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Lorentz invariance violation and generalized uncertainty principle

  • Physics of Elementary Particles and Atomic Nuclei. Theory
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Abstract

There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The generalized uncertainty principle (GUP) is based on a momentum-dependent modification in the standard dispersion relation which is conjectured to violate the principle of Lorentz invariance. From the resulting Hamiltonian, the velocity and time of flight of relativistic distant particles at Planck energy can be derived. A first comparison is made with recent observations for Hubble parameter in redshift-dependence in early-type galaxies. We find that LIV has two types of contributions to the time of flight delay Δt comparable with that observations. Although the wrong OPERA measurement on faster-than-light muon neutrino anomaly, Δt, and the relative change in the speed of muon neutrino Δv in dependence on redshift z turn to be wrong, we utilize its main features to estimate Δv. Accordingly, the results could not be interpreted as LIV. A third comparison is made with the ultra high-energy cosmic rays (UHECR). It is found that an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly spacial relativity and the one assuming a perturbative departure from exact Lorentz invariance. Fixing the sensitivity factor and its energy dependence are essential inputs for a reliable confronting of our calculations to UHECR. The sensitivity factor is related to the special time of flight delay and the time structure of the signal. Furthermore, the upper and lower bounds to the parameter, a that characterizes the generalized uncertainly principle, have to be fixed in related physical systems such as the gamma rays bursts.

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References

  1. L. J. Garay, “Quantum gravity and minimum length,” Int. J. Mod. Phys. A 10, 145–166 (1995); arXiv:gr-qc/9403008.

    Article  ADS  Google Scholar 

  2. C. Kiefer, Compend. Quantum Phys., 565–572 (2009).

    Book  Google Scholar 

  3. C. J. Isham, Lect. Notes Phys. 434, 1–21 (1994).

    Article  MathSciNet  ADS  Google Scholar 

  4. M. Maggiore, “Quantum groups, gravity and the generalized uncertainty principle,” Phys. Rev. D 49, 5182 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Kempf, Report on Symposium at the 21st International Colloquium on Group Theoretical Methods in Physics ICGTMP’96, Goslar, Germany, 1996

    Google Scholar 

  6. C. Bambi, “A revision of the generalized uncertainty principle,” Class. Quant. Grav. 25, 105003 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  7. R. J. Adler, “Six easy roads to the Planck scale,” Am. J. Phys. 78, 925 (2010)

    Article  ADS  Google Scholar 

  8. K. Nozari, P. Pedram, and M. Molkara, “Minimal length, maximal momentum and the entropic force law,” Int. J. Theor. Phys. 51, 1268 (2012).

    Article  MATH  Google Scholar 

  9. D. Amati, M. Ciafaloni, and G. Veneziano, “Classical and quantum gravity effects from planckian energy superstring collisions,” Int. J. Mod. Phys. A 3, 1615 (1988); “Superstring collisions at planckian energies,” Phys. Lett. B 197, 81 (1987); “Higher order gravitational deflection and soft bremsstrahlung in planckian energy superstring collisions,” Nucl. Phys. B 347, 550 (1990).

    Article  ADS  Google Scholar 

  10. A. Farag Ali, S. Das, and E. C. Vagenas, “Discreteness of space from the generalized uncertainty principle,” Phys. Lett. B 678, 497–499 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  11. S. Das, E. C. Vagenas, and A. Farag Ali, “Discreteness of space from GUP II: relativistic wave equations,” Phys. Lett. B 690, 407–412 (2010); Phys. Lett. B 692, 342(E) (2010).

    Article  ADS  Google Scholar 

  12. A. Farag Ali, S. Das, and E. C. Vagenas, “A proposal for testing quantum gravity in the lab,” Phys. Rev. D: Part. Fields 84, 044013 (2011).

    Article  ADS  Google Scholar 

  13. H. Sato and T. Tati, “Hot Universe, cosmic rays of ultrahigh energy and absolute reference system,” Prog. Theor. Phys. 47, 1788 (1972).

