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Minimum length–maximum velocity

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Abstract

We study a framework where the hypothesis of a minimum length in space-time is complemented with the notion of reference frame invariance. It turns out natural to interpret the action of the obtained reference frame transformations in the context of doubly special relativity. As a consequence of this formalism we find interesting connections between the minimum length properties and the modified velocity-energy relation for ultra-relativistic particles. For example, we can predict the ratio between the minimum lengths in space and time using the results from OPERA on superluminal neutrinos.

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References

  1. L.J. Garay, Int. J. Mod. Phys. A 10, 145–166 (1995). arXiv:gr-qc/9403008

    Article  ADS  Google Scholar 

  2. M. Kato, Phys. Lett. B 245, 43 (1990)

    Article  ADS  Google Scholar 

  3. K. Konishi, G. Paffuti, P. Provero, Phys. Lett. B 234, 276 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  4. A. Ashtekar, C. Rovelli, L. Smolin, Phys. Rev. Lett. 69, 237 (1992). arXiv:hep-th/9203079

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. C. Rovelli, Nucl. Phys. B 405, 797 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. Maggiore, Phys. Lett. B 304, 65 (1993). arXiv:hep-th/9301067

    Article  ADS  Google Scholar 

  7. A. Kempf, G. Mangano, Phys. Rev. D 55, 7909–7920 (1997). arXiv:hep-th/9612084

    Article  ADS  Google Scholar 

  8. G. Piacitelli, SIGMA 6, 073 (2010). arXiv:1004.5261 [math-ph]

    MathSciNet  Google Scholar 

  9. G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35–60 (2002). arXiv:gr-qc/0012051

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. K. Mimasu, S. Moretti, arXiv:1108.3280 [hep-ph]

  11. M. Kober, Phys. Rev. D 82, 085017 (2010). arXiv:1008.0154 [physics.gen-ph]

    Article  ADS  Google Scholar 

  12. S. Hossenfelder, Class. Quantum Gravity 25, 038003 (2008). arXiv:0712.2811 [hep-th]

    Article  MathSciNet  Google Scholar 

  13. S. Hossenfelder, Phys. Rev. D 73, 105013 (2006). arXiv:hep-th/0603032

    Article  ADS  Google Scholar 

  14. A. Kempf, G. Mangano, R.B. Mann, Phys. Rev. D 52, 1108–1118 (1995). arXiv:hep-th/9412167

    Article  MathSciNet  ADS  Google Scholar 

  15. G. Amelino-Camelia, Phys. Lett. B 510, 255–263 (2001). arXiv:hep-th/0012238

    Article  ADS  MATH  Google Scholar 

  16. S. Hossenfelder, Class. Quantum Gravity 23, 1815–1821 (2006). arXiv:hep-th/0510245

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. J. Magueijo, L. Smolin, Phys. Rev. D 67, 044017 (2003). arXiv:gr-qc/0207085

    Article  MathSciNet  ADS  Google Scholar 

  18. J.L. Cortes, J. Gamboa, Phys. Rev. D 71, 065015 (2005). arXiv:hep-th/0405285

    Article  MathSciNet  ADS  Google Scholar 

  19. S. Hossenfelder, Mod. Phys. Lett. A 19, 2727 (2004). arXiv:hep-ph/0410122

    Article  ADS  MATH  Google Scholar 

  20. S. Hossenfelder, M. Bleicher, S. Hofmann, J. Ruppert, S. Scherer, H. Stoecker, Phys. Lett. B 575, 85 (2003). arXiv:hep-th/0305262

    Article  ADS  MATH  Google Scholar 

  21. A.F. Ali, S. Das, E.C. Vagenas, arXiv:1001.2642 [hep-th]

  22. A.F. Ali, Class. Quantum Gravity 28, 065013 (2011). arXiv:1101.4181 [hep-th]

    Article  ADS  Google Scholar 

  23. G. Amelino-Camelia, Symmetry 2, 230 (2010). arXiv:1003.3942 [gr-qc]

    Article  Google Scholar 

  24. J. Magueijo, Rep. Prog. Phys. 66, 2025 (2003). arXiv:astro-ph/0305457

    Article  MathSciNet  ADS  Google Scholar 

  25. S. Judes, M. Visser, Phys. Rev. D 68, 045001 (2003). arXiv:gr-qc/0205067

    Article  MathSciNet  ADS  Google Scholar 

  26. S. Hossenfelder, Phys. Lett. B 649, 310–316 (2007). arXiv:gr-qc/0612167

    Article  MathSciNet  ADS  Google Scholar 

  27. D. Kimberly, J. Magueijo, J. Medeiros, Phys. Rev. D 70, 084007 (2004). arXiv:gr-qc/0303067

    Article  MathSciNet  ADS  Google Scholar 

  28. M. Li, T. Wang, arXiv:1109.5924 [hep-ph]

  29. R. Aloisio, P. Blasi, A. Galante et al., Lect. Notes Phys. 669, 1–30 (2005)

    Article  ADS  Google Scholar 

  30. F.W. Stecker, Astropart. Phys. 35, 95 (2011). arXiv:1102.2784 [astro-ph]

    Article  ADS  Google Scholar 

  31. J. Abraham et al. (Pierre Auger Collaboration), Phys. Rev. Lett. 101, 061101 (2008). arXiv:0806.4302 [astro-ph]

    Article  ADS  Google Scholar 

  32. L. Maccione, A.M. Taylor, D.M. Mattingly, S. Liberati, J. Cosmol. Astropart. Phys. 0904, 022 (2009). arXiv:0902.1756 [astro-ph]

    Article  ADS  Google Scholar 

  33. T. Adam et al. (OPERA Collaboration), arXiv:1109.4897 [hep-ex]

  34. X.-J. Bi, P.-F. Yin, Z.-H. Yu, Q. Yuan, arXiv:1109.6667 [hep-ph]

  35. M.J. Longo, Phys. Rev. D 36, 3276 (1987)

    Article  ADS  Google Scholar 

  36. K. Hirata et al., Phys. Rev. Lett. 58, 1490 (1987)

    Article  ADS  Google Scholar 

  37. R.M. Bionta et al., Phys. Rev. Lett. 58, 1494 (1987)

    Article  ADS  Google Scholar 

  38. P. Adamson et al. (MINOS Collaboration), Phys. Rev. D 76, 072005 (2007). arXiv:0706.0437 [hep-ex]

    Article  ADS  Google Scholar 

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Correspondence to Boris Panes.

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Panes, B. Minimum length–maximum velocity. Eur. Phys. J. C 72, 1930 (2012). https://doi.org/10.1140/epjc/s10052-012-1930-4

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  • DOI: https://doi.org/10.1140/epjc/s10052-012-1930-4

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