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arXiv · 1604.01801

The Role of Conservation Principles in the Abraham--Minkowski Controversy

Michael E. Crenshaw
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Abstract

The Abraham--Minkowski controversy refers to a long-standing inability to adequately address certain issues involving the conservation of the momentum of an electromagnetic field in a linear dielectric medium. We apply the usual assumption of a material subsystem that couples to the electromagnetic subsystem such that the total energy and total momentum are conserved. We then construct the total energy--momentum tensor from the total energy density and the total momentum density. Applying conservation principles to the total energy--momentum tensor, we construct the tensor energy--momentum continuity equation. We show that one of the components of the tensor energy--momentum continuity equation, the energy continuity equation, is manifestly false. We conclude that the Abraham--Minkowski controversy is unresolvable because the extant principles of conservation are inconsistent in a simple linear dielectric medium.

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Michael E. Crenshaw. 2016-04-06. The Role of Conservation Principles in the Abraham--Minkowski Controversy. https://arxiv.org/abs/1604.01801

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