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