    Article  ADS  Google Scholar 

  14. S. Coleman and S. L. Glashow, “High-energy tests of Lorentz invariance,” Phys. Rev. D: Part. Fields 59, 116008 (1999).

    Article  ADS  Google Scholar 

  15. F. W. Stecker and S. L. Glashow, “New tests of Lorentz invariance following from observations of the highest energy cosmic gamma-rays,” Astropart. Phys. 16, 97–99 (2001).

    Article  ADS  Google Scholar 

  16. E. J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and A. S. Sakharov, “Quantum-gravity analysis of gammaray bursts using wavelets,” Astron. Astrophys. 402, 409 (2003)

    Article  MATH  ADS  Google Scholar 

  17. S. E. Boggs, C. B. Wunderer, K. Hurley, and W. Coburn, “Testing Lorentz non-invariance with GRB021206,” Astrophys. J. 611, L77–L80 (2004).

    Article  ADS  Google Scholar 

  18. S. Liberati and L. Maccione, “Lorentz violation: motivation and new constraints,” Ann. Rev. Nucl. Part. Sci. 59, 245–267 (2009); arXiv:0906.0681 [astro-ph.HE].

    Article  ADS  Google Scholar 

  19. I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and C. Brukner, “Probing planck-scale physics with quantum optics,” Nature Phys. 8, 393–397 (2012).

    Article  ADS  Google Scholar 

  20. S. Hossenfelder, “Minimal length scale scenarios for quantum gravity,” Living Rev. Rel. 16, 2 (2013); arXiv:1203.6191 [gr-qc].

    Google Scholar 

  21. A. Tawfik and A. Diab, “Generalized uncertainty principle: approaches and applications,” Int. J. Mod. Phys. D 23, 1430025 (2014); arXiv:1410.0206 [gr-qc].

    Article  MathSciNet  ADS  Google Scholar 

  22. S. Das and E. C. Vagenas, “Universality of quantum gravity corrections,” Phys. Rev. Lett. 101, 221301 (2008); arXiv:0810.5333[hep-th].

    Article  ADS  Google Scholar 

  23. A. F. Ali, S. Das, and E. C. Vagenas, “The generalized uncertainty principle and quantum gravity phenomenology,” arXiv:1001.2642 [hep-th].

  24. S. Das and E. C. Vagenas, “Phenomenological implications of the generalized uncertainty principle,” Can. J. Phys. 87, 233 (2009); arXiv:0901.1768 [hep-th].

    Article  ADS  Google Scholar 

  25. I. Elmashad, A. F. Ali, L. I. Abou-Salem, J.-U. Nabi, and A. Tawfik, “Quantum gravity effect on the quarkgluon plasma,” SOP Trans. Theor. Phys. 1, 1–6 (2014); arXiv:1208.4028 [hep-ph].

    Google Scholar 

  26. W. Chemissany, S. Das, A. F. Ali, and E. C. Vagenas, “Effect of the generalized uncertainty principle on post-inflation preheating,” J. Cosmos. Astrophys. Part. 1112, 017 (2011); arXiv:1111.7288 [hep-th].

    Article  ADS  Google Scholar 

  27. A. Tawfik, H. Magdy, and A. F. Ali, “Effects of quantum gravity on the inflationary parameters and thermodynamics of the early Universe,” Gen. Rel. Grav. 45, 1227–1246 (2013); arXiv:1208/5655 [gr-qc].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. A. F. Ali, “No existence of black holes at LHC due to minimal length in quantum gravity,” J. High Energy Phys. 1209, 067 (2012); arXiv:1208/6584 [hep-th].

    Article  ADS  Google Scholar 

  29. A. Tawfik, “Impacts of generalized uncertainty principle on black hole thermodynamics and SaleckerWigner inequalities,” J. Cosmos. Astrophys. Part. 1307, 040 (2013); arXiv:1307.1894 [gr-qc].

    Article  ADS  Google Scholar 

  30. A. Farag Ali and A. N. Tawfik, “Impacts of generalized uncertainty principle on black hole thermodynamics and Salecker-Wigner inequalities,” Int. J. Mod. Phys. D 22, 1350020 (2013); arXiv:1301.6133 [gr-qc].

