Electrodynamic forces in elastic matter

A macroscopic theory for the dynamics of elastic, isotropic matter in presence of electromagnetic fields is proposed here. We avail of Gordon’s general relativistic derivation of Abraham’s electromagnetic energy tensor as starting point. The necessary description of the elastic and of the inertial behaviour of matter is provided through a fourdimensional
generalisation of Hooke’s law, made possible by the introduction of a four-dimensional “displacement” vector. As intimated by
Nordstrom, the physical origin of electrostriction and of magnetostriction
is attributed to the change in the constitutive equation of electromagnetism caused by the deformation of matter. The part of the
electromagnetic Lagrangian that depends on that deformation is given explicitly for the case of an isotropic medium and the resulting expression of the electrostrictive force is derived, thus showing how more realistic
equations of motion for matter subjected to electromagnetic fields can be constructed.