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Time-of-flight fuzziness from deformed relativistic symmetries

Giulia Gubitosi1,2, Pietro Pellecchia1,2, and Alessandro Pinto3

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Phys. Rev. D 114, 086023 – Published 28 October, 2026

DOI: https://doi.org/10.1103/ptdr-6sdg

Abstract

A general expectation in quantum gravity is that quantum properties of spacetime manifest themselves as fuzziness, causing an irreducible uncertainty in the measurement of spacetime-related observables. In this work, we derive the time-of-flight fuzziness for free particles within a noncommutative spacetime model with κ-Poincaré deformed relativistic symmetries. To retain the full quantum structure of the theory we work in the corresponding noncommutative space of worldlines. This provides a convenient framework for constructing quantum states and deriving the probability distributions for the parameters characterizing particle trajectories, allowing us to obtain the probability distribution of particle times of flight. Our results reproduce the well-known systematic time-of-flight correction, leading to energy-dependent departures from the special-relativistic expectation, and simultaneously predict a novel stochastic contribution to the time of flight. The systematic contribution scales with the ratio between the particle energy and the quantum-gravity energy scale, amplified by the propagation distance. The stochastic contribution scales as the square root of the product of the quantum-gravity length scale and the mean travel time, multiplied by a prefactor which depends on the particle velocity.

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References (62)

