The wave properties of matter and the zeropoint radiation field

The origin of the wave properties of matter is discussed from the point of view of stochastic electrodynamics. A nonrelativistic model of a changed particle with an effective structure embedded in the random zeropoint radiation field reveals that the field induces a high-frequency vibration on the particle; internal consistency of the theory fixes the frequency of this jittering at mc2/h. The particle is therefore assumed to interact intensely with stationary zeropoint waves of this frequency as seen from its proper frame of reference; such waves, identified here as de Broglie's phase waves, give rise to a modulated wave in the laboratory frame, with de Broglie's wavelength and phase velocity equal to the particle velocity. The time-independent equation that describes this modulated wave is shown to be the stationary Schroedinger equation (or the Klein-Gordon equation in the relativistic version). In a heuristic analysis applied to simple periodic cases, the quantization rules are recovered from the assumption that for a particle in a stationary state there must correspond a stationary modulation. Along an independent and complementary line of reasoning, an equation for the probability amplitude in configuration space for a particle under a general potential V(x) is constructed, and it is shown that under conditions derived from stochastic electrodynamics it reduces to Schroedinger's equation. This equation reflects therefore the dual nature of the quantum particles, by describing simultaneously the corresponding modulated wave and the ensemble of particles