fbpx
Wikipedia

Standard-Model Extension

April 10, 2024

Standard-Model Extension (SME) is an effective field theory that contains the Standard Model, general relativity, and all possible operators that break Lorentz symmetry.[1][2][3][4][5][6][7][8] Violations of this fundamental symmetry can be studied within this general framework. CPT violation implies the breaking of Lorentz symmetry,[9] and the SME includes operators that both break and preserve CPT symmetry.[10][11][12]

Development edit

In 1989, Alan Kostelecký and Stuart Samuel proved that interactions in string theories could lead to the spontaneous breaking of Lorentz symmetry.[13] Later studies have indicated that loop-quantum gravity, non-commutative field theories, brane-world scenarios, and random dynamics models also involve the breakdown of Lorentz invariance.[14] Interest in Lorentz violation has grown rapidly in the last decades because it can arise in these and other candidate theories for quantum gravity. In the early 1990s, it was shown in the context of bosonic superstrings that string interactions can also spontaneously break CPT symmetry. This work[15] suggested that experiments with kaon interferometry would be promising for seeking possible signals of CPT violation due to their high sensitivity.

The SME was conceived to facilitate experimental investigations of Lorentz and CPT symmetry, given the theoretical motivation for violation of these symmetries. An initial step, in 1995, was the introduction of effective interactions.[16][17] Although Lorentz-breaking interactions are motivated by constructs such as string theory, the low-energy effective action appearing in the SME is independent of the underlying theory. Each term in the effective theory involves the expectation of a tensor field in the underlying theory. These coefficients are small due to Planck-scale suppression, and in principle are measurable in experiments. The first case considered the mixing of neutral mesons, because their interferometric nature makes them highly sensitive to suppressed effects.

In 1997 and 1998, two papers by Don Colladay and Alan Kostelecký gave birth to the minimal SME in flat spacetime.[1][2] This provided a framework for Lorentz violation across the spectrum of standard-model particles, and provided information about types of signals for potential new experimental searches.[18][19][20][21][22]

In 2004, the leading Lorentz-breaking terms in curved spacetimes were published,[3] thereby completing the picture for the minimal SME. In 1999, Sidney Coleman and Sheldon Glashow presented a special isotropic limit of the SME.[23] Higher-order Lorentz violating terms have been studied in various contexts, including electrodynamics.[24]

Lorentz transformations: observer vs. particle edit

Main article: Active and passive transformation

The distinction between particle and observer transformations is essential to understanding Lorentz violation in physics because Lorentz violation implies a measurable difference between two systems differing only by a particle Lorentz transformation.

In special relativity, observer Lorentz transformations relate measurements made in reference frames with differing velocities and orientations. The coordinates in the one system are related to those in the other by an observer Lorentz transformation—a rotation, a boost, or a combination of both. Each observer will agree on the laws of physics, since this transformation is simply a change of coordinates. On the other hand, identical experiments can be rotated or boosted relative to each other, while being studied by the same inertial observer. These transformations are called particle transformations, because the matter and fields of the experiment are physically transformed into the new configuration.

In a conventional vacuum, observer and particle transformations can be related to each other in a simple way—basically one is the inverse of the other. This apparent equivalence is often expressed using the terminology of active and passive transformations. The equivalence fails in Lorentz-violating theories, however, because fixed background fields are the source of the symmetry breaking. These background fields are tensor-like quantities, creating preferred directions and boost-dependent effects. The fields extend over all space and time, and are essentially frozen. When an experiment sensitive to one of the background fields is rotated or boosted, i.e. particle transformed, the background fields remain unchanged, and measurable effects are possible. Observer Lorentz symmetry is expected for all theories, including Lorentz violating ones, since a change in the coordinates cannot affect the physics[clarification needed]. This invariance is implemented in field theories by writing a scalar lagrangian, with properly contracted spacetime indices. Particle Lorentz breaking enters if the theory includes fixed SME background fields filling the universe.

