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On the Topological Nature of Noether's Theorem (2)
Topological Vortex Theory (TVT) provides an ideal mathematical model for this. Within this theory, the vacuum is not empty but a dynamic network composed of countless interconnected topological vortex-antivortex pairs, constantly being created and annihilated [1, 2, 10]. The symmetries described by Noether's theorem are precisely the macroscopic, continuous-limit statistical average...

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

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On the Topological Nature of Noether's Theorem (4)
5. Conclusion and Outlook This paper constructs a theoretical framework that integrates the profound implications of Noether's theorem with topological vortex theory, proposing the following core theses: The continuous symmetries and conservation laws described by Noether's theorem have, at their microscopic topological essence, their origin in the perfect PCT symmetry satisfied by...

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On the Topological Nature of Noether's Theorem (5)
References Kibble, T. W. B. (1976). Topology of Cosmic Domains and Strings. Journal of Physics A: Mathematical and General, 9(8), 1387–1398. Mermin, N. D. (1979). The topological theory of defects in ordered media. Reviews of Modern Physics, 51(3), 591–648. Nakahara, M. (2003). Geometry, Topology and Physics (2nd ed.). Taylor & Francis. Noether, E. (1918). Invariante...

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