Inertial Mass from Spin Nonlinearity
Abstract
The inertial mass of a Fermion shows up as chiral crosscoupling in its Dirac system. No scalar term can invariantly couple left and right chirality fields; the Dirac matrices must be spin tensors of mixed chirality. We show how such tensor couplings could arise from nonlinear mixing 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_{α}(x) and bar {q}_{α }(x) that appear in the Dirac operator. The inertial spinors do more than set the spacetime "stage;" they are players in the chiral dynamics. Specifically, we show how the massive 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 gratings implement Penrose's "massscatterings," which keep the null zigzags of the bispinor wave function confined to a timelike world tube. Local perturbations to the inertial spinor fields appear in the Dirac system as Abelian and nonAbelian vector potentials.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 1998
 DOI:
 10.1142/S0218271898000450
 Bibcode:
 1998IJMPD...7..663C