时空流形存在的操作性验证
Operational verification of the existence of a spacetime manifold
AI总结：
本文提出一种与理论无关的思想实验协议，通过实验信号验证时空流形的可观测性，并确立时空涌现的标准，以检验其是否源于更基本概念。
摘要：
我们认为存在一种操作性方法来确立空间和时间概念的可观测性。具体而言，我们提出了一种与理论无关的思想实验协议，其结果是产生一个信号，用以确立时空流形的可观测性，而无需先验地假设其存在。该实验信号包含关于时空维度和拓扑的信息（在当前可达到的精度下），并确立其流形结构，同时尊重其底层的微分同胚对称性。我们还引入并讨论了时空涌现概念的适当标准，任何试探性的理论物理模型必须满足这些标准，才能声称时空确实是从某些更基本的概念中涌现出来的。
英文摘要：
We argue that there exists an operational way to establish the observability of the notions of space and time. Specifically, we propose a theory-independent protocol for a gedanken-experiment, whose outcome is a signal establishing the observability of the spacetime manifold, without a priori assuming its existence. The experimental signal contains the information about the dimension and the topology of spacetime (with the currently achievable precision), and establishes its manifold structure, while respecting its underlying diffeomorphism symmetry. We also introduce and discuss appropriate criteria for the concept of emergence of spacetime, which any tentative theoretical model of physics must satisfy in order to claim that spacetime does emerge from some more fundamental concepts.
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