众所周知，自然界中存在着四种基本相互作用，分别为强相互作用、弱相互作用、电磁相互作用与引力相互作用。然而，前三者可以在量子力学的框架下自洽，只有特殊的引力相互作用尚未与其他相互作用统一。因此，追求引力的量子化是现代物理学最迫切和首要的目标。物理学家们发现，可以利用量子场论的方法来研究引力理论。在这过程中，我们发现量子纠缠、几何以及时空定域性之间的关系，这似乎暗示了通往量子引力的研究方向。通过量子纠缠，我们希望进一步探索量子引力领域，为引力的量子化找到一个突破口，从而发现时空的本质。文章简要回顾量子纠缠熵的历史发展，并讨论纠缠熵与几何之间的关系。
We review recent progresses on entanglement entropy and Page curve of black holes, and discuss the relationship between entanglement entropy and geometry. As is well-known, there are four fundamental interactions in nature: the strong interaction, the weak interaction, the electromagnetic interaction, and gravity. However, the first three interactions have already been unified by quantum theory, with only gravity remaining as a separate theory from the others. Therefore, the most important objective of modern physics is to study the theory of quantum gravity. Physicists have found that they can use quantum field theory to study gravity. In this process, we can discover the relationships among quantum entanglement, geometry, and the localization of spacetime, which implies the direction of the development of quantum gravity. We hope to find a breakthrough in the quantization of gravity through quantum entanglement. We then are able to explore the nature of quantum gravity and further understand the nature of spacetime.
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