The Impedance of Space: Emergent Galactic Dynamics and Baryonic Resonances from a Superfluid Vacuum

Theoretical Companion to Raza (2025a) and Raza (2025b). Abstract: We propose that the physical vacuum is a relativistic superfluid described by a "Stiff" Equation of State (P = rho*c²) and a conserved characteristic impedance of Z₀ approx 377 Ohms. By applying the Principle of Least Action to this medium within the boundary conditions of the Hubble Radius (RH), we provide a first-principles derivation of the MOND acceleration scale (a₀) and the critical baryonic surface density (Sigmaₚsi). Unlike phenomenological models, this framework uniquely predicts the emergence of a characteristic resonant scale for baryonic structures in the low-acceleration regime. We derive a "Vacuum Jeans Length"—defined by the impedance matching of baryonic thermal pressure to the vacuum acceleration limit—yielding a characteristic scale of lambda approx 2. 1 - 2. 5 kpc for typical galactic velocity dispersions. This theoretical prediction aligns with the median resonant wavelength of 2. 47 kpc empirically detected in low-surface-density galaxies (Paper 2). The Vacuum Impedance Series: This paper is Part 3 of a 6-paper series establishing the General Theory of Vacuum Impedance: Phase I: Galactic Dynamics (The Dark Matter Solution) Paper 1 (Discovery): Empirical Evidence of Baryonic Thresholds (DOI: 10. 5281/zenodo. 18035640) Paper 2 (Observation): Resonant Modes in Galactic Disks (DOI: 10. 5281/zenodo. 18110723) Paper 3 (Mechanism): The Impedance of Space (This Work) - Derives the galactic threshold and resonances from Vacuum Impedance. Phase II: Universal Gravitation (The First-Principles Derivation) Paper 4 (Forthcoming): The Newtonian Limit - Deriving the Inverse-Square Law and Solar System Dynamics from Vacuum Impedance. Paper 5 (Forthcoming): The Ultra-High-Density Frontier - Precision Tests across White Dwarfs and Neutron Stars. Paper 6 (Forthcoming): The Complete Vacuum Impedance Theory - Grand Unification of Galactic, Stellar, and Quantum Dynamics.