T3 拓扑弹性场论 从莫比乌斯闭锁到光子开环相变的动力学演化专论 Topological Elastic Field Theory: Monograph on Dynamical Evolution from Möbius Locked‑Loop to Photon Open‑Loop Phase Transition

Abstract Within the framework of T3 topological elastic field theory, this monograph presents a complete dynamical mechanism for the topological phase transition from the electron (Möbius closed‑loop) to the photon (open‑loop helix). Using the T3 non‑associative algebra and Frenet‑Serret frame formalism, we rigorously derive the geometric unlocking process from the full‑power closed‑loop electron state () to the open‑loop photon state () via the superposition‑effect coefficient and dynamical‑velocity formula. A core innovation is the golden‑fractal exponential‑decay ansatz (), which describes the geometric relaxation of outward‑propagating vortex filaments after topological unlocking. We rigorously demonstrate that curvature and torsion must converge to small non‑zero constants. Based on the postulate of multi‑component motion preference and the principle of least action, we provide an active dynamical interpretation: the helical configuration of the photon is an orthogonally‑superposed geometry actively selected by motion to minimize action and maximize energy efficiency. Two post‑transition branches are established by decay properties: finite‑arc‑length evolution produces a “virtual‑vortex cloud” as the geometric origin of the electron anomalous magnetic moment; asymptotic evolution over infinite arc‑length yields real‑photon radiation with polarization handedness determined by the sign of torsion. Finally, rigorous defensive statements are given concerning non‑associative algebraic corrections and the phenomenological nature of golden‑ratio decay. Keywords: T3 topological elastic field theory; Möbius loop; topological phase transition; golden‑fractal decay; virtual‑vortex cloud; photonic helix; principle of least action 摘要 本报告基于T3拓扑弹性场论框架,提出了从电子(莫比乌斯闭环)向光子(开环螺旋)拓扑相变的完整动态演化机制。报告引入T3代数基底与Frenet‑Serret标架,通过叠加效应系数与动力学速度公式,严格推导了电子闭环满功率态()向光子开环态()的几何解锁过程。核心创新在于提出了黄金分形指数衰减动力学假设(),用以描述相变解锁后涡旋丝沿轴向向外延展的几何松弛行为。报告严格论证了曲率与挠率必须收敛于非零小常数,并基于“多分量运动偏好”与“最小作用量原理”给出了主动的动力学解释:光子的螺旋态是运动为追求最小作用量、实现能量效率最大化而主动选择的正交叠加构型。基于衰减特征,报告证明了相变后的两种分支:有限弧长演化形成“虚涡旋云”(几何起源为反常磁矩),无限弧长渐近展开形成“实光子辐射”(挠率符号决定偏振)。最后,报告对非结合代数修正项与黄金衰减的唯象性进行了严格的防御性声明。 关键词:T3拓扑弹性场论;莫比乌斯环;拓扑相变;黄金分形衰减;虚涡旋云;光子螺旋;最小作用量