    Google Scholar 

  31. A. Farag Ali and A. Tawfik, “Modified Newton’s law of gravitation due to minimal length in quantum gravity,” Adv. High Energy Phys. 2013, 126528 (2013); arXiv:1301.3508 [gr-qc].

    MathSciNet  Google Scholar 

  32. G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, “Tests of quantum gravity from observations of gamma-ray bursts,” Nature 393, 763–765 (1998).

    Article  ADS  Google Scholar 

  33. A. Tawfik, T. Harko, H. Mansour, and M. Wahba, “Dissipative processes in the early Universe: bulk viscosity,” Uzb. J. Phys. 12, 316–321 (2010).

    Google Scholar 

  34. A. Tawfik, in Proceeding of the 12th Marcel Grossmann Meeting on General Relativity, Paris, France, 2009.

  35. A. Tawfik, M. Wahba, H. Mansour, and T. Harko, “Viscous quark-gluon plasma in the early Universe,” Ann. Phys. (N.Y.) 523, 194–207 (2011).

    Article  ADS  Google Scholar 

  36. A. Tawfik, “Thermodynamics in the viscous early Universe,” Can. J. Phys. 88, 825–831 (2010).

    Article  ADS  Google Scholar 

  37. A. Tawfik, M. Wahba, H. Mansour, and T. Harko, “Hubble parameter in QCD Universe for finite bulk viscosity,” Ann. Phys. 522, 912–923 (2010).

    Article  Google Scholar 

  38. A. Tawfik, “The Hubble parameter in the early Universe with viscous QCD Matter and finite cosmological constant,” Ann. Phys. 523, 423–434 (2011).

    Article  Google Scholar 

  39. A. Tawfik and T. Harko, “Quark-hadron phase transitions in viscous early Universe,” Phys. Rev. D: Part. Fields 85, 084032 (2012).

    Article  ADS  Google Scholar 

  40. A. Tawfik and H. Magdy, “Thermodynamics of viscous matter and radiation in the early Universe,” Can. J. Phys. 90, 433–440 (2012).

    Article  ADS  Google Scholar 

  41. L. Samushia and B. Ratra, “Cosmological constraints from Hubble parameter versus redshift data,” Astrophys. J. 650, L5–L8 (2006).

    Article  ADS  Google Scholar 

  42. M. Moresco, A. Cimatti, R. Jimenez, L. Pozzetti, G. Zamorani, M. Bolzonella, J. Dunlop, F. Lamareille, M. Mignoli, H. Pearce, et al., “Improved constraints on the expansion rate of the Universe up to z 1.1 from the spectroscopic evolution of cosmic chronometers,” J. Cosmol. Astropart. Phys. 1208, 006 (2012).

    Article  ADS  Google Scholar 

  43. M. Moresco, L. Verde, L. Pozzetti, R. Jimenez, and A. Cimatti, “New constraints on cosmological parameters and neutrino properties using the expansion rate of the Universe to z 1.75,” J. Cosmol. Astropart. Phys. 1207, 053 (2012).

    Article  ADS  Google Scholar 

  44. R. Jimenez and A. Loeb, “Constraining cosmological parameters based on relative galaxy ages,” Astrophys. J. 573, 37 (2002).

    Article  ADS  Google Scholar 

  45. G. Bruzual and S. Charlot, “Stellar population synthesis at the resolution of 2003,” Mon. Not. R. Astron. Soc. 344, 1000 (2003).

    Article  ADS  Google Scholar 

  46. C. Maraston and G. Stromback, “Stellar population models at high spectral resolution,” Mon. Not. R. Astron. Soc. 418, 2785 (2011); arXiv:1109/0543 [astroph.CO].

    Article  ADS  Google Scholar 

  47. T. Adam et al., “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam,” J. High Energy Phys. 1210, 093 (2012).

    Article  ADS  Google Scholar 

  48. T. Adam et al. (Opera Collab.), “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data,” J. High Energy Phys. 1301, 153 (2013).

