相对性原理与时空线性变换  

THE PRINCIPLE OF RELATIVITY AND THE SPACE-TIME LINEAR TRANSFORMATION

作　　者：戴又善[1,2] DAI Youshan(Zhejiang University City College,Hangzhou Zhejiang 310015;Department of Physics,Zhejiang University,Hangzhou Zhejiang 310027)

机构地区：[1]浙江大学城市学院,浙江杭州310015 [2]浙江大学物理系,浙江杭州310027

出　　处：《物理与工程》2018年第4期70-77,共8页Physics and Engineering

基　　金：浙江省自然科学基金;相对论理论的研究与改进(LY17A050001)

摘　　要：惯性系具有任何方向时空平移不变的特性,依据相对性原理和时空平移不变性证明了惯性系的时空变换必须为线性变换。相对性原理是时空线性变换的真正必要条件。除了伽利略变换具有"同时的绝对性"外,其他的惯性系时空线性变换都具有"同时的相对性"。利用相对性原理还可以证明惯性系的速度变换为单调递增函数,因而存在速度上限,惯性系除伽利略变换外的所有时空线性变换都存在有限的极限速度,进而可以推导出惯性系时空线性变换的广义洛伦兹变换公式,其中极限速度的取值可以通过实验来确定。Inertial reference frames are invariant under translations of space and time in all directions.The principle of relativity,combined with the translational invariance,require that space and time coordinates transform linearly between inertial reference frames.The principle of relativity is a fundamentally necessary condition for the linearity of space-time transformations.All possible linear transformations for inertial frames incorporate a relative notion of simultaneity,except in the special case of the Galilean transformation,for which an absolute notion of simultaneity holds.On the basis of the principle of relativity,it can be proven that the velocity transformation for inertial reference frames monotonically increases,and results in an upper bound for the velocity,which is finite for all linear space-time transformations but the Galilean transformation.The generalized Lorentz transformation formulae for inertial reference frames can then be derived,which contain a universal speed limit whose value can be experimentally determined.

关 键 词：相对性原理 时空平移不变性 时空线性变换 同时的相对性 极限速度 广义洛伦兹变换 

分 类 号：O412.1[理学—理论物理]