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Smooth finitely computable functions are affine, or why quantum systems cause waves

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Abstract

Abstract—It is shown that the class of all C 2-smooth real functions that can be computed (in a new, but natural sense precisely defined below) on Mealy machines (letter-to-letter transducers or, briefly, transducers) consists of affine functions only. Moreover, it turns out that all these functions can be naturally associated with wave functions of particles. Accordingly, this work can be regarded as a mathematical reasoning that the wave properties of quantum systems are caused by the discreteness of matter and causality, since transducers are a mathematical formalization of the law of causality.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    V. S. Anashin

  2. Federal Research Center “Computer Science and Control,”, Russian Academy of Sciences, Moscow, Russia

    V. S. Anashin

Authors
  1. V. S. Anashin
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Correspondence to V. S. Anashin.

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Original Russian Text © V.S. Anashin, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 1, pp. 11–13.

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Anashin, V.S. Smooth finitely computable functions are affine, or why quantum systems cause waves. Dokl. Math. 92, 655–657 (2015). https://doi.org/10.1134/S1064562415060022

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  • DOI: https://doi.org/10.1134/S1064562415060022

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