Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 074, 8 pages      arXiv:1403.2080      https://doi.org/10.3842/SIGMA.2014.074
Contribution to the Special Issue on Deformations of Space-Time and its Symmetries

The Soccer-Ball Problem

Sabine Hossenfelder
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden

Received March 11, 2014, in final form July 03, 2014; Published online July 09, 2014; Text overlap with [24] removed July 29, 2014

Abstract
The idea that Lorentz-symmetry in momentum space could be modified but still remain observer-independent has received quite some attention in the recent years. This modified Lorentz-symmetry, which has been argued to arise in Loop Quantum Gravity, is being used as a phenomenological model to test possibly observable effects of quantum gravity. The most pressing problem in these models is the treatment of multi-particle states, known as the 'soccer-ball problem'. This article briefly reviews the problem and the status of existing solution attempts.

Key words: Lorentz-invariance; quantum gravity; quantum gravity phenomenology; deformed special relativity.

pdf (296 kb)   tex (19 kb)       [previous version:  pdf (301 kb)   tex (20 kb)]

References

  1. Ali A.F., Minimal length in quantum gravity, equivalence principle and holographic entropy bound, Classical Quantum Gravity 28 (2011), 065013, 10 pages, arXiv:1101.4181.
  2. Amelino-Camelia G., Testable scenario for relativity with minimum length, Phys. Lett. B 510 (2001), 255-263, hep-th/0012238.
  3. Amelino-Camelia G., Doubly special relativity, Nature 418 (2002), 34-35, gr-qc/0207049.
  4. Amelino-Camelia G., Doubly-special relativity: first results and key open problems, Internat. J. Modern Phys. D 11 (2002), 1643-1669, gr-qc/0210063.
  5. Amelino-Camelia G., On the fate of Lorentz symmetry in relative-locality momentum spaces, Phys. Rev. D 85 (2012), 084034, 16 pages, arXiv:1110.5081.
  6. Amelino-Camelia G., Freidel L., Kowalski-Glikman J., Smolin L., The principle of relative locality, Phys. Rev. D 84 (2011), 084010, 13 pages, arXiv:1101.0931.
  7. Amelino-Camelia G., Freidel L., Kowalski-Glikman J., Smolin L., Relative locality and the soccer ball problem, Phys. Rev. D 84 (2011), 087702, 5 pages, arXiv:1104.2019.
  8. Amelino-Camelia G., Freidel L., Kowalski-Glikman J., Smolin L., Reply to ''Comment on 'Relative locality and the soccer ball problem''', Phys. Rev. D 88 (2013), 028702, 5 pages, arXiv:1307.0246.
  9. Amelino-Camelia G., Matassa M., Mercati F., Rosati G., Taming nonlocality in theories with Planck-scale deformed Lorentz symmetry, Phys. Rev. Lett. 106 (2011), 071301, 4 pages, arXiv:1006.2126.
  10. Calmet X., Hossenfelder S., Percacci R., Deformed special relativity from asymptotically safe gravity, Phys. Rev. D 82 (2010), 124024, 7 pages, arXiv:1008.3345.
  11. Carmona J.M., Cortés J.L., Mazón D., Mercati F., About locality and the relativity principle beyond special relativity, Phys. Rev. D 84 (2011), 085010, 9 pages, arXiv:1107.0939.
  12. Chandra N., Chatterjee S., Thermodynamics of ideal gas in doubly special relativity, Phys. Rev. D 85 (2012), 045012, 9 pages, arXiv:1108.0896.
  13. Chang L.N., Minic D., Okamura N., Takeuchi T., Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations, Phys. Rev. D 65 (2002), 125027, 8 pages, hep-th/0201017.
  14. Das S., Ghosh S., Roychowdhury D., Relativistic thermodynamics with an invariant energy scale, Phys. Rev. D 80 (2009), 125036, 8 pages, arXiv:0908.0413.
  15. Fityo T.V., Statistical physics in deformed spaces with minimal length, Phys. Lett. A 372 (2008), 5872-5877, arXiv:0712.0891.
  16. Girelli F., Livine E.R., Physics of deformed special relativity: relativity principle revisited, gr-qc/0412004.
  17. Hossenfelder S., A note on theories with a minimal length, Classical Quantum Gravity 23 (2006), 1815-1821, hep-th/0510245.
  18. Hossenfelder S., Interpretation of quantum field theories with a minimal length scale, Phys. Rev. D 73 (2006), 105013, 9 pages, hep-th/0603032.
  19. Hossenfelder S., Deformed special relativity in position space, Phys. Lett. B 649 (2007), 310-316, gr-qc/0612167.
  20. Hossenfelder S., Multiparticle states in deformed special relativity, Phys. Rev. D 75 (2007), 105005, 8 pages, hep-th/0702016.
