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

TL;DR

This paper proposes a classical random field-based model to explain quantum measurement phenomena, deriving quantum probabilities and wave function collapse from classical interactions with threshold detectors, offering a new perspective on the measurement problem.

Contribution

It introduces the prequantum classical statistical field theory (PCSFT) that models quantum systems as classical fields interacting with detectors, explaining quantum effects without traditional quantum formalism.

Findings

PCSFT reproduces quantum measurement statistics.

Threshold detectors explain wave function collapse.

The model derives Born's rule from classical field properties.

Abstract

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