Deformable micro-continua in which quantum mysteries reside  

作　　者：Heng XIAO 

机构地区：[1]Shanghai Institute of Applied Mathematics & Mechanics, College of Mechanics and Engineering Science, Shanghai University [2]College of Mechanics and Construction Engineering, MOE Lab of Disaster Forecast and Control in Engineering, Jinan University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第12期1805-1830,共26页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.11372172)

摘　　要：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 Schrodinger 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 Schrodinger equation become self-evident and,in particular,any probabilistic indeterminacy becomes irrelevant.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 Schr¨odinger 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 Schr¨odinger equation become self-evident and, in particular, any probabilistic indeterminacy becomes irrelevant.

关 键 词：QUANTUM entity micro-continuum Hencky STRAIN-ENERGY density nonlinear dynamic EQUATION exact linearization Schrodinger EQUATION deterministic pattern 

分 类 号：O33[理学—一般力学与力学基础] O413[理学—力学]