2016/04/06 by Michael E. Crenshaw, Crenshaw, Michael E.
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Optics (physics.optics) #physics.class-ph #physics.optics
paper · pdf · doi:10.48550/arxiv.1604.01801
arxiv created 2016/04/06 · arxiv updated 2016/04/08
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.