Physical meaning of the de Broglie waves

Commonly regarded as an abstract entity, de Broglie waves represent a real thing making the wave-particle duality an operative factor with a wealth of consequences. Waves as probabilities in Schr\"{o}dinger's quantum mechanics are due to interactive holography that builds up on top of the suggested cellular automaton model of the physical Universe [1]. This model implementing a rule of mutual synchronization produces a set of helicoidal solitons that corresponds exactly to the whole spectrum of elementary particles of matter, no more and no less. The particle-like behavior of the solitons exhibits periodic synchro activities that constitute a wave. The wavelength is inversely proportional to the momentum of these elementary particles, and they distinctly show characteristic qualities of the micro world. The condition of translation-rotation congruity foresees a very small decrease of photons speed with their frequency and polarization, while smoothness of this condition for neutrinos accounts for their already observed faster-than-light propagation. Helicoidal solitons create identical impacts from rotation resulting in the same value of spin for different particles irrespective of variations in mass and speed that are related to translational motion. For any given orientation, spin is either ``up'' or ``down'' since helicoidal solitons are flipping this way with every half-turn. Deep inelastic scattering performs sampling of the wave structure of the helicoidal solitons deceptively portraying the outcomes as isolated quarks. [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' http://www.cs.gwu.edu/research/technical-report/170