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On the Topological Nature of Noether's Theorem (3)

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Posted 2025-11-27 01:44:42

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3. Primordial Synchrony and the Instantaneous Changing of Symmetry The perfect P, C, and T symmetries described above exist only at the very moment the vortex-antivortex pair forms—a synchronous space-time singularity. This is the most primitive, ideal state of symmetry, the topological anchor from which conservation laws originate.

However, this state is highly unstable, or rather, subject to instantaneous changing. Consistent with modern cosmological ideas, stable cosmic structures arise from symmetry changing [1, 7]. Similarly, once the topological vortex and its antivortex "precipitate" out from the creation singularity, they become "frozen" into the spacetime background as independent, stable topological defects [1, 10]. This process is accompanied by spontaneous symmetry changing:

a) P Changing: After formation, the specific chirality of the vortex and antivortex becomes fixed; they can no longer be interchanged by simple spatial inversion.

b) C Changing: The signs of the topological charges they carry are determined, separating positive from negative.

c) T Changing: Their formation becomes an irreversible historical event, marking the birth of the arrow of time.

Crucially, this changing is local and instantaneous. The symmetry might still hold on average for the entire sea of vortex-antivortex pairs, but for each individual pair, symmetry is lost immediately after birth. Noether's theorem describes conservation when symmetry holds, yet our world is precisely built upon the products of this instantaneous symmetry changing [7].

4. The Unity of Material Properties and the Nature of Our World

In the Standard Model of particle physics, every fermion has its corresponding antimatter partner, with opposite properties under C and P transformations. This leads to an unresolved puzzle: why is there a predominance of matter over antimatter in the universe? [7]

Our topological vortex theory offers a radical and unifying answer: The so-called "topological vortex" and "anti-topological vortex" possess completely identical material properties after their formation.

The labels "vortex" and "antivortex" only have meaning within the context of their mutually opposing yet interdependent relationship during formation. They are like the two sides of a coin—different labels, but made of the same material. Once the coin is minted (symmetry changed), both sides are real and material. The "anti" relationship refers to their opposition in topological charge or chirality, not an annihilating difference in material substance [2, 9].

Therefore, once symmetry is changed at the moment of formation, all stable topological defects—regardless of whether they were initially labeled "vortex" or "antivortex"—become the ordinary matter constituting our world. They no longer possess a matter-antimatter relationship that leads to mutual annihilation upon encounter. They are matter itself. Everything we see, the particles that constitute our bodies, are collections of these symmetry-changed topological defects. This, here, is our world [7].

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