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A Mathematical and Physical Analysis On the Origin of Objects (or Matters) in Space (3)3.2 Topological Defects as Precursors of Matter In TVT, the essence of an object is a topological vortex in the spatial superfluid. Considering a vortex in a two-dimensional cross-section with a winding number \(n \in \mathbb{Z}\): \[\oint_C \nabla \theta \cdot d\mathbf{l} = 2\pi n\] This vortex possesses: 1)A core: \(\Psi = 0\), corresponding to a localized region of spatial "excitation,"...0 Commentaires 0 Parts 77 Vue 0 Aperçu
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A Mathematical and Physical Analysis On the Origin of Objects (or Matters) in Space (4)4.3 Testable Predictions 1) Cosmological aspects: TVT predicts remnant topological defects (e.g., cosmic strings) in the early universe [3], with observational signatures different from those predicted by inflation alone. 2) Laboratory simulation: The mechanism of matter formation in TVT can be simulated in superfluid systems like Bose-Einstein Condensates (BEC) [4, 6], verifying the...0 Commentaires 0 Parts 90 Vue 0 Aperçu
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A Mathematical and Physical Analysis On the Origin of Objects (or Matters) in Space (5)Academic Statement 1) This paper is an exploratory and deductive academic paper based on the specific theoretical framework of Topological Vortex Theory (TVT). The viewpoints, mechanisms, and conclusions presented herein are logical deductions and hypotheses within this framework, aiming to explore a possible approach to the question of material origin. 2) Topological Vortex Theory (TVT)...0 Commentaires 0 Parts 85 Vue 0 Aperçu
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On the Topological Nature of Noether's Theorem (1)Abstract Noether's theorem, a cornerstone of modern physics, profoundly reveals the equivalence between symmetries and conservation laws. Traditionally, it is understood as a global or local consequence of continuous symmetries. This paper aims to propose a novel perspective, arguing from the framework of Topological Vortex Theory (TVT) that the root of Noether's theorem lies in the...0 Commentaires 0 Parts 701 Vue 0 Aperçu
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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...0 Commentaires 0 Parts 716 Vue 0 Aperçu
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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,...0 Commentaires 0 Parts 735 Vue 0 Aperçu
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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...0 Commentaires 0 Parts 762 Vue 0 Aperçu
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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...0 Commentaires 0 Parts 800 Vue 0 Aperçu
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