论文标题
证明相对论旋转悖论
Proving the Relativistic Rotation Paradox
论文作者
论文摘要
爱因斯坦（Einstein）相对论特殊理论的明显悖论，被称为原子物理学中的托马斯预肠旋转，已经通过多种方式进行了实验验证。但是，有些令人惊讶的是，尚未使用Lorentz-Matrix-algebra以简单的方式进行代数证明。过去，作者求助于计算机验证或过于复杂的派生，使本科生尤其具有这种印象，即这是一种神秘且数学上难以接近的现象。这是令人惊讶的，因为如本注中所示，可以使用正交Lorentz矩阵的基本属性，以及与相关惯性框架配置配置的明智选择，以提供非常透明的代数证明。对于物理学生，尤其是在本科级别的教学上，探索这一点是有用的。它不仅在可访问的数学层面上阐明了悖论的性质，还阐明了洛伦兹矩阵和相对移动的框架的某些数学特性。它还说明了与无启发的计算或折磨的推导相比，对物理问题可能带来的清晰数学理解可以带来的满意度。
An apparent paradox in Einstein's Special Theory of Relativity, known as a Thomas precession rotation in atomic physics, has been verified experimentally in a number of ways. However, somewhat surprisingly, it has not yet been demonstrated algebraically in a straightforward manner using Lorentz-matrix-algebra. Authors in the past have resorted instead to computer verifications, or to overly-complicated derivations, leaving undergraduate students in particular with the impression that this is a mysterious and mathematically inaccessible phenomenon. This is surprising because, as shown in the present note, it is possible to use a basic property of orthogonal Lorentz matrices and a judicious choice for the configuration of the relevant inertial frames to give a very transparent algebraic proof. It is pedagogically useful for physics students particularly at undergraduate level to explore this. It not only clarifies the nature of the paradox at an accessible mathematical level and sheds additional light on some mathematical properties of Lorentz matrices and relatively-moving frames. It also illustrates the satisfaction that a clear mathematical understanding of a physics problem can bring, compared to uninspired computations or tortured derivations.
