T₃ Topological Vortex Unified Field Theory T₃ 拓扑涡旋统一场论

Abstract This paper proposes a unified helical motion framework based on 3D number algebra, incorporating wave-particle duality, the relativistic energy-momentum relation, the constancy of the speed of light, the origin of mass, dark energy, and the accelerated expansion of the universe into a single geometric picture. Key findings include: (1) All elementary particles share a universal proper speed V₀=c√2, with the speed of light c being merely an upper bound on the axial projection speed; (2) Photon helical motion exhibits self-similarity—the radius Rᵧ=λ/(2π), all frequencies share the same helical shape up to scale, and the arc-length-to-axial-distance ratio ds/dz=√2 is constant for all photons; (3) The relativistic energy-momentum relation E²=(pc)²+(m₀c²)² is a natural consequence of the helical geometric constraint ; (4) Complete conversion of mass into kinetic energy corresponds to a phase transition as δ→0, not continuous acceleration; (5) The vacuum intrinsic field resistance ξᵥc=lnαg/L₀ (αg=3+√5, L₀=1.944 mm) yields a cosmic eigenfrequency fᵥc=c/L₀≈154 GHz, consistent with the CMB peak frequency; (6) The universe may be an S³ hypersphere undergoing helical motion in higher-dimensional space, with dark energy being the hyperbolic degree δᵥₑᵢᵣₛ≈1.21 of the universe, and accelerated expansion being a mathematical theorem of helical geometry. 摘要 本文提出一个基于三维数代数的螺旋运动统一框架,将波粒二象性、相对论能量-动量关系、光速不变原理、质量起源、暗能量和宇宙加速膨胀纳入同一几何图景。核心发现包括: (1) 所有基本粒子共享同一本征速度 V₀=c√2,光速c仅是轴向投影速度的上限; (2) 光子螺旋运动具有自相似性——半径Rᵧ=λ/(2π),所有频率共享同一螺旋形状,只是尺度缩放,且单位轴向距离弧长比ds/dz=√2对所有光子恒定; (3) 相对论能量-动量关系E²=(pc)²+(m₀c²)²是螺旋几何约束V₀²=vᵣᵢₜ²+vₐ₝ᵢₛ²的自然导出; (4) 质量完全转化为动能对应δ→0的相变而非连续加速; (5) 真空本征场阻ξᵥc=lnαg/L₀(αg=3+√5,L₀=1.944 mm)给出宇宙本征频率fᵥc=c/L₀≈154 GHz,与CMB峰值频率吻合; (6) 宇宙可能是S³超闭合球在更高维空间中的螺旋运动,暗能量即宇宙的双曲度δᵥₑᵢᵣₛ≈1.21,加速膨胀是螺旋几何的数学定理。