III. Mathematical Framework of TVSTO
The mathematical framework of TVSTO is based on topological fluid dynamics, and its core equations and models can be summarized into the following key parts:
3.1 Vortex Dynamics Equation: Uses a modified form of the generalized Navier-Stokes equation to describe the generation and evolution of topological vortices in an ideal fluid:
∂v/∂t + (v·∇)v = −∇p + κ∇²v + F_topo
Here, κ is the vortex topological invariant (e.g., winding number), and F_topo represents the topological interaction force between vortices.
Introduces the quantization condition ∮v·dl = nℏ/m (n is an integer), linking vortex circulation quantized angular momentum.
3.2 Spacetime Topology Model:
3.2.1 Depicts the birth of spacetime through the Vortex Nucleation Model: Background space undergoes a topological phase transition under critical conditions, forming a vortex network with genus g. Its metric tensor g_{μν} is determined by the vortex density field ρ_v:
ds² = ρ_v(φ)dt² − ρ_v⁻¹(φ)dφ²
where φ is the topological phase of the vortex field.
3.2.2 Establishes the Conservation Law of Winding Number:
W = (1/4π) ∫ v · (∇ × v) d³x = const.
This equation ensures the geometric stability of vortex correlations and directly supports the non-locality interpretation of quantum entanglement.
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