Electrodynamic forces in elastic matter

A macroscopic theory for the dynamics of elastic, isotropic matter in the p resence of electromagnetic fields is proposed here. We avail of Gordon's ge neral relativistic derivation of Abraham's electromagnetic energy tensor as starting point. The necessary description of the elastic and of the inerti al behaviour of matter is provided through a four-dimensional generalisatio n of Hooke's law, made possible by the introduction of a four-dimensional " displacement" vector. As intimated by Nordstrom, the physical origin of ele ctrostriction and of magnetostriction is attributed to the change in the co nstitutive equation of electromagnetism caused by the deformation of matter . The part of the electromagnetic Lagrangian that depends on that deformati on is given explicitly for the case of an isotropic medium and the resultin g expression of the electrostrictive force is derived, thus showing how mor e realistic equations of motion for matter subjected to electromagnetic fie lds can be constructed.