A Unified Field Theory Based on Superdense Ether: Topological Solitons, Two-Mode Gravity, and Experimental Predictions

This work presents a deterministic field theory in which the physical vacuum is interpreted as a superdense (ρE ≈ 10¹3 kg/m³), superfluid, and practically incompressible medium — the ether. Material particles (electrons, nucleons) are treated as stable topological solitons — Hopf knots — within this medium. Particle mass is proportional to the Hopf invariant H, naturally explaining mass quantization. All fundamental interactions emerge from a unified hydrodynamics of the ether: gravity as a pressure gradient, electromagnetism as transverse waves (shear), and nuclear forces as topological entanglement of ether filaments. The model introduces a separation of gravitational interaction into longitudinal (instantaneous, c_∥ → ∞) and transverse (propagating at speed c) modes. This reconciles the instantaneous nature of the Newtonian potential with LIGO observations detecting gravitational waves propagating at c. A deviation of the Shapiro parameter γ from unity at the level of 2×10^-5 is predicted, testable with SKA and LISA. A laboratory protocol is developed to test the key prediction: anomalously long relaxation of water's dielectric permittivity following resonant acoustic excitation, attributed to the rearrangement of molecular topological structure. The theory resolves major conceptual issues of the standard model and general relativity: quantum entanglement nonlocality (explained by instantaneous longitudinal ether tension), dark matter and dark energy (interpreted as excess topological density and ether pressure), and singularities (replaced by limiting topological density). The model provides a deterministic substrate foundation for quantum mechanics, restoring causality in its classical understanding.