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Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond

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Abstract

Recently a new attempt to go beyond quantum mechanics (QM) was presented in the form of so called prequantum classical statistical field theory (PCSFT). Its main experimental prediction is violation of Born’s rule which provides only an approximative description of real probabilities. We expect that it will be possible to design numerous experiments demonstrating violation of Born’s rule. Moreover, recently the first experimental evidence of violation was found in the triple slit interference experiment, see Sinha, et al. (Foundations of Probability and Physics-5. American Institute of Physics, Ser. Conference Proceedings, vol. 1101, pp. 200–207, 2009). Although this experimental test was motivated by another prequantum model, it can be definitely considered as at least preliminary confirmation of the main prediction of PCSFT. In our approach quantum particles are just symbolic representations of “prequantum random fields,” e.g., “electron-field” or “neutron-field”; photon is associated with classical random electromagnetic field. Such prequantum fields fluctuate on time and space scales which are essentially finer than scales of QM, cf. ’t Hooft’s attempt to go beyond QM (see ’t Hooft arXiv:hep-th/0105105, 2001; arXiv:quant-ph/0212095, 2002; arXiv:quant-ph/0701097, 2007). In this paper we elaborate a detection model in the PCSFT-framework. In this model classical random fields (corresponding to “quantum particles”) interact with detectors inducing probabilities which match with Born’s rule only approximately. Thus QM arises from PCSFT as an approximative theory. New tests of violation of Born’s rule are proposed.

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  1. International Center for Mathematical Modelling in Physics and Cognitive Sciences, University of Växjö, 35195, Vaxjo, Sweden

    Andrei Khrennikov

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  1. Andrei Khrennikov
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Khrennikov, A. Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond. Found Phys 39, 997–1022 (2009). https://doi.org/10.1007/s10701-009-9312-y

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