Continuum Mechanics of Space and Unification
C. I. Christov
Dept. of Mathematics,
University of Louisiana at Lafayette, Lafayette
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. Through a judicious distinction between the referential (Lagrange) and local (Euler) descriptions, the principle of material invariance (frame indifference) is established and shown to be a true covariance 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 relation. We show that the Ampere-Oersted and Biot-Savart laws can be derived from the frame-indifferent modification of the Maxwell displacement current. Thus we arrive at the idea that space is a material manifold called metacontinuum, which is governed by the law of continuum mechanics. 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 intrinsic property of the proposed model. Thus one does not need the Lorentz Transformation to explain the Lorentz contraction. We address also the conundrum connected with the detectability of the absolute continuum. We reexamine the famous experiment of Ives and Stilwell using a modified Bohr-Rydberg formula for the emitted frequencies which formula accounts 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 assume 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, allowing detecting the relative speed with respect to what is called the preferred frame. On the next level, the metacontinuum of electrodynamics is considered to be a three-dimensional layer in the four dimensional space (a hypershell). A dispersive nonlinear equation governs the flexural deformations of the hypershell. It admits solitary wave solutions (solitons) that behave as particles upon collisions (called quasi-particles or QPs). We stipulate here that the material particles are our perception of the QPs of the ``master'' equation (schaumkommen in Schrodinger's own words). The QPs do not move through, but rather propagate over the surface of the metacontinuum. We show the passage from the continuous to the discrete Lagrangian of the centers of QPs and introduce the concept of (pseudo)mass. The membrane tension results into an attractive force acting between the QPs propositional to the inverse square of the distance between the QPs. This unifies also the gravitation.