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The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their known couplings, in particular piezoelectricity and photoelasticity. Despite the strange Helmholtz and Mach-Lippmann analogies existing between them, no classical technique may provide a common setting. However, unexpected arguments discovered independently by the brothers E. and F. Cosserat in 1909 for EL and by H. Weyl in 1918 for EM are leading to construct a new differential sequence called Spencer sequence in the framework of the formal theory of Lie pseudo groups and to introduce it for the conformal group of space-time with 15 parameters. Then, all the previous explicit couplings can be deduced abstractly and one must just go to a laboratory in order to know about the coupling constants on which they are depending, like in the Hooke or Minkowski constitutive relations existing respectively and separately in EL or EM. We finally provide a new combined experimental and theoretical proof of the fact that any 1-form with value in the second order jets (elations) of the conformal group of space-time can be uniquely decomposed into the direct sum of the Ricci tensor and the electromagnetic field. This result questions the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT). In particular, the Einstein operator (6 terms) must be thus replaced by the adjoint of the Ricci operator (4 terms only) in the study of gravitational waves.
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篇名 The Mathematical Foundations of Elasticity and Electromagnetism Revisited
来源期刊 现代物理(英文) 学科 数学
关键词 ELASTICITY Electromagnetism Mach-Lippman ANALOGY HELMHOLTZ ANALOGY PIEZOELECTRICITY PHOTOELASTICITY Differential Sequences ADJOINT Operator Double Duality
年,卷(期) xdwlyw_2019,(13) 所属期刊栏目
研究方向 页码范围 1566-1595
页数 30页 分类号 O17
字数 语种
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研究主题发展历程
节点文献
ELASTICITY
Electromagnetism
Mach-Lippman
ANALOGY
HELMHOLTZ
ANALOGY
PIEZOELECTRICITY
PHOTOELASTICITY
Differential
Sequences
ADJOINT
Operator
Double
Duality
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研究去脉
引文网络交叉学科
相关学者/机构
期刊影响力
现代物理(英文)
月刊
2153-1196
武汉市江夏区汤逊湖北路38号光谷总部空间
出版文献量(篇)
1826
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0
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