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The quantum measurement problem as was formulated by von Neumann in 1933 canbe solved by going beyond the operational quantum formalism. In our "prequantummodel" quantum systems are symbolic representations of classical random fields.The Schr\"odinger's dynamics is a special form of the linear dynamics ofclassical fields. Measurements are described as interactions of classicalfields with detectors. Discontinuity, the "collapse of the wave function", hasthe trivial origin: usage of threshold type detectors. The von Neumannprojection postulate can be interpreted as the formal mathematical encoding ofthe absence of coincidence detection in measurement on a single quantum system,e.g., photon's polarization measurement. Our model, prequantum classicalstatistical field theory (PCSFT), in combination with measurements by thresholddetectors satisfies the quantum restriction on coincidence detections: thesecond order coherence is less than one (opposite to all known semiclassicaland classical feld models). The basic rule of quantum probability, the Born'srule, is derived from properties of prequantum random felds interacting withthreshold type detectors. Comparison with De Broglie's views to quantummechanics as theory of physical waves with singularities is presented.

Measurement problem: from de Broglie to theory of classical random fields interacting with threshold detectors