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Einstein-Cartan Spacetime Torsion is NOT Sourced by Traditional Spin Density

Nielsen, Jenny Lorraine · 2025
PhilArchive · Papers · 2025
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philosophy
In gauge gravity unification on the complex Hopf fibration (Topological Unified Field Theory of "TUFT", gauge fields arise with the connection and torsion of the complex Hopf fibration S¹ → S^(2n+1) → CPⁿ, and spacetime torsion is sourced by the electromagnetic gauge field through its fiber holonomy. The dynamical operator is the Beltrami operator B = ⋆d on the contact distribution — not the Dirac operator — and its eigenmodes are the field configurations that couple to the fiber. From this vantage point, the Einstein–Cartan–Sciama–Kibble (ECSK) coupling of torsion to spin density is revealed as an artifact: Sciama and Kibble gauged the Poincaré group of flat spacetime and coupled only Dirac spinors to the resulting connection, excluding the gauge field from torsion by construction. In TUFT, no such separation exists — the gauge field and spin connection are components of a single unified connection, and their non-commutativity produces torsion directly. We identify the topology of electromagnetism, in which classical radiation fields are Hopf maps S³ → S² with topologically quantized helicity, as the natural field-theoretic realization of this coupling. Combining these results with the demonstration by Ciappina, Iorio, Pais, and Zampeli that torsion couples to electromagnetic fields through holonomy in the nonlinear response regime, we propose a specific physical mechanism: water molecules driven by rotating electric fields in a concentric cavity, coupling to the U(1) gauge field through their electric dipole moment to create an electromagnetic knot whose Hopf invariant sources fiber torsion. The resulting torsion gravitational field generates an effective warp geometry around the hull without exotic matter, with the Hopf invariant as the quantized control parameter. First presented at APEC 11/29/2025.
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