  The connection between the Dirac field as the field of matter and the
spacetime metric is discussed within the framework of classical field theory.
Polarization structure of the Dirac field is shown to be rich enough to
determine the spacetime metric locally and to explain the emergence of observed
matter as localized waveforms. The localization of the waveforms is explained
as the result of the local time slowdown and the Lorentz contraction as a
dynamic re-shaping of the waveforms in the course of their acceleration. A
definition of mass as a limiting curvature of the spinor-induced metric is
proposed. A view of the vacuum as a uniformly distributed unit invariant
density of the Dirac field with an explicitly preserved invariance of the light
cone is brought forward. Qualitative explanation of the observed charge
asymmetry as the consequence of the dynamics of localization is given. The
origin of the CP-violation is associated with the loss of the Poincare
invariance due to localization. Neutrinos are identified with the signals
emitted in the abrupt processes of creation or decay of localized objects and
the concept of the Majorana neutrino is revisited. The wave equation for the
classical pion field is derived from the Dirac equation. Its connection with
stresses, mass and charge fluxes in localized waveforms of the Dirac field is
traced. Some implications of the finite size of colliding objects for
high-energy processes are discussed. A possible difference between the
lifetimes and gyromagnetic ratios for positive and negative charges is
predicted. A hypothesis that known internal degrees of freedom are the local
spacetime (angular) coordinates that have no precise counterparts in Riemannian
geometry is proposed.
