INERTIAL MASS FROM SPIN NONLINEARITY

The inertial mass of a Fermion shows up as chiral cross-coupling in it s Dirac system. No scalar term can invariantly couple left and right c hirality fields; the Dirac matrices must be spin tensors of mixed chir ality. We show how such tensor couplings could arise from nonlinear mi xing of four spinor fields, two representing the local electron fields and two inertial spinor fields sourced in the distant masses. We thus give a model that implements Mach's principle. Following Mendel Sachs ,(1) we let the inertial spinors factor the moving spacetime tetrads q (alpha)(x) and (q) over bar(alpha)(x) that appear in the Dirac operato r. The inertial spinors do more than set the spacetime ''stage;'' they are players in the chiral dynamics. Specifically, we show how the mas sive Dirac system arises as the envelope modulation equations coupling left and right chirality electron fields on a Friedmann universe via nonlinear ''spin gratings'' with the inertial spinor fields. These gra tings implement Penrose's ''mass-scatterings,'' which keep the null zi g-zags of the bispinor wave function confined to a timelike world tube . Local perturbations to the inertial spinor fields appear in the Dira c system as Abelian and non-Abelian vector potentials.