Building the SME edit

The SME can be expressed as a Lagrangian with various terms. Each Lorentz-violating term is an observer scalar constructed by contracting standard field operators with controlling coefficients called coefficients for Lorentz violation. These are not parameters, but rather predictions of the theory, since they can in principle be measured by appropriate experiments. The coefficients are expected to be small because of the Planck-scale suppression, so perturbative methods are appropriate. In some cases[which?], other suppression mechanisms could mask large Lorentz violations. For instance, large violations that may exist in gravity could have gone undetected so far because of couplings with weak gravitational fields.[25] Stability and causality of the theory have been studied in detail.[26]

Spontaneous Lorentz symmetry breaking edit

In field theory, there are two possible ways to implement the breaking of a symmetry: explicit and spontaneous. A key result in the formal theory of Lorentz violation, published by Kostelecký in 2004, is that explicit Lorentz violation leads to incompatibility of the Bianchi identities with the covariant conservation laws for the energy–momentum and spin-density tensors, whereas spontaneous Lorentz breaking evades this difficulty.[3] This theorem requires[clarification needed] that any breaking of Lorentz symmetry must be dynamical. Formal studies of the possible causes of the breakdown of Lorentz symmetry include investigations of the fate of the expected Nambu–Goldstone modes. Goldstone's theorem implies that the spontaneous breaking must be accompanied by massless bosons. These modes might be identified with the photon,[27] the graviton,[28][29] spin-dependent interactions,[30] and spin-independent interactions.[25]

Experimental searches edit

The possible signals of Lorentz violation in any experiment can be calculated from the SME.[31][32][33][34][35][36] It has therefore proven to be a remarkable tool in the search for Lorentz violation across the landscape of experimental physics. Up until the present, experimental results have taken the form of upper bounds on the SME coefficients. Since the results will be numerically different for different inertial reference frames, the standard frame adopted for reporting results is the Sun-centered frame. This frame is a practical and appropriate choice, since it is accessible and inertial on the time scale of hundreds of years.

Typical experiments seek couplings between the background fields and various particle properties such as spin, or propagation direction. One of the key signals of Lorentz violation arises because experiments on Earth are unavoidably rotating and revolving relative to the Sun-centered frame. These motions lead to both annual and sidereal variations of the measured coefficients for Lorentz violation. Since the translational motion of the Earth around the Sun is nonrelativistic, annual variations are typically suppressed by a factor 10−4. This makes sidereal variations the leading time-dependent effect to look for in experimental data.[37]

Measurements of SME coefficients have been done with experiments involving:

All experimental results for SME coefficients are tabulated in the Data Tables for Lorentz and CPT Violation.[38]

