论文标题
Minkowski时空的公理系统
A system of axioms for Minkowski spacetime
论文作者
论文摘要
我们为Minkowski时空的几何形状提供了一个基本系统。它在简单和流线的公理集之间达到了平衡，并尝试在[Maudlin 2012]中的Minkowski Spacetime的标准帐户的一阶逻辑中进行直接形式化，而[Malament，未公开]。它旨在将来在Minkowski时代的物理理论形式上使用。原语的选择是本着[Tarski 1959]的精神：彼此之间的谓词和一个四个地方的谓词，以比较相对论间隔的平方。 Minkowski时空被描述为一个四维的“矢量空间”，可以在[Tarski and Givant，1999]中的欧几里得公理和正交时间式的线条中遵守欧几里得公理。其他“向量”的长度是根据毕达哥拉斯定理计算的。我们以一个表示模型为代表定理结束了我们的系统的$ \ mathfrak {m} $ $ \ mathcal {m}^1 $，使二阶连续性与数学结构$ \ langle \ langle \ mathbb {r}^{4}^{4}，η_{ab} {ab {ab} \ rangle $ spackient callationd patiftions nation patiftient clatchski，
We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional `vector space' that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other `vectors' are calculated according to Pythagoras' theorem. We conclude with a Representation Theorem relating models $\mathfrak{M}$ of our system $\mathcal{M}^1$ that satisfy second order continuity to the mathematical structure $\langle \mathbb{R}^{4}, η_{ab}\rangle$, called `Minkowski spacetime' in physics textbooks.
