In the third of this four-part paper we apply the unified, deterministic model of particles and fields based on the postulated existence of soliton-type (metron) solutions of the higher-dimensional gravitational equations, which was summarized in Part 1 and developed in more detail for the Maxwell-Dirac-Einstein system in Part 2, to explain various quantum phenomena. The wave-particle duality paradoxes, which motivated the formulation of quantum theory, are resolved in terms of the deterministic metron picture. The widely held view, based on Bell's theorem for the EPR experiment, that deterministic hidden-variable theories are inherently incapable of explaining microphysical phenomena, is shown to be invalid for the metron model. Essential for Bell's theorem is the existence of an arrow of time, which contradicts the time symmetry of the metron model. Following a general discussion of time symmetry, the metron interpretation of the EPR experiment is presented. The wavelike interference phenomena of microphysics are explained by the periodic (de Broglie) far fields of the metron particles. The appearance of interference patterns in particle scattering distributions is attributed to resonant interactions between the particles and the scattered wavefields. The mechanism is illustrated for Bragg scattering and atomic spectra. In the latter case, the existence of discrete atomic spectra results from the resonant interaction between an eigenmode of the metron Marwell-Dirac system [which is identical to quantum electrodynamics (QED) at the lowest-order tree level] and the orbiting electron. For circular orbits the resonant condition reproduces the Bohr condition. Thus the metron picture of atomic spectra represents an interesting amalgam of QED and the original Bohr orbital theory. The metron formalism for computing radiation-induced or spontaneous transitions between discrete atomic states is shown to be essentially identical to the QED computations at the tree level. It is anticipated, but not demonstrated, that higher-order metron computations will not encounter divergence problems. It remains also to be investigated whether higher-order computations with the metron model will reproduce observed atomic spectra to the same accuracy as QED.
