Topological Vortex Theory and the Scientific Validation of the...

Topological Vortex Theory and the Scientific Validation of the Dialectical Materialist Law of Unity of Opposites (3)

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Posted 2025-12-15 04:49:29

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3. Self-Organization and Interaction: A Network of Contradictions Constituting Complex Spacetime

3.1 Self-Organization of Vortex Systems: Dynamic Equilibrium of the Unity of Opposites

Isolated vortices are unstable; they form complex vortex lattices, turbulent structures, or fractal networks through interactions (attraction, repulsion, entanglement, renormalization). This self-organizing process demonstrates:

(1) Contradictory Struggle Drives Structural Evolution: Competition and cooperation among vortices of different and the same chirality drive the system toward states of lower energy, higher entropy, or greater topological stability [2].

(2) Relative Balance of Opposites Forms Stable Structures: Under specific conditions, the number and distribution of left- and right-handed vortices reach a dynamic balance, forming macroscopically stable spacetime structures (e.g., vortex arrays). This balance is not static but a statistical equilibrium under constant microscopic fluctuations.

(3) Transformation of Principal and Secondary Contradictions: At different scales or energy levels, the contradictions dominating system evolution differ (e.g., vortex-antivortex annihilation dominates at short ranges, while collective modes of vortex lattices dominate at long ranges).

3.2 Hierarchical Nature of Spacetime Structure: Universal Connection and Particularity of Contradiction

Topological vortex theory predicts that through multi-stage phase transitions and self-organization, vortex systems can form multi-level nested structures from the microscopic to the macroscopic. Each level possesses its own specific form of contradiction:

(1) Microscopic Level: The unity of opposites between left- and right-handed vortices.

(2) Mesoscopic Level: The interaction between vortex lattices and the background fluid, as evidenced by studies on structured waves [3].

(3) Macroscopic Level: The interrelation between overall spacetime geometry and matter distribution.

This hierarchy precisely confirms the dialectical materialist view that "contradiction is universal in all things, but the contradictions of different things have their particularity." Simultaneously, the levels are interconnected through nonlinear coupling, embodying the principle of universal connection.

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