相对论现象的抽象数学处理
Abstract mathematical treatment of relativistic phenomena
摘要：
这个预印本涉及相对论中一个有趣的物理现象的数学严格处理。我们想提请读者特别注意相对论的抽象数学形式（在\cite{matolcsi2}中得到了充分详细的发展）。这样的处理方法使所有数学导向的读者在理解相对论时，不会感到在阅读了关于相对论的标准文本后常见的尴尬的模棱两可。在处理托马斯旋转的相对论现象的大量文献中，已经开发了几种方法来计算陀螺仪沿圆形世界线的托马斯旋转角。然而，最有吸引力的方法之一\cite{rindler}随后导致了\cite{herrera}中的矛盾，当对于同一圆形世界线获得三个不同的托马斯旋转角时。在本文中，我们解决这个矛盾，严格审查的理论背景和限制的原则，\cite{rindler}。
英文摘要：
This preprint concerns a mathematically rigorous treatment of an interesting physical phenomenon in relativity theory. We would like to draw the reader's attention particularly to the abstract mathematical formalism of relativity (which was developed in full detail in \cite{matolcsi2}). This treatment allows all mathematically oriented readers to understand relativity without feeling the awkward ambiguities that are so common after reading a standard text on relativity. In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing methods \cite{rindler}, however, subsequently led to a contradiction in \cite{herrera} when three different Thomas rotation angles were obtained for the same circular world line. In this paper we resolve this contradiction by rigorously examining the theoretical background and the limitations of the principle of \cite{rindler}.
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