Analyzing the Scientific Nature and Verifiability of Topological Vortex Theory (2)
I. The Plurality of Scientific Verification: Beyond Narrow Positivism
1.1 Evolution in Philosophy of Science: From Logical Positivism to Explanatory Power Paradigms
1.2 The Scientific Value of Indirect Verification and Mathematical Consistency
II. Core Tenets and Mathematical Framework of Topological Vortex Theory
2.1 Theoretical Overview: From Topological Defects to Dynamical Stability
Topological Vortex Theory (TVT) posits that in physical systems with continuous symmetries (such as ideal or perfect fluids, inviscid fluids, super fluids, superconductors, electromagnetic fields, gravitational fields, etc.), topological defects can form stable vortex structures [4]. These structures are characterized by topological invariants (such as winding numbers, linking numbers) [1], and their stability stems from topological protection rather than dynamical details. The theory explains the persistent existence of vortices across various scales and physical contexts through topological conservation laws [2]. Fetter, Alexander L’s variational treatment of a system of many identical vortices in a container shows that the energy is lowest for a uniform distribution, and that the number of vortices per unit area ν agrees with Feyman’s result v=2mωh. In the classical limit (h–>0), the angular momentum and energy approach the values for solid-body rotation [5].
2.2 Mathematical Idealization: The Power of Scientific Abstraction
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