results on atmospheric neutrino oscillations”, Eur. Phys. J. C, 33, s826–s828, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-ex/0406037. 6.8.1 source

In the paper

“In the presence of dynamical Lorentz violation, where the entire action is diffeomorphism invariant, one generically expects new gravitational wave polarizations.”

In the paper

“It has been shown [18] that Lorentz violation can in fact raise (or lower) this bound significantly.”

What the sources say

• Not checked yetcites [18] Amelino-Camelia, G., Arzano, M., Ng, Y.J., Piran, T., and van Dam, H., “Implications of spacetime quantization for the Bahcall-Waxman neutrino bound”, J. Cosmol. Astropart. Phys., 0402, 009, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0307027. 6.8.1, 30 source

In the paper

“Currently, we have no experimental evidence that Lorentz symmetry is not an exact symmetry in nature.”

In the paper

“Neutrino oscillations are sensitive enough to directly probe non-renormalizable Lorentz violating terms.”

In the paper

“The above approach, modified conservation plus unchanged matrix element/rate when the reaction is allowed, is not correct when a low energy particle is involved.”

In the paper

“The first is simply that neutrino oscillation still occurs even if the mass is zero.”

In the paper

“Barring cancellations this translates to a very strong bound of order 10−7 on the coefficients ci in the aether action.”

What the sources say

• Not checked yetcites [277] Will, C.M., “The Confrontation between General Relativity and Experiment”, Living Rev. Relativity, 4(4), lrr-2001-4, (2001). URL (cited on 22 February 2005): http://www.livingreviews.org/lrr-2001-4. 3.2, 3.3, 4.4, 31, 7.3, 7.3

In the paper

“Hence DSR cannot be ruled out or confirmed by any threshold type analysis we currently have.”

In the paper

“By comparing this effect with observed nucleosynthesis limits, Carroll and Lim are able to constrain the size of c1, c2, and c3.”

What the sources say

• Not checked yetcites [76] Carroll, S.M., and Lim, E.A., “Lorentz-violating vector fields slow the universe down”, Phys. Rev. D, 70, 123525, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0407149. 34 source

In the paper

“More detailed calculations [222, 111, 221] show that in the case of the Crab nebula Equation (103) is correct”

What the sources say

• Not checked yetcites [222] Montemayor, R., and Urrutia, L.F., “Synchrotron radiation in Myers-Pospelov effective electrodynamics”, Phys. Lett. B, 606, 86–94, (2005). Related online version (cited on 22 February 2005): http://arXiv.org/abs/hep-th/0410143. 6.7 source
• Not checked yetcites [111] Ellis, J.R., Mavromatos, N.E., and Sakharov, A.S., “Synchrotron radiation from the Crab Nebula discriminates between models of space-time foam”, Astropart. Phys., 20, 669–682, (2004). Related online version (cited on 08 June 2005): http://arXiv.org/abs/astro-ph/0308403. 6.7 source
• Not checked yetcites [221] Montemayor, R., and Urrutia, L.F., “Synchrotron radiation in Lorentz-violating electrodynamics: The Myers-Pospelov model”, (2005). URL (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0505135. 6.7

In the paper

“Neutrinos can provide excellent probes of Lorentz violation, as their mass is much smaller than any other known particle.”

In the paper

“Unfortunately, few constraints currently exist on dynamical Lorentz violation from gravitational wave observations as the spectrum is only part of the story.”

In the paper

“Looking solely at the kinematical threshold condition, they find that all cosmic ray protons would undergo photo-pion production at energies above 1015 eV.”

What the sources say

• Not checked yetcites [11] Aloisio, R., Blasi, P., Galante, A., Ghia, P.L., and Grillo, A.F., “Space time fluctuations and ultra high energy cosmic ray interactions”, Astropart. Phys., 19, 127–133, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/astro-ph/0205271. 6.6.2 source

In the paper

“However, the actual shift of threshold energies due to DSR is negligible at the level of sensitivity we have with astrophysical observations [21].”

What the sources say

• Not checked yetcites [21] Amelino-Camelia, G., Kowalski-Glikman, J., Mandanici, G., and Procaccini, A., “Phenomenology of doubly special relativity”, (2003). URL (cited on 22 February 2005): http://arXiv.org/abs/gr-qc/0312124. 3, 17, 6.6.1

In the paper

“However, the synchrotron constraint can be combined with Čerenkov constraints to create a two sided bound [155].”

What the sources say

• Not checked yetcites [155] Jacobson, T.A., Liberati, S., and Mattingly, D., “Lorentz violation at high energy: Concepts, phenomena and astrophysical constraints”, (2005). URL (cited on 08 June 2005): http://arXiv.org/abs/astro-ph/0505267. 1, 6.5.4, 6.5.5, 29

In the paper

“Jacobson et al. [153] noticed that the synchrotron emission from the Crab nebula (and other astrophysical objects) is very sensitive to n = 3 modified dispersion relations.”

What the sources say

• Not checked yetcites [153] Jacobson, T.A., Liberati, S., and Mattingly, D., “Lorentz violation and Crab synchrotron emission: A new constraint far beyond the Planck scale”, Nature, 424, 1019–1021, (2003). Related online version (cited on 22 February 2005): http://arXiv.org/abs/astro-ph/0212190. 6.7, 6.7, 28 source

In the paper

“We currently have bounds on Lorentz violation strong enough that there is no easy way to put Lorentz violating operators of dimension ≤ 6 coming solely from Planck scale physics into our field theories.”

In the paper

“By using the pseudo-momentum π and and energy ϵ one can show that if a reaction does not occur in ordinary Lorentz invariant physics, it does not occur in DSR [146].”

What the sources say

• Not checked yetcites [146] Heyman, D., Hinteleitner, F., and Major, S., “On reaction thresholds in doubly special relativity”, Phys. Rev. D, 69, 105016, (2004). Related online version (cited on 22 February 2005): http://arXiv.org/abs/gr-qc/0312089. 2.3.3, 6.6.1 source

In the paper

“Therefore, at this point there is no method by which the ERS parameters can be used to constrain Lorentz violating theories.”

In the paper

“The first difference between DSR and EFT is that DSR evades all of the photon decay and vacuum Čerenkov constraints that give strong limits on EFT Lorentz violation.”

In the paper

“This same type of argument can be rapidly extended to n = 4 dispersion, yielding a cutoff in the spectrum at 1018 eV.”

In the paper

“Demanding that high energy cosmic rays not emit these extra modes and assuming no significant Lorentz violation for cosmic rays yields the bounds 102 on the coefficents in Equation (48).”

What the sources say

• Not checked yetcites [105] Elliott, J.W., Moore, G.D., and Stoica, H., “Constraining the New Aether: Gravitational Cherenkov Radiation”, J. High Energy Phys., 2005(08), 066, (2005). Related online version (cited on 08 June 2005): http://arXiv.org/abs/hep-ph/0505211. 12, 6.5.7, 6.5.7, 31 source