论文标题
关于相对性原则的绝对观点
A Categorical View on the Principle of Relativity
论文作者
论文摘要
类别理论在数学方面起着特殊的特征 - 它在同一形式主义下统一了不同的分支。尽管在数学方面具有这种综合性，但它似乎也为实验物理学家提供了适当的基础。在这项工作中，我们介绍了与相对论原理有关的物理学类别的另一种应用。 （惯性）参考框架的操作结构表明，只有一个和另一个框架之间的运动足以区分它们。当人们仅应用群体理论连接帧时，这一事实就会隐藏。实际上，旋转和翻译只会改变坐标，保持框架惰性。镜架的变化只能通过伽利略和洛伦兹（Poincaré）组的古典和相对论政权的提升来实现。除了提供类别理论在物理学中应用的非平凡示例外，当人们直接将群体理论应用于连接帧时，我们还达到了所提出的差距。
Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this work, we present another application of category in physics, related to the principle of relativity. The operational construction of (inertial) frames of reference indicates that only the movement between one and another frame is enough to differentiate both of them. This fact is hidden when one applies only group theory to connect frames. In fact, rotations and translations only change coordinates, keeping the frame inert. The change of frames is only attainable by boosts in the classical and relativistic regimes for both Galileo and Lorentz (Poincaré) groups. Besides providing a non-trivial example of application of category theory in physics, we also fulfill the presented gap when one directly applies group theory for connecting frames.
