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Applied Mathematics and Mechanics

, Volume 40, Issue 12, pp 1805–1830 | Cite as

Deformable micro-continua in which quantum mysteries reside

  • Heng XiaoEmail author
Article
  • 28 Downloads

Abstract

Deformable micro-continua of highly localized nature are found to exactly exhibit all quantum effects commonly known for quantum entities at microscopic scale. At every instant, the spatial configuration of each such micro-continuum is prescribed by four spatial distributions of the mass, the velocity, the internal stress, and the intrinsic angular momentum. The deformability features of such micro-continua in response to all configuration changes are identified with a constitutive equation that specifies how the internal stress responds to the mass density field. It is shown that these microcontinua are endowed with the following unique response features: (i) the coupled system of the nonlinear field equations governing their dynamic responses to any given force and torque fields is exactly reducible to a linear dynamic equation governing a complex field variable; (ii) this fundamental dynamic equation and this complex field variable are just the Schrödinger equation and the complex wave function in quantum theory; and, accordingly, (iii) the latter two and all quantum effects known for quantum entities are in a natural and unified manner incorporated as the inherent response features of the micro-continua discovered, thus following objective and deterministic response patterns for quantum entities, in which the physical origins and meanings of the wave function and the Schrödinger equation become self-evident and, in particular, any probabilistic indeterminacy becomes irrelevant.

Key words

quantum entity micro-continuum Hencky strain-energy density nonlinear dynamic equation exact linearization Schrödinger equation deterministic pattern 

Chinese Library Classification

O33 O413 

2010 Mathematics Subject Classification

74A99 81P05 81S99 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics & Mechanics, College of Mechanics and Engineering ScienceShanghai UniversityShanghaiChina
  2. 2.College of Mechanics and Construction Engineering, MOE Lab of Disaster Forecast and Control in EngineeringJinan UniversityGuangzhouChina

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