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

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.