用斜交坐标轴画二维对称时空图

Using Oblique Coordinate Axes for Two-Dimentional Symmetric Space-time Diagrams

传统的二维时空图的画法,习惯上使基本坐标系的时空坐标轴相互垂直,但其他惯性坐标系的时空轴不可能再画得垂直,并且只要坐标系不同,则同类坐标轴上的相同长度表示的物理量大小就并不相同,即传统的时空图并不对称。对此,黄献民先生提出应将时空图画成对称的形式,并给出了一个特例,但并未说明对称时空图的普遍画法。事实上根据几何知识和狭义相对论的基本原理,对称时空图中的两套坐标系,必须让一个坐标系的空间轴垂直于另一个坐标系的时间轴,而让时间轴垂直于另一个坐标系的空间轴。在这样的时空图中尽管时空坐标轴是斜交的,但两个对称的坐标系中轴上相同长度代表着相同大小的物理量。此外还得到了一些有用的结果。

〔Abstract〕Traditional two-dimentional space-time diagrams are often drawn with time and space axes perpendicular to each other in the basic coordinate system but not perpendicular in other inertial coordinate systems. And per unit length of the same coordinate axis in different coordinate systems usually represents different physical quantity. Therefore, Huang Xianmin proposes that space-time diagrams should be symmetric and offers a special case but never explains its general drawing method. In fact, according to geometry and special relativity, in two coordinate systems of symmetric space-time diagrams, the space axis of one coordinate system must be perpendicular to the time axis of the other and the time axis of one coordinate system must be perpendicular to the space axis of the other. In this diagram, although with oblique space-time axes, per unit length of axis in two symmetric coordinate systems represents the same physical quantity. Other useful results are also obtained.