ATPEW — Star Formation and Multi-Scale Vortex Dynamics: Topological Phase Transitions from Atoms to Galaxies

This work develops the ATPEW (Ascending–Transcendent Primordial Energy Wave) framework applied to star formation and multi-scale vortex dynamics. Within ATPEW, stars are not modeled as purely gravitational gas spheres but as collective topological vortices emerging from phase synchronization of lower-level atomic vortices embedded in a galactic phase field.

We address five fundamental questions concerning hierarchical causality: whether galactic phases constrain stellar phases, how stellar birth differs from Jeans gravitational collapse, how billions of atomic vortices integrate into a coherent stellar vortex, the origin of the initial fluctuation, and whether the universe evolves through ascending, descending, or bidirectionally coupled dynamics.

Star formation is described as a discrete topological phase transition, characterized by a change in circulation ∮dθ from 0 to 2π. Gravitational attraction emerges as a consequence of phase gradients rather than as the primary cause of collapse. A key dynamical ingredient is the spectral gap in harmonic levels (n = 15–17), which enforces a direct jump from molecular coherence (n ≈ 12–13) to stellar coherence (n ≈ 18–20). This mechanism predicts a natural mass threshold consistent with the observed brown dwarf–star boundary.

The framework further introduces a bidirectional hierarchical structure: the early universe is purely ascending (structure emerging from fluctuations of the Primordial Wave), while mature cosmic epochs exhibit coupled upward and downward constraints between galaxies, stars, atoms, and subatomic vortices.

A tentative extension proposes that matter–antimatter asymmetry may arise from entropy-driven symmetry breaking during cosmic expansion, favoring one topological charge over the other.

The document provides analytical developments, explicit scaling estimates, and outlines testable predictions, including stellar mass thresholds, IMF structure, and phase-based galactic constraints.