Relativistic Hydrodynamic Vacuum: A Covariant Foundation for the Emergence of Quantum Phenomena

The physical nature of the vacuum ground state remains a central open question in foundational physics. While quantum field theory typically treats the vacuum as a probabilistic state, recent developments in topological order suggest that spacetime and gauge fields may emerge from a highly entangled quantum liquid. In this work, we investigate the hypothesis that the vacuum possesses a hydrodynamic limit described by an effective field theory. By characterizing the vacuum's spectral response via an intrinsic impedance parameter, we demonstrate that Planck's law of blackbody radiation can be recovered from the thermodynamic equilibrium between matter oscillators and the background medium. In the microscopic regime (L LC, with coherence length LC 10^-9\, m), the balance between radiative damping and stochastic vacuum influx is shown to support a stable limit cycle, consistent with the ground state stability of the hydrogen atom. Extending this to scattering dynamics, we further explore how wave-particle duality and interference patterns may arise deterministically from the non-local phase memory of the vacuum fluid. Finally, we examine the macroscopic implications of this framework. By introducing a geometric scaling against the cosmological horizon, the model recovers a critical acceleration scale a₀ cH₀ from the vacuum's intrinsic stiffness. These results suggest that the probabilistic statistics of the quantum realm and the kinematic scaling of large-scale structures share a common geometric origin within a coherent topological vacuum.