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The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors: I. General theory

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The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors : I. General theory. / Goto, Shinichiro; Tucker, Robin; Walton, Timothy.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 467, No. 2125, 08.01.2011, p. 59-78.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Goto, S, Tucker, R & Walton, T 2011, 'The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors: I. General theory', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 467, no. 2125, pp. 59-78. https://doi.org/10.1098/rspa.2010.0110

APA

Vancouver

Goto S, Tucker R, Walton T. The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors: I. General theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2011 Jan 8;467(2125):59-78. doi: 10.1098/rspa.2010.0110

Author

Goto, Shinichiro ; Tucker, Robin ; Walton, Timothy. / The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors : I. General theory. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2011 ; Vol. 467, No. 2125. pp. 59-78.

Bibtex

@article{15a40f6e45ca476ea6ad09ccb15a9d65,
title = "The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors: I. General theory",
abstract = "This is paper I of a series of two papers, offering a self-contained analysis of the role of electromagnetic stress–energy–momentum tensors in the classical description of continuous polarizable perfectly insulating media. While acknowledging the primary role played by the total stress–energy–momentum tensor on spacetime we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor, when defined with respect to a particular splitting. The relevance of tensors, associated with the electromagnetic fields that appear in Maxwell{\textquoteright}s equations for polarizable media, to the forces and torques that they induce has been a matter of some debate since Minkowski, Einstein and Laub, and Abraham considered these issues over a century ago. The notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium. Consistency with the laws of Newtonian continuum mechanics demands that the total force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the total stress–energy–momentum tensor. The fact that, unlike the tensor proposed by Minkowski, the divergence of the Abraham tensor depends explicitly on the local acceleration field of the medium as well as the electromagnetic field sets it apart from many other terms in the total stress–energy–momentum tensor for a medium. In this paper, we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular Killing symmetries. It is shown how the drive-forms associated with translational Killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the Minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature.",
keywords = "electrodynamics , continuum mechanics, constitutive theory , relativity",
author = "Shinichiro Goto and Robin Tucker and Timothy Walton",
year = "2011",
month = jan,
day = "8",
doi = "10.1098/rspa.2010.0110",
language = "English",
volume = "467",
pages = "59--78",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "1364-5021",
publisher = "Royal Society of Chemistry Publishing",
number = "2125",

}

RIS

TY - JOUR

T1 - The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors

T2 - I. General theory

AU - Goto, Shinichiro

AU - Tucker, Robin

AU - Walton, Timothy

PY - 2011/1/8

Y1 - 2011/1/8

N2 - This is paper I of a series of two papers, offering a self-contained analysis of the role of electromagnetic stress–energy–momentum tensors in the classical description of continuous polarizable perfectly insulating media. While acknowledging the primary role played by the total stress–energy–momentum tensor on spacetime we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor, when defined with respect to a particular splitting. The relevance of tensors, associated with the electromagnetic fields that appear in Maxwell’s equations for polarizable media, to the forces and torques that they induce has been a matter of some debate since Minkowski, Einstein and Laub, and Abraham considered these issues over a century ago. The notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium. Consistency with the laws of Newtonian continuum mechanics demands that the total force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the total stress–energy–momentum tensor. The fact that, unlike the tensor proposed by Minkowski, the divergence of the Abraham tensor depends explicitly on the local acceleration field of the medium as well as the electromagnetic field sets it apart from many other terms in the total stress–energy–momentum tensor for a medium. In this paper, we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular Killing symmetries. It is shown how the drive-forms associated with translational Killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the Minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature.

AB - This is paper I of a series of two papers, offering a self-contained analysis of the role of electromagnetic stress–energy–momentum tensors in the classical description of continuous polarizable perfectly insulating media. While acknowledging the primary role played by the total stress–energy–momentum tensor on spacetime we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor, when defined with respect to a particular splitting. The relevance of tensors, associated with the electromagnetic fields that appear in Maxwell’s equations for polarizable media, to the forces and torques that they induce has been a matter of some debate since Minkowski, Einstein and Laub, and Abraham considered these issues over a century ago. The notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium. Consistency with the laws of Newtonian continuum mechanics demands that the total force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the total stress–energy–momentum tensor. The fact that, unlike the tensor proposed by Minkowski, the divergence of the Abraham tensor depends explicitly on the local acceleration field of the medium as well as the electromagnetic field sets it apart from many other terms in the total stress–energy–momentum tensor for a medium. In this paper, we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular Killing symmetries. It is shown how the drive-forms associated with translational Killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the Minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature.

KW - electrodynamics

KW - continuum mechanics

KW - constitutive theory

KW - relativity

U2 - 10.1098/rspa.2010.0110

DO - 10.1098/rspa.2010.0110

M3 - Journal article

VL - 467

SP - 59

EP - 78

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2125

ER -