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

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 Schrödinger's dynamics is a special form of...

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Bibliographic Details
Published in:Journal of physics. Conference series 2013-01, Vol.442 (1), p.12011-13
Main Author: Khrennikov, Andrei
Format: Article
Language:English
Subjects:
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Detectors
Dynamics
Field theory
Fields (mathematics)
Matematik
Mathematical models
Mathematics
Physics
Quantum mechanics
Quantum theory
Schroedinger equation
Sensors
Statistical analysis
Threshold detectors (dosimeters)
Thresholds
Wave functions
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Summary: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 Schrödinger'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.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/442/1/012011