A Hydrodynamic Interpretation of Vacuum Impedance: Deriving μ₀ and ε₀ from the Mechanical Properties of a Scalar Field

Background: In standard quantum electrodynamics (QED), vacuum permittivity (ϵ 0 ) and permeability (µ 0 ) are often treated as fundamental dimensional constants.While mathematically robust, this treatment lacks an underlying mechanical description of the vacuum substrate itself.Methods: We propose a hydrodynamic interpretation of the vacuum state by modeling it as a Lorentz-covariant scalar field.We establish a formal isomorphism where Maxwell's constants map directly to fluid dynamic parameters: µ 0 corresponds to inertial mass density (ρ) and ϵ 0 corresponds to elastic compliance (κ).Lorentz invariance is preserved through an effective acoustic metric that reduces to the Minkowski metric in the vacuum ground state.Results: Within this framework, the characteristic impedance of free space (Z 0 ≈ 377Ω) emerges as the acoustic impedance of the scalar fluid.We derive a quantitative prediction for a local impedance shift (∆Z) in constrained geometries, such as Casimir cavities.Specifically, we provide an observable phase signature (∆ϕ obs ) for multipass XUV interferometry, demonstrating that a 5 nm cavity gap yields a signal-to-noise ratio approaching unity.Furthermore, we identify the fine structure constant α as a hydrodynamic coupling efficiency related to quantized vortex filaments.Conclusion: This isomorphism provides a consistent mechanical basis for wave propagation and mass generation while maintaining the predictive accuracy of QED.By offering a falsifiable bridge to next-generation vacuum interferometry, this model suggests that the fundamental constants of electromagnetism are emergent properties of a structured vacuum substrate.