See also edit

References edit

  1. ^ a b Colladay, Don; Kostelecký, V. Alan (1997-06-01). "CPT violation and the standard model". Physical Review D. 55 (11): 6760–6774. arXiv:hep-ph/9703464. Bibcode:1997PhRvD..55.6760C. doi:10.1103/physrevd.55.6760. ISSN 0556-2821. S2CID 7651433.
  2. ^ a b Colladay, D.; Kostelecký, V. Alan (1998-10-26). "Lorentz-violating extension of the standard model". Physical Review D. 58 (11): 116002. arXiv:hep-ph/9809521. Bibcode:1998PhRvD..58k6002C. doi:10.1103/physrevd.58.116002. ISSN 0556-2821. S2CID 4013391.
  3. ^ a b c Kostelecký, V. Alan (2004-05-17). "Gravity, Lorentz violation, and the standard model". Physical Review D. 69 (10): 105009. arXiv:hep-th/0312310. Bibcode:2004PhRvD..69j5009K. doi:10.1103/physrevd.69.105009. ISSN 1550-7998. S2CID 55185765.
  4. ^ Is Special Relativity Wrong? by Phil Schewe and Ben Stein, AIP Physics News Update Number 712 #1, December 13, 2004.
  5. ^ Cho, A. (2005-02-11). "Special Relativity Reconsidered". Science. 307 (5711): 866–868. doi:10.1126/science.307.5711.866. ISSN 0036-8075. PMID 15705835. S2CID 28092885.
  6. ^ Has time run out on Einstein's theory?, CNN, June 5, 2002.
  7. ^ Was Einstein Wrong? Space Station Research May Find Out, JPL News, May 29, 2002.
  8. ^ Peering Over Einstein's Shoulders by J.R. Minkel, Scientific American, June 24, 2002.
  9. ^ Greenberg, O. W. (2002-11-18). "CPT Violation Implies Violation of Lorentz Invariance". Physical Review Letters. 89 (23): 231602. arXiv:hep-ph/0201258. Bibcode:2002PhRvL..89w1602G. doi:10.1103/physrevlett.89.231602. ISSN 0031-9007. PMID 12484997. S2CID 9409237.
  10. ^ Kostelecký, Alan. The Search for Relativity Violations. Scientific American.
  11. ^ Russell, Neil. Fabric of the final frontier, New Scientist Magazine issue 2408, 16 August 2003.
  12. ^ Time Slows When You're on the Fly by Elizabeth Quill, Science, November 13, 2007.
  13. ^ Kostelecký, V. Alan; Samuel, Stuart (1989-01-15). "Spontaneous breaking of Lorentz symmetry in string theory". Physical Review D. 39 (2): 683–685. Bibcode:1989PhRvD..39..683K. doi:10.1103/physrevd.39.683. hdl:2022/18649. ISSN 0556-2821. PMID 9959689.
  14. ^ Breaking Lorentz symmetry, Physics World, Mar 10, 2004.
  15. ^ Alan Kostelecký, V.; Potting, Robertus (1991). "CPT and strings". Nuclear Physics B. 359 (2–3): 545–570. Bibcode:1991NuPhB.359..545A. doi:10.1016/0550-3213(91)90071-5. hdl:2022/20736. ISSN 0550-3213.
  16. ^ Kostelecký, V. Alan; Potting, Robertus (1995-04-01). "CPT, strings, and meson factories". Physical Review D. 51 (7): 3923–3935. arXiv:hep-ph/9501341. Bibcode:1995PhRvD..51.3923K. doi:10.1103/physrevd.51.3923. ISSN 0556-2821. PMID 10018860. S2CID 1472647.
  17. ^ IU Physicist offers foundation for uprooting a hallowed principle of physics 2012-09-29 at the Wayback Machine, Indiana University News Room, January 5, 2009.
  18. ^ New Ways Suggested to Probe Lorentz Violation, American Physical Society News, June 2008.
  19. ^ Ball, Philip (2004). "Back to the future". Nature. 427 (6974): 482–484. doi:10.1038/427482a. ISSN 0028-0836. PMID 14765166. S2CID 29609511.
  20. ^ Lorentz Violations? Not Yet by Phil Schewe, James Riordon, and Ben Stein, Number 623 #2, February 5, 2003.
