转盘时空中的同时面与周长佯谬

Synchronous surface and the perimeter paradox in the rotating disc spacetime

证明了转盘时空中所有以z轴为对称轴的圆柱面,以及通过z轴的平面均为二维同时面.因而,在转动系中对位于圆柱面上的圆周周长进行测量是有意义的.在转动系中计算出了转盘周长,以及与转盘圆周"重合"但静止在惯性系中的圆周长,所得的结果与惯性系中所测相同,从而解决了周长佯谬问题.

It is proven that all of the cylinders symmetrized to the rotating axis, the z-axis, and the planes passing through the z-axis, are 2-dimensional synchronous surfaces. Therefore, the measure to the length of a circumference located on a cylinder symmetrized to the z-axis in the rotating coordinate sysyem is suitable. The circumference is measured in rotating coordinate system and static coordinate system, respectively. The perimeter paradox is solved.