The Lorentz-Möbius Torsion Theorem presented in this paper establishes a rigorous connection between special relativity, spacetime torsion, and the hydrodynamic interpretation of quantum mechanics. By demonstrating that the integral of the Lorentz factor over all normalized velocities equals π/2, the theorem reveals an underlying angular normalization analogous to the quantization in spin fields. This result reflects the cumulative effects of relativistic transformations, where integrating over velocities yields a discrete angular measure akin to the quantized spin values in quantum mechanics. The theorem is explored in the context of Lorentz transformations and Möbius mappings, connecting these to physical phenomena such as rapidity, the behavior of spinors under boosts, and the intrinsic spin in quantum fields. Additionally, the discussion extends to the implications of spacetime torsion, as predicted by the Einstein-Cartan theory, and its unifying role in describing particles, black holes, and potential dark matter candidates through the lens of the holographic principle. This unified framework highlights how local spin-induced torsion can influence gravitational behavior, aligning with observations that suggest non-trivial topologies and quantum effects at cosmic scales.

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