符合“欧氏几何”的洛伦兹变换图示法的设计

A DESIGN OF GRAPHIC METHOD OF THE LORENTZ TRANSFORMATION ACCORDING WITH EUCLIDEAN GEOMETRY

文章将洛伦兹变换简化为几何函数形式,根据这些几何函数构造若干直角三角形,表示洛伦兹变换的两参考系时空坐标值相互关系,逐步设计了与“闵氏几何”的闵可夫斯基时空图不同的洛伦兹变换图示法,以符合“欧氏几何”的形式表示洛伦兹变换。设计过程中,提出一种“火车铁轨”模型,结合图示法,描述了狭义相对论时空中的几种典型物理现象,包括两参考系相互观察、异地同时性的破坏和长度收缩。此图示法可以作为一种借鉴,帮助初学者和爱好者学习洛伦兹变换和狭义相对论。

This paper simplifies the Lorentz transformation to a set of geometric functions,and constructs right triangles according to these functions,to represent the relations of the coordinates of time and space axes of two reference systems.Step by step,this paper designs a graphical method of the Lorentz transformation which accord with Euclidean geometry and is distinct from geometry of Minkowski space-time.In the designing process,this paper establishes a“train-rail”model,in conjunction with the graphic method,to describe several typical physical phenomena in space-time of the special theory of relativity,including mutual observation in two reference systems,failure of simultaneity at a distance and the Lorentz contraction.The graphic method can be used as a reference for learners and amateurs to understand the Lorentz transformation and the special theory of relativity.