Minimal-length kinematics of coherent light and a proposed two-color vacuum chronoscopy
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 QFT-natural prescription 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.
Versions
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BibTeX
@misc{wang2026minimallength,
title = {{Minimal-length kinematics of coherent light and a proposed two-color vacuum chronoscopy}},
author = {Zhi-Wei Wang and Saurya Das and Samuel L. Braunstein},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26892},
eprint = {2610.26892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26892},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal-length kinematics of coherent light and a proposed two-color vacuum chronoscopy
AU - Zhi-Wei Wang
AU - Saurya Das
AU - Samuel L. Braunstein
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.26892
UR - https://arxiv.org/abs/2610.26892
AB - 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 QFT-natural prescription 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.
ER -