  21. ^ Lamoreaux, Steve K. (2002). "Testing times in space". Nature. 416 (6883): 803–804. doi:10.1038/416803a. ISSN 0028-0836. PMID 11976666. S2CID 28341801.
  22. ^ Catching relativity violations with atoms by Quentin G. Bailey, APS Viewpoint, Physics 2, 58 (2009).
  23. ^ Coleman, Sidney; Glashow, Sheldon L. (1999-04-28). "High-energy tests of Lorentz invariance". Physical Review D. 59 (11): 116008. arXiv:hep-ph/9812418. Bibcode:1999PhRvD..59k6008C. doi:10.1103/physrevd.59.116008. ISSN 0556-2821. S2CID 1273409.
  24. ^ Kostelecký, V. Alan; Mewes, Matthew (2009-07-29). "Electrodynamics with Lorentz-violating operators of arbitrary dimension". Physical Review D. 80 (1): 015020. arXiv:0905.0031. Bibcode:2009PhRvD..80a5020K. doi:10.1103/physrevd.80.015020. ISSN 1550-7998. S2CID 119241509.
  25. ^ a b Kostelecký, V. Alan; Tasson, Jay D. (2009-01-05). "Prospects for Large Relativity Violations in Matter-Gravity Couplings". Physical Review Letters. 102 (1): 010402. arXiv:0810.1459. Bibcode:2009PhRvL.102a0402K. doi:10.1103/physrevlett.102.010402. ISSN 0031-9007. PMID 19257171. S2CID 15236830.
  26. ^ Kostelecký, V. Alan; Lehnert, Ralf (2001-02-13). "Stability, causality, and Lorentz and CPT violation". Physical Review D. 63 (6): 065008. arXiv:hep-th/0012060. Bibcode:2001PhRvD..63f5008K. doi:10.1103/physrevd.63.065008. ISSN 0556-2821. S2CID 119074843.
  27. ^ Bluhm, Robert; Kostelecký, V. Alan (2005-03-22). "Spontaneous Lorentz violation, Nambu-Goldstone modes, and gravity". Physical Review D. 71 (6): 065008. arXiv:hep-th/0412320. Bibcode:2005PhRvD..71f5008B. doi:10.1103/physrevd.71.065008. ISSN 1550-7998. S2CID 119354909.
  28. ^ Kostelecký, V. Alan; Potting, Robertus (2009-03-19). "Gravity from spontaneous Lorentz violation". Physical Review D. 79 (6): 065018. arXiv:0901.0662. Bibcode:2009PhRvD..79f5018K. doi:10.1103/physrevd.79.065018. ISSN 1550-7998. S2CID 119229843.
  29. ^ V.A. Kostelecký and R. Potting, Gravity from Local Lorentz Violation, Gen. Rel. Grav. 37, 1675 (2005).
  30. ^ N. Arkani-Hamed, H.C. Cheng, M. Luty, and J. Thaler, Universal dynamics of spontaneous Lorentz violation and a new spin-dependent inverse-square law force, JHEP 0507, 029 (2005).
  31. ^ Unification could be ripe for the picking, Physics World, Jan 13, 2009.
  32. ^ Michelson–Morley experiment is best yet by Hamish Johnston, Physics World, Sep 14, 2009.
  33. ^ Neutrinos: The key to a theory of everything by Marcus Chown, New Scientist Magazine issue 2615, 1 August 2007.
  34. ^ Einstein's relativity survives neutrino test, Indiana University News Room, October 15, 2008.
  35. ^ Relativity violations may make light by Francis Reddy, Astronomy Magazine, June 21, 2005.
  36. ^ Antimatter and matter may have different properties 2005-11-08 at the Wayback Machine, Indiana University News Room.
  37. ^ Lorentz symmetry stays intact, Physics World, Feb 25, 2003.
  38. ^ Kostelecký, V. Alan; Russell, Neil (2011-03-10). "Data tables for Lorentz and CPT violation". Reviews of Modern Physics. 83 (1): 11–31. arXiv:0801.0287. Bibcode:2011RvMP...83...11K. doi:10.1103/revmodphys.83.11. ISSN 0034-6861. S2CID 3236027.

External links edit

  • Background information on Lorentz and CPT violation
  • Data Tables for Lorentz and CPT Violation

April 10, 2024
standard, model, extension, effective, field, theory, that, contains, standard, model, general, relativity, possible, operators, that, break, lorentz, symmetry, violations, this, fundamental, symmetry, studied, within, this, general, framework, violation, impl. Standard Model Extension SME is an effective field theory that contains the Standard Model general relativity and all possible operators that break Lorentz symmetry 1 2 3 4 5 6 7 8 Violations of this fundamental symmetry can be studied within this general framework CPT violation implies the breaking of Lorentz symmetry 9 and the SME includes operators that both break and preserve CPT symmetry 10 11 12 Contents 1 Development 2 Lorentz transformations observer vs particle 3 Building the SME 4 Spontaneous Lorentz symmetry breaking 5 Experimental searches 6 See also 7 References 8 External linksDevelopment editIn 1989 Alan Kostelecky and Stuart Samuel proved that interactions in string theories could lead to the spontaneous breaking of Lorentz symmetry 13 Later studies have indicated that loop quantum gravity non commutative field theories brane world scenarios and random dynamics models also involve the breakdown of Lorentz invariance 14 Interest in Lorentz violation has grown rapidly in the last decades because it can arise in these and other candidate theories for quantum gravity In the early 1990s it was shown in the context of bosonic superstrings that string interactions can also spontaneously break CPT symmetry This work 15 suggested that experiments with kaon interferometry would be promising for seeking possible signals of CPT violation due to their high sensitivity The SME was conceived to facilitate experimental investigations of Lorentz and CPT symmetry given the theoretical motivation for violation of these symmetries An initial step in 1995 was the introduction of effective interactions 16 17 Although Lorentz breaking interactions are motivated by constructs such as string theory the low energy effective action appearing in the SME is independent of the underlying theory Each term in the effective theory involves the expectation of a tensor field in the underlying theory These coefficients are small due to Planck scale suppression and in principle are measurable in experiments The first case considered the mixing of neutral mesons because their interferometric nature makes them highly sensitive to suppressed effects In 1997 and 1998 two papers by Don Colladay and Alan Kostelecky gave birth to the minimal SME in flat spacetime 1 2 This provided a framework for Lorentz violation across the spectrum of standard model particles and provided information about types of signals for potential new experimental searches 18 19 20 21 22 In 2004 the leading Lorentz breaking terms in curved spacetimes were published 3 thereby completing the picture for the minimal SME In 1999 Sidney Coleman and Sheldon Glashow presented a special isotropic limit of the SME 23 Higher order Lorentz violating terms have been studied in various contexts including electrodynamics 24 Lorentz transformations observer vs particle editMain article Active and passive transformation The distinction between particle and observer transformations is essential to understanding Lorentz violation in physics because Lorentz violation implies a measurable difference between two systems differing only by a particle Lorentz transformation In special relativity observer Lorentz transformations relate measurements made in reference frames with differing velocities and orientations The coordinates in the one system are related to those in the other by an observer Lorentz transformation a rotation a boost or a combination of both Each observer will agree on the laws of physics since this transformation is simply a change of coordinates On the other hand identical experiments can be rotated or boosted relative to each other while being studied by the same inertial observer These transformations are called particle transformations because the matter and fields of the experiment are physically transformed into the new configuration In a conventional vacuum observer and particle transformations can be related to each other in a simple way basically one is the inverse of the other This apparent equivalence is often expressed using the terminology of active and passive transformations The equivalence fails in Lorentz violating theories however because fixed background fields are the source of the symmetry breaking These background fields are tensor like quantities creating preferred directions and boost dependent effects The fields extend over all space and time and are essentially frozen When an experiment sensitive to one of the background fields is rotated or boosted i e particle transformed the background fields remain unchanged and measurable effects are possible Observer Lorentz symmetry is expected for all theories including Lorentz violating ones since a change in the coordinates cannot affect the