托马斯旋转与参考系的角速度的关系
On the relation of Thomas rotation and angular velocity of reference frames
摘要：
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。在\cite{rindler}中引入的最吸引人的概念之一是考虑与陀螺仪共同运动的旋转参考系，并将陀螺仪的进动与参考系的角速度相关联。然而，最近的论文\cite{herrera}将这一原理应用于三个不同的同向移动旋转参考系，并得到三个不同的托马斯旋转角。出现这种明显矛盾的原因是，\cite{rindler}的原则被用于一种它并不适用的情况。在本文中，我们严格审查的理论背景和适用性的\cite{rindler}原则的限制。在此过程中，我们还建立了一些一般性质的{ \it旋转参考系}，这可能是独立的利益。
英文摘要：
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 concepts, introduced in \cite{rindler}, is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper \cite{herrera}, however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of \cite{rindler} is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of \cite{rindler}. Along the way we also establish some general properties of {\it rotating reference frames}, which may be of independent interest.
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