Nonlinear continuum mechanics with defects resembles electrodynamics—A comeback of the aether?

Abstract The dynamics of an incompressible, isotropic elastic continuum are discussed. Starting from the Lorentz‐invariant motion of defects in elastic continua, MacCullagh's aether theory (1839) of an incompressible elastic solid is reconsidered. Since MacCullagh's theory, based on linear elasticity, cannot describe charges, particular attention is given to a topological defect that causes large deformations and, therefore, requires a nonlinear description. While such a twist disclination can take the role of a charge, the deformation field of a large number of these defects produces a microstructure of deformation related to a Cosserat continuum (1909). On this microgeometric level, a complete set of quantities can be defined that satisfies equations equivalent to Maxwell's. From a broader perspective, the elastic continuum approach appears to be intriguing, yet it has considerable difficulties in describing Dirac's large numbers, another unresolved mystery in fundamental physics. Despite this shortcoming, I think, however, that this paper may stimulate further research.