Deterministic Nature of Quantum Probability: Hydrodynamic Interpretation of the Schrödinger Equation and Substratum Topology

The Copenhagen interpretation of quantum mechanics views the microscopic world as a fundamentally probabilistic system where the principle of determinism is violated. This paper proposes an alternative, deterministic approach based on the hydrodynamic formalism of quantum equations. Using the Madelung transformation, we demonstrate that the Schrödinger equation is mathematically identical to the Euler equation describing the dynamics of an ideal fluid (the Substratum) subject to a quantum potential. Within this framework, the wave function ($\Psi$) is interpreted not as an abstract probability amplitude, but as the physical density distribution of the Substratum. The paper further explains orbital quantization and spin based on topological constraints of fluid circulation.