广义相对论速度与时空代数的叠加
Generalized relativistic velocity addition with spacetime algebra
摘要：
利用时空代数，时空的几何代数，速度的相对论性添加的一般问题进行处理。然后在闵可夫斯基时空中研究了非共线洛伦兹助推的连续应用。即使是空间向量，例如两个参考系的相对速度，也是在其适当的设置下进行分析的：作为属于四维时空流形的向量，而不是作为普通三维（欧几里德）空间中的向量。这是一个清晰的物理结果，说明了洛伦兹助推不形成群的事实。整个推导过程没有使用光速第二公设，从而强调了狭义相对论的框架不依赖于电磁学。
英文摘要：
Using spacetime algebra, the geometric algebra of spacetime, the general problem of relativistic addition of velocities is addressed. The successive application of non-collinear Lorentz boosts is then studied in Minkowski spacetime. Even spatial vectors, such as the relative velocity of two reference frames, are analyzed in their proper setting: as vectors belonging to a four-dimensional spacetime manifold and not as vectors in ordinary three-dimensional (Euclidean) space. This is a clear and physical result that illustrates the fact that Lorentz boosts do not form a group. The entire derivation is carried through without using the second postulate on the speed of light, thereby stressing that the framework of special relativity does not depend on electromagnetism.
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