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Foundations of Electromagnetism

We prove that, when linearized, the governing equations of an incompressible elastic liquid yield Maxwell's equations as corollaries. The divergence of the deviator stress tensor is interpreted as the electric field, while the vorticity (the curl of velocity field) is interpreted as the magnetic field.  Thus we establish that the electrodynamics can be fully explained if one assumes that it is the manifestation of the internal forces of an un-derlying elastic material which we term the metacontinuum.  Through judicious distinc-tion between the referential (Lagrange) and local (Euler) descriptions, the principle of material invariance (frame indifference) is established and shown to be a true covari-ance principle, unlike the Lorentz covariance, which is valid only for non-deforming frames in rectilinear relative motion.

The new nonlinear formulation of the electrodynamics incorporates the Lorentz force as an integral part of Faraday's law, rather than as an additional empirical observable rela-tion.  We show that the Ampere-Oersted and Biot-Savart laws can be derived from the frame-indifferent modification of the Maxwell displacement current. A viscous term in the constitutive relation can explain quantitatively Ohm's law.  The material invariance of the model entails Galilean invariance as a limiting case.

The main objection against the presence of an absolute medium stems from the per-ception that the particles and charges (the matter) move through it. We propose a new concept in which the particles and charges are  considered as localized nonlinear waves (solitons) of the metacontinuum. They do not move through, but rather propagate over the surface of the metacontinuum. We show that a localized screw deformation in the metacontinuum possesses a topological charge and for all practical purposes can be interpreted as the charge. A most important property of a propagating phase pattern is that it is contracted in the direction of propagation by the Lorentz factor (which is a well established fact in soliton theory). This means that the Lorentz contraction is an in-trinsic property of the proposed model. Thus one does not need the Lorentz Transfor-mation to explain the Lorentz contraction.

We address also the conundrum connected with the detectability of the absolute contin-uum.  The phase change concept of Michelson interferometer proved unable to detect the first-order Doppler effect, while the second-order  is exactly cancelled by the Lorentz contraction. The difficulties stem from the fact that any observational frame is composed by localized patterns while the electromagnetic waves propagate in the absolute me-dium. Keeping this in mind, we reexamine the famous experiment of Ives and Stilwell using a modified Bohr-Rydberg formula for the emitted frequencies which formula ac-counts for the motion of the emitting atom. We show that the results of Ives and Stilwell are fully compatible with the presence of an absolute medium, without the need to as-sume time dilation.  Finally, we propose a new two-beam interferometry concept based on the beat frequency which can produce results for the first-order Doppler effect, al-lowing detecting the relative speed with respect to what is called the preferred frame.