We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to construct matrices of inner products which are then factored using the singular value decomposition to give coordinates in Minkowski spacetime. Results are presented showing good quality embeddings into Minkowski spacetime for dimensions d = 2, 3, 4. The method applies in any dimension and does not require spacelike distances to be used as an input. It offers a new way to define spatial orientation and spacelike distances in a causal set.

中文翻译：

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将因果集嵌入闵可夫斯基时空

我们提出了一种将因果集嵌入 Minkowski 时空区间的新方法。该方法使用因果相关元素的时空体积来定义 Minkowski 内积的因果集类比。这些用于构造内积矩阵，然后使用奇异值分解对内积矩阵进行因式分解，给出闵可夫斯基时空的坐标。呈现的结果显示了良好质量的嵌入到 Minkowski 时空中的维度d= 2, 3, 4。该方法适用于任何维度，不需要将空间距离用作输入。它提供了一种在因果集中定义空间方向和空间距离的新方法。