The quantum is not a cat that is both dead and alive (3)

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3. Spin: The Intrinsic Geometric Dynamics of a Topological Vortex

The most mysterious intrinsic property in quantum mechanics—"spin"—finds a natural and elegant interpretation in TVT. It is no longer the difficult-to-visualize "intrinsic angular momentum" of textbooks, but the direct manifestation of the rotational dynamics of the topological vortex's own spacetime structure[7]. A topological vortex can be analogized to a knotted, rotating microscopic "string loop" or "field line bundle" in a higher-dimensional spacetime. Its "spin" is the stable rotational motion of this topological structure around its own axis. This rotation is quantized, intrinsic, and topologically stable:

  1. Half-integer spin (Fermions): Corresponds to topological structures requiring a 720-degree rotation to return to their initial state (e.g., Möbius strip-like structures), explaining the statistical properties of fermions.
  2. Integer spin (Bosons): Corresponds to topological structures returning to their original state after a 360-degree rotation.

Thus, the "spin" described by quantum mechanics is no longer an abstract operator property but the geometric-dynamical essence of the fundamental topological vortex entity[7,8]. The quantization of the energy unit and the quantization of spin are unified here under a single geometric origin.

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