Emergent Gauge and Gravity Fields from the Kinematics of a Micropolar Elastic Substrate

We present a unified field theory based on the mechanics of a continuous, isotropic, micropolar elastic medium. By decomposing the displacement gradient tensor into irreducible representations, we identify the symmetric strain sector with linearized General Relativity (Spin-2) and the antisymmetric rotational sector with Maxwell’s Electromagnetism (Spin-1). We rigorously derive the electromagnetic field variables as canonical momenta from the elastic Lagrangian, avoiding arbitrary identifications. We explicitly model the incompressibility condition through a diverging bulk modulus, showing that longitudinal modes decouple at low energies. Crucially, we identify the sources of these fields with topological defects in the vacuum texture: mass arises from disclinations (curvature sources), while electric charge arises from dislocations (torsion sources). Finally, we derive the fundamental constants (G, ϵ0) from the vacuum’s elastic moduli and perform a dimensional consistency check relating the elementary charge to the lattice spacing.