Electrodynamic forces in elastic matter

TL;DR

This paper develops a macroscopic, relativistic theory describing how elastic, isotropic materials respond dynamically to electromagnetic fields, incorporating electrostriction and magnetostriction effects.

Contribution

It introduces a four-dimensional generalization of Hooke's law and explicitly derives electrostrictive forces within a relativistic framework for the first time.

Findings

Derived explicit electrostrictive force expressions.

Formulated a relativistic elastic-electromagnetic coupling model.

Provided a foundation for more realistic electromagnetic-elastic matter equations.

Abstract

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 four dimensional generalisation of Hooke's law, made possible by the introduction of a four dimensional ``displacement'' vector. As intimated by Nordstroem, 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.