AI 中文总结
该研究提出狭义相对论表述，从伽利略空间变换出发，经分析得出公理结构与洛伦兹变换，还考虑惯性电荷系统，推导电磁场方程和力定律，为林德曼断言提供框架，且结果与单位选择无关，能推断现象在不同时空的表现。
AI 中文摘要
我们提出了一种狭义相对论的表述，这与F.A.林德曼的断言相关，即该理论‘在艾萨克·牛顿之后不久就可以通过纯粹逻辑得出’。我们从‘直观上合理’的伽利略空间变换对开始。这些简单关系具有丰富的十种性质结构。从中可辨别出一种公理结构（和同步约定），从而导出包含通用常数\(V^2\)的著名洛伦兹型变换。对菲佐实验（1851年）的分析表明\(V^2 = c^2\)，其中\(c\)是真空中的光速，由此得到洛伦兹变换。这种表述的必要条件（伽利略相对性原理、分析力学、改变假设的方法等）在17世纪和18世纪出现。这些观察为林德曼的断言提供了一个框架。我们还考虑了惯性运动的电荷系统，并通过将洛伦兹型变换应用于静电学理论来推导电磁场方程和力定律。结果与任何单位选择无关，并且从它们对\(V^2\)的依赖关系可以推断出某些现象在三种可能的时空类型中的每一种中是如何表现的。
英文摘要
We present a formulation of the special theory of relativity which bears on F.A. Lindemann's assertion that this theory could have been reached "by pure logic soon after Isaac Newton". We start with the "intuitively plausible" pair of Galilean spatial transformations. These simple relations possess a rich structure of ten properties. From these, one discerns an axiomatic structure (and a synchrony convention) leading to the well-known Lorentz-type transformations which contain a universal constant, $V^2$. Analysis of Fizeau's experiment (1851) shows that $V^2 = c^2$, where $c$ is the speed of light in vacuo. Hence one obtains the Lorentz transformation. Requisites for such a formulation (Galileo's relativity principle, analytical mechanics, the method of changing a postulate, etc.) emerged during the 1600s and 1700s. These observations provide a framework for Lindemann's assertion. We also consider inertially-moving systems of charge, and derive electromagnetic field equations and a force law by applying the Lorentz-type transformations to the theory of electrostatics. The results are independent of any choice of units, and from their dependence on $V^2$ one can infer how certain phenomena manifest in each of the three possible types of space-time.
