Interaction Dependent Deformation Parameters: Reconciling Generalized Uncertainty Principles with Multi-Messenger Constraints

Purpose: Standard Generalized Uncertainty Principle (GUP) models with a universal deformation parameter () are under increasing tension from precision Gamma-Ray Burst (GRB) and LHAASO observations. This work resolves the tension by introducing an interaction-dependent framework in which the deformation parameter is not a universal property of the vacuum but is determined by the gauge coupling of the propagating species. Methods: I develop the framework on the deformed Heisenberg algebras of Kempf, Mangano, and Mann (quadratic, ) and Ali, Das, and Vagenas (linear-plus-quadratic, ), promoting the algebra’s deformation parameter to a sector-dependent quantity: , . Modified dispersion relations and cosmological time-of-flight delays for photons, neutrinos, and hadrons are derived in both scenarios. The framework is tested against current multi-messenger constraints (GRB 221009A, the Crab Nebula PeVatron, Big Bang Nucleosynthesis, GZK threshold consistency) and macroscopic equivalence-principle bounds (MICROSCOPE), with the soccer-ball / composite-systems problem addressed via the algebraic suppression of Amelino-Camelia (2013) and Bosso (2023) combined with the framework’s gravitational-sector exclusion. Results: The predicted sector hierarchy () naturally satisfies all current observational bounds. The photonic deformation is suppressed (), evading GRB time-of-flight constraints, while the hadronic sector remains of order unity. The framework predicts a unique, species-dependent timing signature with a parameter-free cross-species ratio determined entirely by Standard Model gauge couplings: This ratio is independent of the deformation strength, the source energy, the source redshift, and the choice of . Universal GUP models predict the same ratio to be unity, identically. Conclusion: The framework reopens the parameter space for linear () quantum gravity models, predicts macroscopic delays of order tens of seconds for PeV neutrinos at cosmological distances in the linear scenario, and predicts picosecond-scale delays accessible to stacking analysis in the quadratic scenario. The cross-species ratio provides a falsifiable signature accessible to current and future neutrino observatories, including the planned IceCube-Gen2.