Unification of gravity and the harmonic oscillator on a quantum black hole horizon I: Nonperturbative particle scattering and Veneziano amplitudes

A relativistic quantum model of particle scattering near the horizon of a microscopic black hole unifies gravity and the harmonic-oscillator force. The model is obtained by modifying a harmonic-oscillator nonstandard Lagrangian for a closed system of relativistic quarks to eliminate any cosmic background frame. Formulated in terms of the Planck units, the model has only one parameter, the cosmic number N2. Other results include (1) quark confinement through cluster decomposition rather than a binding potential, (2) lepton substructure without violation of known experimental results, (3) a spontaneously broken symmetry between leptons and hadrons with leptons behaving as free particles and hadrons which scatter with Veneziano-type amplitudes, (5) realistic particle masses and sizes, and (6) a solution of a cosmic-number problem in cosmology.