Scale Motion as an Independent Degree of Freedom, the Principle of Scale Relativity, and the Scale Radiation Equation 尺度运动独立自由度、尺度相对性原理与标度辐射方程

Abstract Traditional physics confines motion to changes of position within three-dimensional Euclidean coordinates and treats scale merely as an auxiliary parameter of coordinates. Based on T₃ topological elastic field theory, this report proposes a dynamical channel fully on an equal footing with positional motion—Scale Dynamics. In the T₃ hyper-Euler algebra , the scalar amplitude constitutes an independent intrinsic scale degree of freedom. This report rigorously derives the kinematic quantities of pure scale motion (the scale rate , the scale acceleration ), the conserved quantity under the mid-path constraint (the scale momentum ), and constructs the power equation for the scale radiation produced by scale acceleration. More centrally, this report proposes and proves the “Principle of Scale Relativity and Equivalence Theorem”: the active expansion of an object () and the passive contraction of the background space () are completely observationally equivalent. It further proposes a scale-confinement mechanism: at low energy and ordinary temperature, is topologically locked by the associator; it is released only at high-energy singularities. This theory provides a new dynamical-channel explanation for high-energy cosmological phenomena, dark energy, and topological phase transitions. Research statement: In this report, the scale-radiation power equation is a tentative dynamical conjecture constructed in analogy with classical electromagnetic radiation (the Larmor formula); a complete rigorous derivation requires starting from the action of the T₃ topological elastic field and integrating the retarded topological stress, which constitutes next-stage work. The framework’s central prediction (release of the scale-radiation channel at high energy) is falsifiable in principle. Keywords: Scale motion; Principle of scale relativity; Scale momentum; Scale radiation; Scale confinement; T₃ topological elastic field theory 摘要 传统物理学将运动局限于三维欧氏坐标内的位置变化,将尺度视为坐标的附属参数。本报告基于 T₃ 拓扑弹性场论,提出一种与位置运动完全平权的独立动力学通道——尺度运动(Scale Dynamics)。 在 T₃ 超欧拉代数 中,标量振幅 构成独立的内禀尺度自由度。本报告严格推导了纯尺度运动的运动学量(标度速率 、标度加速度 )、中道约束下的守恒量(标度动量 ),并构造了标度加速度产生标度辐射的功率方程。 更为核心的是,本报告提出并证明了”尺度相对性原理与等效性定理”:客体主动膨胀()与背景空间被动收缩()在观测上完全等效。同时提出尺度禁闭机制:低能常温下 被结合子拓扑锁定,高能奇点处才解禁。这一理论为宇宙高能现象、暗能量以及拓扑相变提供了全新的动力学通道解释。 研究声明:本报告中标度辐射功率方程为对标经典电磁辐射(拉莫尔公式)构造的试探性动力学猜想式,完整严格推导需要从 T₃ 拓扑弹性场的作用量、推迟拓扑应力积分出发,属于下一阶段工作。本框架的核心预言(高能下标度辐射通道解禁)具备原则上的可证伪性。 关键词:尺度运动;尺度相对性原理;标度动量;标度辐射;尺度禁闭;T₃拓扑弹性场论