适度相对性理论初探
A Preliminary Exploration of the Theory of Moderate Relativity
摘要
狭义相对论经受住了无数高能物理实验（包括极端情况下）的考验，但是所有实验室参考系都不是严格的惯性系；而在经典力学框架下，一个基于平动参考系形式不变的适度相对性原理已经在质点动力学上得到了简洁明确的实现，并且提示参考系的运动对动力学的影响只能直接且唯一地归结为参考物的真实受力。因此，有必要在理论上探讨光速不变原理与加速平动参考系（即原点可任意加速，坐标轴不转动）结合的可能性。本文在加速平动参考系中通过引入弹性坐标（指坐标标度随加速平动参考质点自带的时钟和标尺的变化而调整的坐标系），指出在弹性坐标系中，坐标光速仍可保持不变，且时空度规仍维持为闵可夫斯基形式。由此给出了在平动参考系变换下保持形式不变的相对论性的质点动力学方程。根据因果对称的基本要求，与观测相对应的力学量必须定义为待考察质点和参考质点的受力相对统计，在表述上需要引入四维的相对统计的单位质量受力的协变矢量代替原来的四维力矢量。在变换性质方面，所有瞬时的四维协变量在任意平动参考系之间（相差U和A ）的变换规则中，除相对协变量在相对匀速 的参考系之间遵循洛伦兹变换外，还必须直接加上协变量在瞬时静止但存在相对加速 的平动参考系之间变换带来的增量。
Abstract
Special relativity has withstood the test of a wide range of high-energy physics experiments, including those under extreme conditions. However, no laboratory reference frame is strictly inertial. Within the framework of classical mechanics, a moderate principle of relativity, based on the formal invariance of physical laws in translational reference frames (non-rotating), has been elegantly realized for particle dynamics. This principle indicates that the influence of a reference frame's motion on particle dynamics can be directly and uniquely attributed to the real forces acting on the reference object. Therefore, it is necessary to theoretically explore the possibility of integrating the principle of the constancy of the speed of light and the moderate principle of relativity with accelerated translational reference frames. This paper explores introducing scale-varying coordinates (a coordinate system where the coordinate scale adjusts according to changes in the clock and ruler carried by the reference particle) within an accelerated translational reference frame. It is only possible to achieve the invariance of the coordinate speed of light while maintaining the Minkowski metric for coordinate space-time in this way. Consequently, a generalized relativistic particle dynamics equation that remains formally invariant in any accelerated translational reference frames is derived. Based on the fundamental requirement of causal symmetry, mechanical quantities corresponding to observations must be defined as the relative forces acting on the particle under study and the reference particle. This necessitates introducing a four-dimensional relative force vector to replace the original four-dimensional force vector in the formulation. The transformation of all instantaneous four-covariant quantities between arbitrary translational reference frames must satisfy the following rule: In addition to following the Lorentz trans formation between reference frames moving with constant relative velocity, the transformation must also directly incorporate the increment resulting from the transformation of covariant quantities between translation reference frames that are instantaneously at rest relative to each other, but which possess relative acceleration.关键词
加速平动参考系/光速不变原理/弹性坐标/相对论性质点动力学方程Key words
accelerated translational reference frame/the principle of the constancy of the speed of light/scale-varying coordinate/relativistic particle dynamics引用本文复制引用
陈驰一.适度相对性理论初探[EB/OL].(2026-03-03)[2026-03-07].https://chinaxiv.org/abs/202603.00032.学科分类
物理学
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