physics clarification needed This invariance is implemented in field theories by writing a scalar lagrangian with properly contracted spacetime indices Particle Lorentz breaking enters if the theory includes fixed SME background fields filling the universe Building the SME editThe SME can be expressed as a Lagrangian with various terms Each Lorentz violating term is an observer scalar constructed by contracting standard field operators with controlling coefficients called coefficients for Lorentz violation These are not parameters but rather predictions of the theory since they can in principle be measured by appropriate experiments The coefficients are expected to be small because of the Planck scale suppression so perturbative methods are appropriate In some cases which other suppression mechanisms could mask large Lorentz violations For instance large violations that may exist in gravity could have gone undetected so far because of couplings with weak gravitational fields 25 Stability and causality of the theory have been studied in detail 26 Spontaneous Lorentz symmetry breaking editIn field theory there are two possible ways to implement the breaking of a symmetry explicit and spontaneous A key result in the formal theory of Lorentz violation published by Kostelecky in 2004 is that explicit Lorentz violation leads to incompatibility of the Bianchi identities with the covariant conservation laws for the energy momentum and spin density tensors whereas spontaneous Lorentz breaking evades this difficulty 3 This theorem requires clarification needed that any breaking of Lorentz symmetry must be dynamical Formal studies of the possible causes of the breakdown of Lorentz symmetry include investigations of the fate of the expected Nambu Goldstone modes Goldstone s theorem implies that the spontaneous breaking must be accompanied by massless bosons These modes might be identified with the photon 27 the graviton 28 29 spin dependent interactions 30 and spin independent interactions 25 Experimental searches editThe possible signals of Lorentz violation in any experiment can be calculated from the SME 31 32 33 34 35 36 It has therefore proven to be a remarkable tool in the search for Lorentz violation across the landscape of experimental physics Up until the present experimental results have taken the form of upper bounds on the SME coefficients Since the results will be numerically different for different inertial reference frames the standard frame adopted for reporting results is the Sun centered frame This frame is a practical and appropriate choice since it is accessible and inertial on the time scale of hundreds of years Typical experiments seek couplings between the background fields and various particle properties such as spin or propagation direction One of the key signals of Lorentz violation arises because experiments on Earth are unavoidably rotating and revolving relative to the Sun centered frame These motions lead to both annual and sidereal variations of the measured coefficients for Lorentz violation Since the translational motion of the Earth around the Sun is nonrelativistic annual variations are typically suppressed by a factor 10 4 This makes sidereal variations the leading time dependent effect to look for in experimental data 37 This article is in list format but may read better as prose You can help by converting this article if appropriate Editing help is available March 2016 Measurements of SME coefficients have been done with experiments involving birefringence and dispersion from cosmological sources clock comparison measurements CMB polarization collider experiments electromagnetic resonant cavities equivalence principle gauge and Higgs particles high energy astrophysical observations laboratory and gravimetric tests of gravity matter interferometry neutrino oscillations oscillations and decays of K B D mesons particle antiparticle comparisons post newtonian gravity in the solar system and beyond second and third generation particles space based missions spectroscopy of hydrogen and antihydrogen spin polarized matter All experimental results for SME coefficients are tabulated in the Data Tables for Lorentz and CPT Violation 38 See also editAntimatter tests of Lorentz violation Lorentz violating electrodynamics Lorentz violating neutrino oscillations Bumblebee Models Tests of special relativity Test theories of special relativityReferences edit a b Colladay Don Kostelecky V Alan 1997 06 01 CPT violation and the standard model Physical Review D 55 11 6760 6774 arXiv hep ph 9703464 Bibcode 1997PhRvD 55 6760C doi 10 1103 physrevd 55 6760 ISSN 0556 2821 S2CID 7651433 a b Colladay D Kostelecky V Alan 1998 10 26 Lorentz violating extension of the standard model Physical Review D 58 11 116002 arXiv hep ph 9809521 Bibcode 1998PhRvD 58k6002C doi 10 1103 physrevd 58 116002 ISSN 0556 2821 S2CID 4013391 a b c Kostelecky V Alan 2004 05 17 Gravity Lorentz violation and the standard model Physical Review D 69 10 105009 arXiv hep th 0312310 Bibcode 2004PhRvD 69j5009K doi 10 1103 physrevd 69 105009 ISSN 1550 7998 S2CID 55185765 Is Special Relativity