Geodesic
Quantum rule for detection probability from Brownian motion in the~space of classical fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 342-352

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We obtain Born's rule from the classical theory of random waves in combination with the use of threshold-type detectors. We consider a model of classical random waves interacting with classical detectors and reproducing Born's rule. We do not discuss complicated interpretational problems of quantum foundations. The reader can select between the “weak interpretation”, the classical mathematical simulation of the quantum measurement process, and the “strong interpretation”, the classical wave model of the real quantum (in fact, subquantum) phenomena.
Keywords: foundations of quantum mechanics, Born's rule, detection probability, classical random field, threshold detector. 
@article{TMF_2013_174_2_a13,
     author = {A. Yu. Khrennikov and B. Nilsson and S. Nordebo},
     title = {Quantum rule for detection probability from {Brownian} motion in the~space of classical fields},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {342--352},
     publisher = {mathdoc},
     volume = {174},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a13/}
}
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A. Yu. Khrennikov; B. Nilsson; S. Nordebo. Quantum rule for detection probability from Brownian motion in the~space of classical fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 342-352. http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a13/