Resolution of the Abraham–Minkowski controversy

The momentum of light inside ponderable media has an electromagnetic part and a mechanical part. The local and instantaneous density of the electromagnetic part of the momentum is given by the Poynting vector divided by the square of the speed of light in vacuum, irrespective of the nature of the electromagnetic fields or the local or global properties of the material media. The mechanical part of the momentum is associated with the action of the electromagnetic field on the atomic constituents of the media, as specified by the Lorentz law of force. Proper interpretation and application of the Maxwell–Lorentz equations within the material bodies as well as at their surfaces and interfaces is all that is needed to obtain a complete picture of the momentum of light, including detailed numerical values at each and every point in space and time. That the Abraham–Minkowski controversy surrounding the momentum of light inside material media has persisted for nearly a century is due perhaps to an insufficient appreciation for the completeness and consistency of the macroscopic Maxwell–Lorentz theory, inadequate treatment of the electromagnetic force and torque at the material boundaries, and an undue emphasis on the necessity of coupling the equations of electrodynamics to those of the theory of elasticity for proper treatment of mechanical momentum. The present paper reports the resolution of the Abraham–Minkowski controversy within the framework of the classical theory of electrodynamics, without resort to such complicating and ultimately unnecessary factors as pseudo-momentum, special surface forces, alternative energy–momentum tensors, and hidden momenta, that have caused so much confusion for such a long period of time.