Note compares quadratic photon dispersion predictions with current astrophysical time-of-flight constraints, suggesting compatibility with gamma-ray data.
Chrono-Grid Dynamics (CGD) predicts a modified photon dispersion relation of quadratic form, E² = p² + ξ p⁴/M_Pl², where the dimensionless coefficient is fixed by the Barbero-Immirzi parameter as ξ = -β/12. Using β ≈ 0.26, one obtains ξ ≈ -0.022. This note compares this prediction with present astrophysical time-of-flight constraints derived from HESS, MAGIC, Fermi-LAT, and the latest LHAASO observations (GRB 221009A and Cygnus X 2.5 PeV). Even the most stringent LHAASO limit (E_QG,2 > 7.6×10¹⁶ GeV) remains four orders of magnitude above the CGD value. Hence CGD is fully compatible with all current gamma-ray timing data. The quadratic suppression inherent to CGD naturally evades the strong constraints on linear Lorentz violation. This work is part of the Chrono-Grid Dynamics (CGD) research program.
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Nebojša Jovanović (2026) studied this question.
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