On the Nonlinear Continuum Mechanics of Space and the Notion of Luminiferous Medium

TL;DR

This paper demonstrates that Maxwell's equations emerge from an elastic continuum model, proposing that electrodynamics is a manifestation of an underlying elastic medium, and introduces a frame-indifferent formulation that includes Lorentz force and explains classical laws.

Contribution

It establishes a nonlinear continuum mechanics foundation for electrodynamics, introducing a new covariance principle and a frame-indifferent formulation that incorporates Lorentz force naturally.

Findings

Maxwell's equations derive from an elastic continuum model.

The new formulation incorporates Lorentz force within Faraday's law.

Proposes experiments to detect the absolute elastic medium.

Abstract

We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material invariance 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. Thus, this paper establishes that 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 metacontinuum. The new frame-indifferent formulation of electrodynamics is shown to incorporate the Lorentz force as an integral part of Faraday's law, rather than as an additional empirical variable. Respectively, if the upper-convected derivative is added in Maxwell's displacement current it can explain Biot-Savart's and Oersted-Ampere's laws. An immediate corollary of the material invariance is the Galilean invariance of the model. The possible detection of the absolute continuum is also discussed. First, 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 are fully compatible with the presence of an absolute medium. Second, 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.