不要求速度不变的洛伦兹变换
Getting the Lorentz transformations without requiring an invariant speed
摘要:
洛伦兹变换的结构完全是由于没有特殊的惯性参考系和变换的群结构(复合下的封闭)-这两个假设是简单的,而且是物理上必要的。不变速度的存在是\textit{not}的一个必要假设,事实上是相对性原理的一个结果(当然,这个速度的有限值必须从实验中获得)。冯·伊格纳托夫斯基在1911年得出了这个结果,但它仍然不广为人知,并且在大多数教科书中都没有。在这里,我们提出了一个完全初等的证明结果,适用于在狭义相对论的入门课程。
英文摘要:
The structure of the Lorentz transformations follows purely from the absence of privileged inertial reference frames and the group structure (closure under composition) of the transformations---two assumptions that are simple and physically necessary. The existence of an invariant speed is \textit{not} a necessary assumption, and in fact is a consequence of the principle of relativity (though the finite value of this speed must, of course, be obtained from experiment). Von Ignatowsky derived this result in 1911, but it is still not widely known and is absent from most textbooks. Here we present a completely elementary proof of the result, suitable for use in an introductory course in special relativity.
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