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On the Topological Nature of Noether's Theorem (4)

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Posted 2025-11-27 01:53:33

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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 topological vortex-antivortex pairs at the instant of their creation within the spacetime background [4, 8].
This perfect symmetry exists only at the synchronous creation singularity and is instantaneous. The subsequent symmetry changing stabilizes the vortex and antivortex as independent topological defects [1, 2, 7].
The post-changing topological vortex and anti-topological vortex no longer exhibit matter-antimatter annihilation properties but collectively constitute particles with identical material attributes. This elegantly explains why our universe is matter-dominated—because all stable topological defects are matter [7].

This theory shifts the root of symmetry from continuous geometric attributes to discrete topological structures, offering a fresh perspective for understanding the origin of matter, the cosmological constant problem, and quantum gravity. Future work will focus on developing a rigorous mathematical formulation for this framework, particularly using methods of quantum field theory on topologically non-trivial backgrounds [3, 6, 10] to quantitatively describe the production and symmetry-changing mechanism of these vortex pairs, and to search for possible observable signatures.

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