  21. Hossenfelder S., The box-problem in deformed special relativity, arXiv:0912.0090.
  22. Hossenfelder S., Bounds on an energy-dependent and observer-independent speed of light from violations of locality, Phys. Rev. Lett. 104 (2010), 140402, 4 pages, arXiv:1004.0418.
  23. Hossenfelder S., Comment on ''Relative locality and the soccer ball problem'', Phys. Rev. D 88 (2013), 028701, 2 pages, arXiv:1202.4066.
  24. Hossenfelder S., Minimal length scale scenarios for quantum gravity, Living Rev. Relativity 16 (2013), 2, 90 pages, arXiv:1203.6191.
  25. Jacob U., Mercati F., Amelino-Camelia G., T. P., Modifications to Lorentz invariant dispersion in relatively boosted frames, Phys. Rev. D 82 (2010), 084021, 11 pages, arXiv:1004.0575.
  26. Judes S., Visser M., Conservation laws in ''doubly special relativity'', Phys. Rev. D 68 (2003), 045001, 4 pages, gr-qc/0205067.
  27. Kalyana Rama S., Some consequences of the generalized uncertainty principle: statistical mechanical, cosmological, and varying speed of light, Phys. Lett. B 519 (2001), 103-110, hep-th/0107255.
  28. Kostelecký V.A., Russell N., Data tables for Lorentz and CPT violation, Rev. Modern Phys. 83 (2011), 11, 21 pages, arXiv:0801.0287.
  29. Kowalski-Glikman J., Observer-independent quantum of mass, Phys. Lett. A 286 (2001), 391-394, hep-th/0102098.
  30. Kowalski-Glikman J., Doubly special quantum and statistical mechanics from quantum $\kappa$-Poincaré algebra, Phys. Lett. A 299 (2002), 454-460, hep-th/0111110.
  31. Kowalski-Glikman J., Introduction to doubly special relativity, in Planck Scale Effects in Astrophysics and Cosmology, Lecture Notes in Phys., Vol. 669, Editors G. Amelino-Camelia, J. Kowalski-Glikman, Springer, Berlin - New York, 2005, 131-159, hep-th/0405273.
  32. Kowalski-Glikman J., Nowak S., Doubly special relativity and de Sitter space, Classical Quantum Gravity 20 (2003), 4799-4816, hep-th/0304101.
  33. Liberati S., Sonego S., Visser M., Interpreting doubly special relativity as a modified theory of measurement, Phys. Rev. D 71 (2005), 045001, 9 pages, gr-qc/0410113.
  34. Magueijo J., Could quantum gravity be tested with high intensity lasers?, Phys. Rev. D 73 (2006), 124020, 11 pages, gr-qc/0603073.
  35. Magueijo J., Smolin L., Lorentz invariance with an invariant energy scale, Phys. Rev. Lett. 88 (2002), 190403, 4 pages, hep-th/0112090.
  36. Magueijo J., Smolin L., Generalized Lorentz invariance with an invariant energy scale, Phys. Rev. D 67 (2003), 044017, 12 pages, gr-qc/0207085.
  37. Nozari K., Fazlpour B., Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics, Gen. Relativity Gravitation 38 (2006), 1661-1679, gr-qc/0601092.
  38. Olmo G.J., Palatini actions and quantum gravity phenomenology, J. Cosmol. Astropart. Phys. 2011 (2011), no. 10, 018, 15 pages, arXiv:1101.2841.
  39. Pedram P., New approach to nonperturbative quantum mechanics with minimal length uncertainty, Phys. Rev. D 85 (2012), 024016, 12 pages, arXiv:1112.2327.
  40. Percacci R., Vacca G.P., Asymptotic safety, emergence and minimal length, Classical Quantum Gravity 27 (2010), 245026, 16 pages, arXiv:1008.3621.
  41. Pikovski I., Vanner M.R., Aspelmeyer M., Kim M.S., Brukner Č., Probing Planck-scale physics with quantum optics, Nature Phys. 8 (2012), 393-397, arXiv:1111.1979.
  42. Quesne C., Tkachuk V.M., Composite system in deformed space with minimal length, Phys. Rev. A 81 (2010), 012106, 8 pages, arXiv:0906.0050.
  43. Schützhold R., Unruh W.G., Large-scale nonlocality in ''doubly special relativity'' with an energy-dependent speed of light, JETP Lett. 78 (2003), 431-435, gr-qc/0308049.
  44. Smolin L., On limitations of the extent of inertial frames in non-commutative spacetimes, arXiv:1007.0718.
  45. Smolin L., Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity, Gen. Relativity Gravitation 43 (2011), 3671-3691, arXiv:1004.0664.
  46. Wang P., Yang H., Zhang X., Quantum gravity effects on compact star cores, Phys. Lett. B 718 (2012), 265-269, arXiv:1110.5550.
  47. Zhang X., Shao L., Ma B.-Q., Photon gas thermodynamics in doubly special relativity, Astropart. Phys. 34 (2011), 840-845, arXiv:1102.2613.

Previous article  Next article   Contents of Volume 10 (2014)