Potential Deterministic Foundations of Quantum Probability: Hydrodynamic Interpretation of the Schrödinger Equation and the Mechanical Origin of the Electron g-factor

This paper explores a refined deterministic and hydrodynamic framework for the genesis of matter, offering a mechanistically causal alternative to the probabilistic interpretations of quantum fluctuations. We postulate the physical vacuum as a continuous energetic medium (the "Substratum") characterized by ultra-low viscosity and a definite elastic saturation limit. By applying continuum mechanics and assuming a spherical localization model based on the reduced Compton radius (h-bar/mc), we rigorously derive the critical energy density threshold (rhocrit) required for a localized phase transition from the vacuum state to ponderable matter. The derivation demonstrates that this materialization threshold scales inextricably with the fourth power of mass (m⁴), incorporating a specific geometric factor (3/4pi). This structural scaling is shown to be in exact analytical convergence with the mass-scaling of the Schwinger Limit established in Quantum Electrodynamics (QED). Furthermore, we present a mechanical derivation for the electron g-factor, where the base value g=2 emerges from vortex filament topology, and the anomalous correction (alpha/2pi) is attributed to the vortex's self-interaction with its acoustic field. We also provide a cosmological argument for the universe's infinite spatial extent, derived from the principle of hydrostatic equilibrium. This framework offers a deterministic alternative for reconciling sub-atomic stability and cosmological dynamics within a strictly 3-dimensional mechanical ontology.