From the Maxwell’s Equations of Lattice Deformations to the Description of the Universe by a « Crystalline Ether »

Using Eulerian coordinates to describe solid lattice deformations, it has been shown that the set of equations known as Maxwell’s equations —typically applied to electromagnetic phenomena in vacuum or matter—can also describe the elastic, anelastic, and plastic deformations of isotropic solid lattices containing topological defects such as dislocations and disclinations, under conditions of constant and homogeneous expansion. The analogy between the two physical systems is complete: it extends beyond one of the two Maxwell equation pairs in vacuum to both pairs, and includes analogues to dielectric polarization, magnetization, electric charges, and currents. In the Eulerian approach, Maxwell’s equations emerge as a special case derived from a tensor theory of lattice deformation, reducible to a vector formulation only for constant and homogeneous expansion. When dynamic and non-homogeneous expansions are considered, the tensorial nature of the theory becomes essential. This generalization naturally leads to a new conceptual framework for the Universe based on the existence of a crystalline ether . This framework offers a simple, unified, and coherent description of all major theories of modern physics—including electromagnetism, relativity, gravitation, quantum physics, cosmology, and the Standard Model of particle physics.