  1. A. Kempf, G. Mangano, and R. B. Mann, Phys. Rev. D 52, 1108 (1995).
  2. L. J. Garay, Phys. Rev. Lett. 80, 2508 (1998).
  3. A. Kempf, Rep. Math. Phys. 43, 171 (1999).
  4. G. Amelino-Camelia, Phys. Lett. B 510, 255 (2001).
  5. G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002).
  6. J. Kowalski-Glikman and S. Nowak, Phys. Lett. B 539, 126 (2002).
  7. J. Magueijo and L. Smolin, Phys. Rev. Lett. 88, 190403 (2002).
  8. H.-J. Matschull and M. Welling, Classical Quantum Gravity 15, 2981 (1998).
  9. S. Majid, Lect. Notes Phys. 541, 227 (2000).
  10. G. Amelino-Camelia and S. Majid, Int. J. Mod. Phys. A 15, 4301 (2000).
  11. C. Meusburger and B. J. Schroers, Classical Quantum Gravity 20, 2193 (2003).
  12. L. Freidel and E. R. Livine, Phys. Rev. Lett. 96, 221301 (2006).
  13. F. Cianfrani, J. Kowalski-Glikman, D. Pranzetti, and G. Rosati, Phys. Rev. D 94, 084044 (2016).
  14. G. Amelino-Camelia, M. M. Da Silva, M. Ronco, L. Cesarini, and O. M. Lecian, Phys. Rev. D 95, 024028 (2017).
  15. G. Rosati, Phys. Rev. D 96, 066027 (2017).
  16. A. Addazi et al., Prog. Part. Nucl. Phys. 125, 103948 (2022).
  17. G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature (London) 393, 763 (1998).
  18. V. Vasileiou, J. Granot, T. Piran, and G. Amelino-Camelia, Nat. Phys. 11, 344 (2015).
  19. J. Kowalski-Glikman, Lect. Notes Phys. 669, 131 (2005).
  20. G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman, and L. Smolin, Phys. Rev. D 84, 084010 (2011).
  21. L. Barcaroli and G. Gubitosi, Phys. Rev. D 93, 124063 (2016).
  22. G. Amelino-Camelia, L. Barcaroli, G. Gubitosi, and N. Loret, Classical Quantum Gravity 30, 235002 (2013).
  23. G. Amelino-Camelia, N. Loret, and G. Rosati, Phys. Lett. B 700, 150 (2011).
  24. L. Diosi and B. Lukacs, Phys. Lett. A 142, 331 (1989).
  25. G. Amelino-Camelia, Nature (London) 398, 216 (1999).
  26. G. Amelino-Camelia, Phys. Rev. D 62, 024015 (2000).
  27. Y. J. Ng and H. van Dam, Found. Phys. 30, 795 (2000).
  28. W. A. Christiansen, Y. J. Ng, and H. van Dam, Phys. Rev. Lett. 96, 051301 (2006).
  29. G. Amelino-Camelia, Symmetry 17, 1993 (2025).
  30. G. Amelino-Camelia, V. Astuti, and G. Rosati, Phys. Rev. D 87, 084023 (2013).
  31. D. Carney, M. Karydas, and A. Sivaramakrishnan, Phys. Rev. D 113, 106002 (2026).
  32. L. Freidel and R. Oberfrank, arXiv:2601.17849.
  33. S. Doplicher, K. Fredenhagen, and J. E. Roberts, Commun. Math. Phys. 172, 187 (1995).
  34. R. J. Szabo, Phys. Rep. 378, 207 (2003).
  35. S. Majid and H. Ruegg, Phys. Lett. B 334, 348 (1994).
  36. G. Gubitosi, F. Lizzi, J. J. Relancio, and P. Vitale, Phys. Rev. D 105, 126013 (2022).
  37. J. Lukierski, A. Nowicki, H. Ruegg, and V. N. Tolstoi, Phys. Lett. B 264, 331 (1991).
  38. J. Lukierski, A. Nowicki, and H. Ruegg, Phys. Lett. B 293, 344 (1992).
  39. A. Ballesteros, I. Gutierrez-Sagredo, and F. J. Herranz, Phys. Lett. B 792, 175 (2019).
  40. A. Ballesteros, G. Gubitosi, I. Gutierrez-Sagredo, and F. Mercati, J. High Energy Phys. 12 (2021) 080.
  41. G. Amelino-Camelia, M. Arzano, J. Kowalski-Glikman, G. Rosati, and G. Trevisan, Classical Quantum Gravity 29, 075007 (2012).
  42. J. Kowalski-Glikman and S. Nowak, Classical Quantum Gravity 20, 4799 (2003).
  43. G. Amelino-Camelia, V. Astuti, and G. Rosati, Eur. Phys. J. C 73, 2521 (2013).
  44. N. R. Bruno, G. Amelino-Camelia, and J. Kowalski-Glikman, Phys. Lett. B 522, 133 (2001).
  45. G. Gubitosi and F. Mercati, Classical Quantum Gravity 30, 145002 (2013).
  46. S. Mignemi, Phys. Rev. D 68, 065029 (2003).
  47. S. Mignemi, Int. J. Mod. Phys. D 15, 925 (2006).
  48. S. Mignemi and G. Rosati, Mod. Phys. Lett. A 35, 2050180 (2020).
  49. G. Amelino-Camelia, G. Gubitosi, P. Pellecchia, M. Refuto, and G. Rosati, Phys. Rev. D 112, 106006 (2025).
  50. A. Ballesteros, I. Gutierrez-Sagredo, and F. J. Herranz, J. Phys. A 55, 435205 (2022).
  51. F. Lizzi, M. Manfredonia, and F. Mercati, Int. J. Geom. Methods Mod. Phys. 17, 2040010 (2020).
  52. G. Amelino-Camelia, Symmetry 2, 230 (2010).
  53. M. Arzano, G. Gubitosi, and J. J. Relancio, Lect. Notes Phys. 1017, 49 (2023).
  54. E. P. Wigner, Phys. Rev. 40, 749 (1932).
  55. H. Benaroya, S. Han, and M. Nagurka, Probability Models in Engineering and Science, Advanced Topics in Mechanical Engineering Series (Taylor & Francis, London, 2005).
  56. L. Morel, Z. Yao, P. Cladé, and S. Guellati-Khélifa, Nature (London) 588, 61 (2020).
  57. A. Ballesteros, I. Gutierrez-Sagredo, and F. J. Herranz, Phys. Lett. B 829, 137120 (2022).
  58. I. Gutierrez-Sagredo, A. Ballesteros, and F. J. Herranz, J. Phys. Conf. Ser. 2912, 012046 (2024).
  59. F. Lizzi, M. Manfredonia, F. Mercati, and T. Poulain, Phys. Rev. D 99, 085003 (2019).
  60. A. de la Torre and D. Goyeneche, arXiv:1004.2620.
  61. J. Guerrero, F. F. López-Ruiz, V. Aldaya, and F. Cossio, J. Phys. A 44, 445307 (2011).
  62. M. Maamache, A. Khatir, H. Lakehal, and J. R. Choi, Sci. Rep. 6, 30538 (2016).

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Phys. Rev. D 114, 086023– Published 28 October, 2026
  • Received 4 August 2026
  • Accepted 5 October 2026
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