Probabilités et fluctuations quantiques (Probabilities and quantum fluctuations)

Michel Fliess 1, 2
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de 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
Contributor : Michel Fliess <>
Submitted on : Sunday, April 15, 2007 - 11:16:26 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:26 PM
Long-term archiving on : Wednesday, April 7, 2010 - 1:58:35 AM

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  • HAL Id : inria-00141719, version 1
  • ARXIV : 0704.2019

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Michel Fliess. Probabilités et fluctuations quantiques (Probabilities and quantum fluctuations). Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2007, 344, pp.663-668. ⟨inria-00141719⟩

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