    Article  ADS  Google Scholar 

  49. P. Adamson et al. (MINOS Collab.), “Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam,” Phys. Rev. D: Part. Fields 76, 072005 (2007).

    Article  ADS  Google Scholar 

  50. K. Hirata et al. (KAMIOKANDE-II Collab.), “Observation of a neutrino burst from the supernova SN 1987a,” Phys. Rev. Lett. 58, 1490–1493 (1987)

    Article  ADS  Google Scholar 

  51. R. Bionta, G. Blewitt, C. Bratton, D. Casper, A. Ciocio, et al., “Observation of a neutrino burst in coincidence with supernova SN 1987a in the Large Magellanic Cloud,” Phys. Rev. Lett. 58, 1494 (1987)

    Article  ADS  Google Scholar 

  52. M. J. Longo, “Tests of relativity from SN1987a,” Phys. Rev. D: Part. Fields 36, 3276 (1987).

    Article  ADS  Google Scholar 

  53. G. Barenboim, O. M. Requejo, and Ch. Quigg, “Diagnostic potential of cosmic-neutrino absorption spectroscopy,” Phys. Rev. D: Part. Fields 71, 083002 (2005).

    Article  ADS  Google Scholar 

  54. A. Kusenko and M. Postma, “Neutrinos produced by ultrahigh-energy photons at high red shift,” Phys. Rev. Lett. 86, 1430–1433 (2001).

    Article  ADS  Google Scholar 

  55. D. Majumdar, “Probing pseudo-Dirac neutrino through detection of neutrino induced muons from GRB neutrinos,” Pramana 70, 51–60 (2008).

    Article  ADS  Google Scholar 

  56. J. Nishimura, M. Fujii, T. Taira, E. Aizu, H. Hiraiwa, T. Kobayashi, K. Niu, I. Ohta, R. L. Golden, T. A. Koss, J. J. Lord, and R. J. Wilkes, “Emulsion chamber observations of primary cosmic ray electrons in the energy range 30 GeV–1000 GeV,” Astrophys. J. 238, 394 (1980).

    Article  ADS  Google Scholar 

  57. T. Tanimori et al. (CANGAROO Collab.), “Detection of gamma-rays up to 50 TeV from the Crab Nebula,” Astrophys. J. 492, L33 (1998).

    Article  ADS  Google Scholar 

  58. K. Hurley, B. L. Dingus, R. Mukherjee, P. Sreekumar, C. Kouveliotou, C. Meegan, G. J. Fishman, D. Band, L. Ford, D. Bertsch, T. Cline, C. Fichtel, R. Hartman, S. Hunter, D. J. Thompson, et al., “Detection of a gamma-ray burst of very long duration and very high energy,” Nature 372, 652–654 (1994).

    Article  ADS  Google Scholar 

  59. G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, “Distance measurement and wave dispersion in a Liouville string approach to quantum gravity,” Int. J. Mod. Phys. A 12, 607–623 (1997).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  60. A. Tawfik, “Orders of Fermiand plasma-accelerations of cosmic rays,” SOP Trans. Theor. Phys. 1, 7–9 (2014); arXiv:1010/5390 [astro-ph.HE].

    Article  Google Scholar 

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Authors and Affiliations

  1. Egyptian Center for Theoretical Physics (ECTP), Modern University for Technology and Information (MTI), 11571, Cairo, Egypt

    Abdel Nasser Tawfik & H. Magdy

  2. World Laboratory for Cosmology and Particle Physics (WLCAPP), 11571, Cairo, Egypt

    Abdel Nasser Tawfik

  3. Physics Department, Faculty of Science, Benha University, Benha, 13518, Egypt

    A. Farag Ali

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  1. Abdel Nasser Tawfik
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  2. H. Magdy
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  3. A. Farag Ali
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Correspondence to Abdel Nasser Tawfik.

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Tawfik, A.N., Magdy, H. & Ali, A.F. Lorentz invariance violation and generalized uncertainty principle. Phys. Part. Nuclei Lett. 13, 59–68 (2016). https://doi.org/10.1134/S1547477116010179

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