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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 2, Pages 342–352
DOI: https://doi.org/10.4213/tmf8416 (Mi tmf8416) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Quantum rule for detection probability from Brownian motion in the space of classical fields

A. Yu. Khrennikov, B. Nilsson, S. Nordebo

International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Växjö, Sweden
Full-text PDF (476 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf8416
Abstract: 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.
Received: 27.09.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 2, Pages 298–306
DOI: https://doi.org/10.1007/s11232-013-0027-z
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Yu. Khrennikov, B. Nilsson, S. Nordebo, “Quantum rule for detection probability from Brownian motion in the space of classical fields”, TMF, 174:2 (2013), 342–352; Theoret. and Math. Phys., 174:2 (2013), 298–306
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf8416
  • https://doi.org/10.4213/tmf8416
  • https://www.mathnet.ru/eng/tmf/v174/i2/p342
    • This publication is cited in the following 5 articles:
    1. A. Khrennikov, “Emergence of quantum mechanics from theory of random fields”, J. Russ. Laser Res., 38:1 (2017), 9–26  crossref  isi  scopus
    2. A. Khrennikov, “The present situation in quantum theory and its merging with general relativity”, Found. Phys., 47:8, SI (2017), 1077–1099  crossref  mathscinet  zmath  isi  scopus
    3. Joffrey K. Peters, Jingyun Fan, Alan L. Migdall, Sergey V. Polyakov, “Experimental Bounds on Classical Random Field Theories”, Found Phys, 45:7 (2015), 726  crossref
    4. A. M. Cetto, L. de la Peña, A. Valdés-Hernández, “Specificity of the Schrödinger equation”, Quantum Stud.: Math. Found., 2:3 (2015), 275  crossref
    5. A. Khrennikov, I. Basieva, “Quantum-state dynamics as linear representation of classical (nonlinear) stochastic dynamics”, J. Russ. Laser Res., 35:1 (2014), 71–78  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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