Modeling The Atomic Structure As Superfluid Vacuum Flow

We present a self-consistent classical framework that derives the stability, scale, and multidimensional geometric profiles of atomic electron orbitals natively from the hydrodynamic and thermodynamic flow of the quantum vacuum. By modeling fundamental particles as localized sinks for the zero-point field (ZPF), we establish that a particle’s mass is proportional to its localized vacuum influx rate (\ (M Q\) ). When an electron is immersed in the immense inward flux field of a dense atomic nucleus, the counter-pressure exerted by its own minor flux field establishes a local stagnation zone. Applying a three-dimensional stochastic Langevin framework and transforming it via the Fokker-Planck equation, we analytically prove that the electron’s time-averaged trajectory does not collapse via classical Larmor radiation, but instead stabilizes dynamically at an expectation value identical to the Bohr radius (\ (a₀\) ). Additionally, we demonstrate that when the system possesses macroscopic angular momentum (\ (l > 0\) ), the inward fluid flow transitions into an irrotational vortex. The resulting anisotropic pressure gradients and Bernoulli constraints natively carve the electron’s probability density function into the exact spherical harmonic geometries of the s, p, d, and f orbitals without invoking conventional quantum wavefunctions.