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

We present the "Relativistic Walker" model, a framework where the laws of quantum mechanics and relativity emerge from fundamental fluid dynamics rather than being axiomatic assumptions.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 elucidates the origin of the quantization of action (E = ℏ ef f Ω), where ℏ ef f is identified not as a fixed universal number, but as a dynamic variable of the vacuum state.Furthermore, we derive inertia as the hydrodynamic drag of the vacuum fluid, leading directly to the mass-energy equivalence (E = mc 2 ) as the dispersion relation for a standing wave packet.This framework provides a logical derivation of the structural relationships between the fundamental constants of physics based on the hydrodynamic properties of the vacuum.