The Elastic Interpretation of Electrodynamics

In his famous treatise, Maxwell presumed explicitly, without developing it, an elastic interpretation of his electrodynamics; the relevant quotation is given in the introduction. It is in that spirit that we have developed the theory of the elastic interpretation here presented. We show that the Maxwell equations and the electrodynamic forces can formally be obtained from the theory of elasticity. An electromagnetic field can be considered as a deformation of a certain elastic medium . This deformation is created by volumetric densities of deforming couples and of irrotational deforming forces that act on . A distribution of electric charges is proportional to the divergence of the deforming couples. The electrodynamic forces are due to the interactions between such deformations. Even though the consistency of the elastic interpretation of electrodynamics is demonstrated by the fact that it gives back Maxwell's equations, and the electrodynamic forces, we show that the elastic interpretation is compatible with Einstein's special relativity. Then we demonstrate that an adequate density of irrotational deforming forces can produce the same effects on light propagation as those of a Schwarzschild metric background. This fact suggests a possible extension to take into account many of the effects attributed to the geometrical structure of the general relativity. Thus, we have given an elastic interpretation to the action at distance, and contributed to eliminate the inconsistency mentioned by Einstein, implying in his view, an incompleteness of the Maxwell theory. In future works, we hope to give an elastic interpretation for additional aspects of the particle waves and of general relativity and for the electroweak and strong fields.