On the Nonlinear Continuum Mechanics of the Luminiferous Medium

Abstract: In this work, we argue that adding the displacement current in Ampere's law by Maxwell was equivalent to considering the field as an elastic continuum. To corroborate this point, we prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. The divergence of the deviator stress tensor is analogous to the electric field, while the vorticity (the \emph{curl} of velocity field) is interpreted as the magnetic field. The nonlinearity of the material time derivative (the advective part of acceleration) is interpreted as the Lorentz force. Thus we have established that the electrodynamics can be fully explained if one assumes that it is the manifestation of the internal forces of an underlying elastic material which we term the \emph{metacontinuum}. 
The possible detection of the absolute continuum is also discussed. First, a new interferometry experiment is proposed in which the first-order Doppler effect can be measured and thus the presence of a medium at rest can be unequivocally established. Second, the famous experiment of Ives and Stilwell is reexamined with a modified Bohr-Rydberg formula for the emitted frequencies from a moving atom, and it is shown that the results of Ives and Stilwell are fully compatible with the presence of an absolute medium.

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