论文标题
时空结构可能是拓扑的，而不是几何学
Space-time structure may be topological and not geometrical
论文作者
论文摘要
在先前的努力[Arxiv：1708.05492]中，我们创建了一个框架，解释了为什么在科学理论中自然出现拓扑结构。也就是说，它们捕获了实验验证的要求。这特别有趣，因为拓扑结构是几何结构的基础，在现代数学物理学中起着基本作用。在本文中，我们将展示一组必要和充分的条件，在这些条件下，这些拓扑结构导致实际数量和歧管，这是几何的典型要求。这些条件将提供一个物理上有意义的过程，这是数学中使用dedekind削减的物理反应部分。然后，我们表明这些条件不太可能在普朗克量表上满足，从而导致订购概念的细分。这将表明在该规模上描述时空所需的数学结构虽然仍然拓扑，但可能不是几何学。
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is particularly interesting because topological structures are at the foundation of geometrical structures, which play a fundamental role within modern mathematical physics. In this paper we will show a set of necessary and sufficient conditions under which those topological structures lead to real quantities and manifolds, which are a typical requirement for geometry. These conditions will provide a physically meaningful procedure that is the physical counter-part of the use of Dedekind cuts in mathematics. We then show that those conditions are unlikely to be met at Planck scale, leading to a breakdown of the concept of ordering. This would indicate that the mathematical structures required to describe space-time at that scale, while still topological, may not be geometrical.
