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Probabilités et fluctuations quantiques

Michel Fliess 1, 2
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Centrale Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty principle, i.e., of the quantum fluctuations, which was brought to the forefront in some fractal approaches. It results, as in Nelson's stochastic mechanics, in stochastic differential equations which are deduced from infinitesimal random walks. An extended english abstract gives most of the details.
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https://hal.inria.fr/inria-00141719
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Submitted on : Sunday, April 15, 2007 - 11:16:26 PM
Last modification on : Friday, February 4, 2022 - 3:16:39 AM
Long-term archiving on: : Wednesday, April 7, 2010 - 1:58:35 AM

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Michel Fliess. Probabilités et fluctuations quantiques. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2007, 344 (10), pp.663-668. ⟨10.1016/j.crma.2007.04.001⟩. ⟨inria-00141719⟩

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