Bridging Spacetime Geometry and Quantum Phenomena: A Triaxillary Model

This paper presents a formal derivation of the field equations for a simplified model of the Triacillary Theory of Spacetime (TSGT), a novel extension of General Relativity that incorporates a dynamic torsion field and an oscillatory scalar field. Built on a Riemann–Cartan geometric framework, the theory treats the axial torsion vector Sμ and scalar field φ as independent, propagating degrees of freedom coupled to quantum matter. Using the Euler–Lagrange formalism, we derive modified field equations that predict a dynamic, propagating torsion field, sourced by the quantum chiral current and the scalar field gradient.Crucially, we propose two experimental signatures of torsion. First, a Chiral Neutron InterferometryTest predicts that quantum interference patterns will show measurable asymmetries or “fuzziness around the edges” due to the influence of a localized torsion field. Second, a Non-Local Torsion Resonance Test proposes that a time-dependent perturbation of a distant entangled particle group can emit a propagating torsion field, which would be detected as a time-synchronized, chiral asymmetry in a separate neutron beam. These two tests offer a dual pathway to a testable bridge between geometry and quantum mechanics, laying a foundation for experimental investigations into spacetime torsion using light or spin-polarized quantum particles.