Wrong by Phil Schewe and Ben Stein AIP Physics News Update Number 712 1 December 13 2004 Cho A 2005 02 11 Special Relativity Reconsidered Science 307 5711 866 868 doi 10 1126 science 307 5711 866 ISSN 0036 8075 PMID 15705835 S2CID 28092885 Has time run out on Einstein s theory CNN June 5 2002 Was Einstein Wrong Space Station Research May Find Out JPL News May 29 2002 Peering Over Einstein s Shoulders by J R Minkel Scientific American June 24 2002 Greenberg O W 2002 11 18 CPT Violation Implies Violation of Lorentz Invariance Physical Review Letters 89 23 231602 arXiv hep ph 0201258 Bibcode 2002PhRvL 89w1602G doi 10 1103 physrevlett 89 231602 ISSN 0031 9007 PMID 12484997 S2CID 9409237 Kostelecky Alan The Search for Relativity Violations Scientific American Russell Neil Fabric of the final frontier New Scientist Magazine issue 2408 16 August 2003 Time Slows When You re on the Fly by Elizabeth Quill Science November 13 2007 Kostelecky V Alan Samuel Stuart 1989 01 15 Spontaneous breaking of Lorentz symmetry in string theory Physical Review D 39 2 683 685 Bibcode 1989PhRvD 39 683K doi 10 1103 physrevd 39 683 hdl 2022 18649 ISSN 0556 2821 PMID 9959689 Breaking Lorentz symmetry Physics World Mar 10 2004 Alan Kostelecky V Potting Robertus 1991 CPT and strings Nuclear Physics B 359 2 3 545 570 Bibcode 1991NuPhB 359 545A doi 10 1016 0550 3213 91 90071 5 hdl 2022 20736 ISSN 0550 3213 Kostelecky V Alan Potting Robertus 1995 04 01 CPT strings and meson factories Physical Review D 51 7 3923 3935 arXiv hep ph 9501341 Bibcode 1995PhRvD 51 3923K doi 10 1103 physrevd 51 3923 ISSN 0556 2821 PMID 10018860 S2CID 1472647 IU Physicist offers foundation for uprooting a hallowed principle of physics Archived 2012 09 29 at the Wayback Machine Indiana University News Room January 5 2009 New Ways Suggested to Probe Lorentz Violation American Physical Society News June 2008 Ball Philip 2004 Back to the future Nature 427 6974 482 484 doi 10 1038 427482a ISSN 0028 0836 PMID 14765166 S2CID 29609511 Lorentz Violations Not Yet by Phil Schewe James Riordon and Ben Stein Number 623 2 February 5 2003 Lamoreaux Steve K 2002 Testing times in space Nature 416 6883 803 804 doi 10 1038 416803a ISSN 0028 0836 PMID 11976666 S2CID 28341801 Catching relativity violations with atoms by Quentin G Bailey APS Viewpoint Physics 2 58 2009 Coleman Sidney Glashow Sheldon L 1999 04 28 High energy tests of Lorentz invariance Physical Review D 59 11 116008 arXiv hep ph 9812418 Bibcode 1999PhRvD 59k6008C doi 10 1103 physrevd 59 116008 ISSN 0556 2821 S2CID 1273409 Kostelecky V Alan Mewes Matthew 2009 07 29 Electrodynamics with Lorentz violating operators of arbitrary dimension Physical Review D 80 1 015020 arXiv 0905 0031 Bibcode 2009PhRvD 80a5020K doi 10 1103 physrevd 80 015020 ISSN 1550 7998 S2CID 119241509 a b Kostelecky V Alan Tasson Jay D 2009 01 05 Prospects for Large Relativity Violations in Matter Gravity Couplings Physical Review Letters 102 1 010402 arXiv 0810 1459 Bibcode 2009PhRvL 102a0402K doi 10 1103 physrevlett 102 010402 ISSN 0031 9007 PMID 19257171 S2CID 15236830 Kostelecky V Alan Lehnert Ralf 2001 02 13 Stability causality and Lorentz and CPT violation Physical Review D 63 6 065008 arXiv hep th 0012060 Bibcode 2001PhRvD 63f5008K doi 10 1103 physrevd 63 065008 ISSN 0556 2821 S2CID 119074843 Bluhm Robert Kostelecky V Alan 2005 03 22 Spontaneous Lorentz violation Nambu Goldstone modes and gravity Physical Review D 71 6 065008 arXiv hep th 0412320 Bibcode 2005PhRvD 71f5008B doi 10 1103 physrevd 71 065008 ISSN 1550 7998 S2CID 119354909 Kostelecky V Alan Potting Robertus 2009 03 19 Gravity from spontaneous Lorentz violation Physical Review D 79 6 065018 arXiv 0901 0662 Bibcode 2009PhRvD 79f5018K doi 10 1103 physrevd 79 065018 ISSN 1550 7998 S2CID 119229843 V A Kostelecky and R Potting Gravity from Local Lorentz Violation Gen Rel Grav 37 1675 2005 N Arkani Hamed H C Cheng M Luty and J Thaler Universal dynamics of spontaneous Lorentz violation and a new spin dependent inverse square law force JHEP 0507 029 2005 Unification could be ripe for the picking Physics World Jan 13 2009 Michelson Morley experiment is best yet by Hamish Johnston Physics World Sep 14 2009 Neutrinos The key to a theory of everything by Marcus Chown New Scientist Magazine issue 2615 1 August 2007 Einstein s relativity survives neutrino test Indiana University News Room October 15 2008 Relativity violations may make light by Francis Reddy Astronomy Magazine June 21 2005 Antimatter and matter may have different properties Archived 2005 11 08 at the Wayback Machine Indiana University News Room Lorentz symmetry stays intact Physics World Feb 25 2003 Kostelecky V Alan Russell Neil 2011 03 10 Data tables for Lorentz and CPT violation Reviews of Modern Physics 83 1 11 31 arXiv 0801 0287 Bibcode 2011RvMP 83 11K doi 10 1103 revmodphys 83 11 ISSN 0034 6861 S2CID 3236027 External links editBackground information on Lorentz and CPT violation Data Tables for Lorentz and CPT Violation Retrieved from https en wikipedia org w index php title Standard Model Extension amp oldid 1191463434, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.