Electromagnetic Stress and Momentum in Matter

Whether the momentum density associated with an electromagnetic wave in a refracting medium is solely determined by its intensity or is dependent on the refractive index is perhaps of little practical importance, and probably beyond the power of present experimental techniques to decide. Nevertheless, since this question was first propounded by Abraham and Minkowski. it has continued to attract physicists’ attention and, to judge by current literature, is still regarded as an open and quite possibly insoluble question. This article expounds some of the approaches to its solution that have been proposed, and shows that one of them leads to a complete solution of both the Abraham—Minkowski controversy and the more general problem of describing the distribution of stress in a material medium in the presence of an electromagnetic disturbance. The treatment emphasizes the significance of the electrostrictive and magnetostrictive terms in the stress tensor. These relatively unfamiliar effects are neither small nor unimportant. They express, in macroscopic terms, consequences of the microscopic structure of a medium which are not adequately described by the usual constitutive relations involving only the relative dielectric constant and the relative magnetic permeability. Their presence in the macroscopic theory ultimately reflects the fact that the individual microscopic charges in matter are subject to forces which, though purely electromagnetic, cannot adequately be described in terms of macroscopic fields., even if these fields are modified by the inclusion of a Lorentz local-field correction. As a result they form a crucial link in the connection between macroscopic and microscopic treatments.