Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Minimal-length kinematics of coherent light and a proposed two-color vacuum chronoscopy

Zhi-Wei Wang1,2,3,*, Saurya Das1,4,†, and Samuel L. Braunstein3,‡

  • *Contact author: zhiweiwang.phy@gmail.com
  • †Contact author: saurya.das@uleth.ca
  • ‡Contact author: sam.braunstein@york.ac.uk

Phys. Rev. D 114, 095011 – Published 5 November, 2026

DOI: https://doi.org/10.1103/qb5g-7khs

Abstract

The unification of quantum theory and general relativity suggests the existence of a minimal measurable length, leading to a generalized uncertainty principle (GUP) and an energy-dependent vacuum group velocity. Testing these effects with macroscopic objects typically encounters the “soccer-ball problem,” where applying Planck-scale deformations to the total momentum predicts observationally ruled-out velocity deviations. We adopt the prescription, natural in quantum field theory, in which the GUP modifies single-mode commutators, and verify by explicit calculation that the macroscopic group velocity of a multimode coherent pulse reduces to the single-photon GUP velocity evaluated at the central wavelength, multiplied by the classical Gaussian-beam factor, with no dependence on the total pulse energy. The energy–momentum relation E=pc itself is unmodified; the deformation enters through the velocity–momentum relation and is equivalent to a modified dispersion relation in the wave vector, with a quadratic coefficient that depends on which of the two variables is used. The soccer-ball problem—which arises only when the GUP is applied to the center-of-mass momentum of a composite system—is therefore absent for coherent light, and macroscopic petawatt pulses probe the same parameter space as single high-energy photons. Building on this framework, we propose a two-color vacuum chronoscopy experiment using a short-pulse petawatt laser and its high-harmonic generation. By systematically varying the macroscopic beam waist, our setup separates Planck-scale kinematic shifts from classical diffraction delays, establishing a controlled, source-independent terrestrial methodology whose sensitivity we assess against current astrophysical bounds and against the dominant waist-independent systematics that limit it, residual-gas dispersion and the harmonic birth-time offset.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (23)

  1. D. J. Gross and P. F. Mende, Nucl. Phys. B303, 407 (1988).
  2. D. Amati, M. Ciafaloni, and G. Veneziano, Phys. Lett. B 216, 41 (1989).
  3. M. Maggiore, Phys. Lett. B 304, 65 (1993).
  4. L. J. Garay, Int. J. Mod. Phys. A 10, 145 (1995).
  5. A. Kempf, G. Mangano, and R. B. Mann, Phys. Rev. D 52, 1108 (1995).
  6. G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002).
  7. F. Scardigli, Phys. Lett. B 452, 39 (1999).
  8. S. Hossenfelder, Living Rev. Relativity 16, 2 (2013).
  9. A. F. Ali, S. Das, and E. C. Vagenas, Phys. Rev. D 84, 044013 (2011).
  10. I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and Č. Brukner, Nat. Phys. 8, 393 (2012).
  11. S. Das, M. Fridman, G. Lambiase, and E. C. Vagenas, Phys. Lett. B 824, 136841 (2022).
  12. S. Das and S. K. Modak, Eur. Phys. J. Plus 138, 366 (2023).
  13. G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature (London) 393, 763 (1998).
  14. A. A. Abdo et al., Nature (London) 462, 331 (2009).
  15. V. Vasileiou, A. Jacholkowska, F. Piron, J. Bolmont, C. Couturier, J. Granot, F. W. Stecker, J. Cohen-Tanugi, and F. Longo, Phys. Rev. D 87, 122001 (2013).
  16. S. Hossenfelder, SIGMA 10, 074 (2014).
  17. M. V. Fedorov and S. V. Vintskevich, Laser Phys. 27, 036202 (2017).
  18. A. F. Ali, S. Das, and E. C. Vagenas, Phys. Lett. B 678, 497 (2009).
  19. Z. Cao et al. (LHAASO Collaboration), Phys. Rev. Lett. 133, 071501 (2024).
  20. Y.-M. Yang, X.-J. Bi, and P.-F. Yin, J. Cosmol. Astropart. Phys. 04 (2024) 060.
  21. L. B. Okun, Sov. Phys. Usp. 32, 629 (1989).
  22. P. Bosso and S. Das, Int. J. Mod. Phys. D 28, 1950068 (2019).
  23. S. Grundmann et al., Science 370, 339 (2020).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation