T₃拓扑弹性场论: 引力‑量子拓扑频率方程与宏观‑微观统一代数推导 T₃ Topological Elastic Field Theory: Gravitational‑Quantum Topological Frequency Equation and Unified Algebraic Derivation of Macro‑Micro Physics

摘要 广义相对论(由引力常数描述)与量子力学(由普朗克常数描述)长期存在理论割裂。本文立足于T₃拓扑弹性场论的基本公理:引力来源于能量激发的拓扑环流场,推导出引力场切向速度与等效能量的统一方程 。联立光子量子能量关系 ,得到引力‑量子拓扑频率方程 ,该式将与T₃拓扑曲率因子纳入同一自洽代数框架。本文采用等效拓扑势能方法完成引力红移严格积分推导,在弱场极限下精确复现史瓦西度规对应的广义相对论引力红移结果。证明在T₃体系中宏观引力效应与微观量子频率是同一拓扑曲率场的不同物理投影。 关键词:拓扑弹性场;统一场论;引力红移;量子引力;拓扑曲率因子 第一章 引言——与的百年理论割裂 自普朗克量子假说提出与广义相对论建立以来,现代物理学形成两大支柱。在现有标准物理框架内,引力常数、普朗克常数与真空光速均作为经验输入常数,理论无法解释其固有数值,也难以说明引力相对其他基本力的极弱耦合(引力相较电磁力弱约倍)。 T₃拓扑弹性场论提出:并非完全相互独立的基础参数,而是底层拓扑弹性场的不同响应属性。引入自定义拓扑曲率因子,可以搭建起引力与量子之间的代数桥梁,实现宏观引力现象与微观量子行为的形式统一。 Abstract General Relativity (described by gravitational constant ) and quantum mechanics (described by Planck constant ) suffer long‑standing theoretical disconnection. Based on the fundamental axiom of T₃ topological elastic field theory that gravity originates from energy‑excited topological circulation fields, we derive a unified equation for tangential velocity and equivalent energy in gravitational field: . Combined with photon quantum energy relation , the gravitational‑quantum topological frequency equation is obtained. This formula incorporates , , and the T₃ topological curvature factor into one self‑consistent algebraic framework. By means of equivalent topological potential, strict integral derivation for gravitational redshift is carried out. In the weak‑field limit, results exactly reproduce gravitational redshift from Schwarzschild metric in General Relativity. It is demonstrated within the T₃ framework that macroscopic gravitational effects and microscopic quantum frequency are different physical projections of the same topological‑curvature field. Keywords: topological elastic field; unified field theory; gravitational redshift; quantum gravity; topological curvature factor 1 Introduction — The Century‑Long Theoretical Separation of and Since the proposal of Planck’s quantum hypothesis and the establishment of General Relativity, modern physics has two major pillars. Within the standard physical framework, , and speed of light are treated as empirical input constants. Existing theories cannot explain their intrinsic numerical values, nor the extreme weakness of gravity compared with other fundamental interactions (gravity is weaker than electromagnetism by a factor of about ). T₃ topological elastic field theory proposes that , and are not fully independent fundamental parameters; instead they represent different response properties of the underlying topological elastic field. By introducing the custom‑defined topological curvature factor , an algebraic bridge between gravitation and quantum physics can be constructed to formally unify macroscopic gravitational phenomena and microscopic quantum behaviours.