Remarks on forces and the energy-momentum tensor in macroscopic electrodynamics

Ginzburg, Vitalii L.; Ugarov, V.A.

doi:10.1070/pu1976v019n01abeh005127

Cited by 43 publications

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“…Note that the linear quantities coincide with the corresponding expressions in (3.8) while quantities in the second approximation, 2 4 3 and 2 44 3, are different. Then, from (4.20) and (4.21) it follows that the time average momentum density 2 3 is equal to zero, i.e.…”

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confidence: 86%

“…In Lagrangian variables, the variation of momentum is definitively related to mass transport, whereas the force is determined by the difference of elastic Lagrangian stresses at the boundaries of a stationary element 4 2 4 1 1 4 2 . A similar controversy in defining radiative stresses is encountered in the definition of the momentum-energy tensor of electromagnetic field in a medium according to Abraham or Minkowski [4,5].…”

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confidence: 99%

“…when the motion of the medium is neglected. The two most frequently used definitions of electromagnetic momentum are those by Minkowski and by Abraham, and which of them is more physical is still a discussed matter [4,5]. The wave pressure and momentum which we are interested in are quadratic in wave amplitudes and, consequently, are quantities of the second order of smallness as compared to the instantaneous elastic stresses and deformations.…”

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confidence: 99%

“…The radiative stress (wave pressure) and the related wave momentum are typical for waves of arbitrary nature: electromagnetic [4,5], optical [6][7][8][9], acoustic [1][2][3]10], surface waves on water [9,11], and elastic waves in solids [12][13][14]. However, while the wave pressure and momentum have been investigated in much detail, both theoretically and experimentally, for optical and electromagnetic waves in a vacuum, where they are regarded to be classical wave properties, the existence and physical meaning of the wave momentum in a continuous medium are still not quite transparent and are still being discussed in the scientific literature [11,[15][16][17][18] so that there is need for a precise study.…”

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Wave Momentum and Radiative Stresses in Elastic Solids

Potapov

Maugin

Trimarco

2005

Mathematics and Mechanics of Solids

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The physical meaning of the notions of wave momentum and radiative stress in elastic bodies is considered. Of great importance for defining and calculating these quantities are the variables in which the wave processes in the medium are described. In Euler variables, the radiative stress is defined as the time average of the momentum flux of the medium across the boundary of a volume that is stationary in space. It differs from the radiative stress calculated in Lagrangian variables by the value of the convective component of momentum flux involved with the motion of particles in the medium. It is shown that, physically, the wave momentum can be defined only in Euler variables. In the linear approximation of the small perturbation theory the wave momentum is a quadratic component of the total mechanical momentum of the medium. The integrals of motion of linear acoustic equations correspond to it, as well as to energy. In the second approximation of the perturbation theory, the wave momentum no longer has a rigorous definition. However, the concept of wave momentum borrowed from the linear approximation can be used for the calculation of average values of stresses and deformations, provided the body is not moving as a whole. 34567895374When wave processes are investigated in elastic bodies, in addition to the variables such as displacement, oscillatory velocity and so on, quantities that are constant in time, i.e. are conserved, are encountered too. These include quantities that are quadratic in the wave amplitude, in particular, energy and wave pressure (radiative stress). The origin of radiative stresses is related to the change of the time averaged momentum of the medium transported by the wave [1-3]. The change of wave momentum may be caused by scattering by inhomogeneities, reflection on obstacles, absorption, or radiation. The notions of wave momentum and radiative stresses have been employed in the analysis of wave processes in continuous media but not so often, so that the present study aims at revealing the physical

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Wave Momentum and Radiative Stresses in Elastic Solids

Potapov

Maugin

Trimarco

2005

Mathematics and Mechanics of Solids

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“…In macroscopic electrodynamics, the volume (mechanical or ponderomotive) forces, acting on a medium, and the corresponding energy density and energy flux are introduced with the help of the energy-momentum tensors and differential balance relations [24], [31], [51], [72], [86], [91]. These forces occur in the equations of motion for a medium or individual charges and, in principle, they can be experimentally tested [32], [69], [74], [92] (see also the references therein). But interpretation of the results should depend on the accepted model of the interaction between the matter and radiation.…”

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Complex Form of Classical and Quantum Electrodynamics

Kryuchkov

Lanfear

Suslov

2017

Springer Proceedings in Mathematics &Amp; Statistics

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Physical laws should have mathematical beauty. " -P. A. M. DiracAbstract. We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the corresponding differential balance equations are given. Conservation laws and quantization of the electromagnetic field will be discussed in this covariant approach elsewhere.

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2015

Electromagnetic Phenomena in Matter

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Remarks on forces and the energy-momentum tensor in macroscopic electrodynamics

Cited by 43 publications

References 1 publication

Wave Momentum and Radiative Stresses in Elastic Solids

Wave Momentum and Radiative Stresses in Elastic Solids

Complex Form of Classical and Quantum Electrodynamics

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