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On the Topological Nature of Noether's Theorem (1)

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Posted 2025-11-27 01:17:43

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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 topological defects of spacetime and their symmetry changing [1, 2, 10]. We propose that the ground state of the physical vacuum is a sea of topological vortex and their twin antivortex pairs. At the moment of their creation, these vortex-antivortex pairs perfectly preserve the combined symmetries of Parity Conservation (P), Charge Conjugation (C), and Time Reversal (T) [8], which corresponds to the topological origin of the conservation laws revealed by Noether's theorem. However, this perfect symmetry exists only at the primordial synchronous space-time singularity of their formation. Once formed, the vortex and antivortex embed themselves as stable topological defects within the fabric of spacetime [1, 5, 9], exhibiting identical material properties and collectively constituting the entire material basis of our observable universe. This explains why our world is dominated by "matter" rather than exhibiting matter-antimatter symmetry [7].

Keywords: Noether's theorem; topological vortex; symmetry changing; PCT theorem; origin of matter; topological defect

1. Introduction: From Continuous Symmetry to Topological Symmetry

The theorem proposed by Emmy Noether in 1918 established that every continuous symmetry of the action corresponds to a conservation law in physics [4]. This principle has become central to all physical theories, from classical mechanics to quantum field theory [6]. Typically, we attribute conservation laws (e.g., conservation of energy, momentum, angular momentum) to the homogeneity and isotropy of spacetime—properties that are continuous and smooth.

A deeper question, however, is: What is the origin of these continuous symmetries themselves? Are they the most fundamental attributes of spacetime? This paper argues that continuous symmetries may be an emergent phenomenon, whose underlying basis is a discrete spacetime endowed with topological structure.

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