关于间隔不变性与洛仑兹变换的几点注记

Notes on the Invariance of the Interval

两个事件之间隔不变性(Δs )2=(Δs)2是狭义相对论的两个基本原理与时空的均匀性及空间各向同性之直接推论;间隔不变性(ds )2=(ds)2=-dx μdx μ=-dxμdxμ给出闵可夫斯基四维空间的度规,决定了狭义相对论的时空性质;由于洛仑兹变换可由间隔不变性直接推出,所以,洛仑兹变换及伽利略变换都是对两个事件之空间、时间坐标差Δxμ与Δx μ而言的;有时,利用间隔不变性讨论问题比利用洛仑兹变换更简便.

The invariance of interval between two point events is directly dervied from Einstein's two postulates of the special theory of relativty, and the uniformity of the time and the uniformity and isotropy of space; the invariant interva(ds)~2=(ds)~2give the 'metric' in the Minkowski-space, and it determine the properties of the time and space in the special theory of relativty; because te Lorentz transformation is a consequence of the invariance of the interval between two events, therefore, the Lorentz and the Galiean transformation is transformation conceming the spatial and temporal separation Δx_μ to Δx~_μ between two events on transition from one inertial frame of reference to another frame; sometime it is easier to think in terms of the invariant interval than in terms of transformation.