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

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.

References in corpus (1)

• Radiation pressure and the linear momentum of the electromagnetic field

Cited by in corpus (2)

• About conservation the angular momentum for asymmetric tensors in electrodynamics
• Electromagnetic energy, momentum and forces in a dielectric medium with losses