Kinematics of Saturated Topological Solitons: Emergent Dirac Spinors, Hydrodynamic Inertia, and Asymptotic Lorentz Symmetry within a Micropolar Continuum.

In a preceding work, the thermodynamic stability of scalar topological solitons within a saturated Cosserat-Korteweg continuum was shown to be strictly governed by the Cubic-Quintic Nonlinear Schrödinger Equation (CQ-NLSE). The present article extends this deterministic framework into the dynamic regime by restoring the full rotational degrees of freedom intrinsic to a micropolar fluid vacuum. Within this formalism, we demonstrate that particle inertia is not required as an axiomatic scalar; rather, it emerges organically as the hydrodynamic added-mass tensor of the fluid substrate, allowing for the direct recovery of the acoustic mass-energy equivalence (E = M c2 S ) via the Hydrodynamic Virial Theorem. By mapping the orientation of the Cosserat micro-rotation trihedron through Spacetime Algebra (Cℓ1,3), we establish that the local conservation of fluid angular momentum for a Möbius-fibered Hopfion naturally factorizes into the Dirac spinor equation. This continuum approach provides a physically tractable resolution to the Zitterbewegung phenomenon, identifying it as the helical precession of a vortex core kinetically locked to the transverse shear wave velocity of the medium.

To reconcile these localized internal dynamics with macroscopic relativistic phenomenology, we introduce a dual-regime rheological model of the substrate. We show that while the high-density soliton core enters a hyper-incompressible jamming phase—acting as a rigid inclusion that inherently breaks Lorentz symmetry at the Planck scale—long-range interactions are mediated exclusively by the surrounding compressible fluid. By applying the Gordon acoustic metric to this irrotational far-field, we demonstrate that Lorentz length contraction and time dilation emerge deterministically as the effective, asymptotic symmetries of the perturbative wave fields. Ultimately, this framework suggests that relativistic quantum kinematics and effective pseudo-Riemannian geometries do not necessitate an a priori empty spacetime manifold, but arise rigorously as the low-energy aeroacoustic phenomenology of non-linear continuum mechanics.