时空代数的被动洛伦兹变换
Passive Lorentz transformations with spacetime algebra
摘要：
在狭义相对论中，时空代数（STA）为物理学的不变公式提供了一个强大而有见地的方法。然而，在这个时空的几何代数中，相对论物理学通常被认为是用词不当：STA为我们提供了一个不变的（无坐标的）公式，因此（被动的）洛伦兹变换似乎是放错了地方。然而，为了解释实验结果，重要的是将不变的物理量与某些参考系联系起来。在本文中，被动洛伦兹变换推导使用STA，但没有使用的第二个假设的光速爱因斯坦。这个推导揭示了STA的物理背景，同时，澄清了在适当的（闵可夫斯基）四维时空设置的洛伦兹变换。
英文摘要：
In special relativity, spacetime algebra (STA) provides a powerful and insightful approach to an invariant formulation of physics. However, in this geometric algebra of spacetime, relativistic physics is usually considered a misnomer: STA provides us with an invariant (coordinate-free) formulation and hence it seems that (passive) Lorentz transformations are misplaced. However, in order to interpret experimental results, it is important to relate invariant physical quantities to some reference frame. In this paper, passive Lorentz transformations are derived using STA but without the second postulate on the speed of light used by Einstein. This derivation sheds light on the physical background of STA and, at the same time, clarifies Lorentz transformations in the proper setting of (Minkowski) four-dimensional spacetime.
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