First Principles of the Relativistic Walker: A Hydrodynamic Derivation of Quantization, Inertia, and Mass-Energy Equivalence

We present the "Relativistic Walker" model, a hydrodynamic framework demonstrating a plausible route toward the emergence of quantum mechanics and relativity from fundamental fluid dynamics.We analyze a pulsing source in a scalar vacuum field and demonstrate that stability requires the coupling strength to follow a geometric scaling law proportional to the square root of the frequency.This relation suggests a hydrodynamic origin for the quantization of action (E = ℏ ef f Ω), where ℏ ef f is identified as a dynamic variable of the vacuum state.Furthermore, we derive inertia as the hydrodynamic drag of the vacuum fluid, recovering the mass-energy equivalence (E = mc 2 ) as the effective dispersion relation for a standing wave packet.This framework offers a novel perspective on the structural relationships between the fundamental constants of physics, grounded in the geometry of the vacuum.