Gravity and Entanglement

理论物理学中一些最重大的未决问题直接存在于量子力学和引力的交汇处。我们的宇宙是如何开始的？它将如何结束？什么是暗能量？黑洞里面有什么？这些问题中的每一个都是我们理解自然的基础，但在一个不包括引力和量子物理学的框架内，它们都无法得到回答。弦理论的最新发展使我们比以往任何时候都更接近于回答这些问题。20年前，弦理论的研究人员发现了量子引力物理学和量子场论物理学之间惊人的联系，量子场论是物理学家用来理解基本粒子及其相互作用的数学模型。通过这种被称为AdS/CFT对应的联系，以前无法回答的量子引力问题可以转化为更简单的问题，可以用量子场论来回答。关于AdS/CFT的一个非常基本的问题是理解动态时空物理学（爱因斯坦引力理论的关键特征）是如何从普通量子场论的物理学中出现的。最近，有许多令人兴奋的进展表明，这个问题的答案在于量子信息理论（量子计算机背后的理论）的新兴领域。根据我们小组和其他人的工作，量子纠缠现象在理解时空和引力的本质方面起着核心作用；这一观察结果有助于更好地理解引力在基本层面上是如何工作的。例如，现在我们知道，量子场论中纠缠的某些度量直接对应于相应引力理论中的几何度量。利用这一点，我们已经证明，在某些情况下，控制时空动力学及其与物质相互作用的爱因斯坦方程可以直接从相应场论中的量子纠缠物理学中推导出来。在提议的研究中，我计划以各种方式利用重力和量子信息理论之间的这些新兴联系。我想把我们对爱因斯坦方程的推导扩展到更广泛的场论状态，并研究这些方程的可能的量子修正。我计划扩展一些早期的工作，以研究来自量子信息理论的各种纠缠约束的引力含义。最后，我计划探索我们最近提出的一种情况，通过这种情况，AdS/CFT对应关系可能被用来提供宇宙学模型，帮助我们更好地理解宇宙的开始，它通过暗能量加速膨胀，以及它的结束。

Some of the grandest open questions in theoretical physics lie directly at the interface of quantum mechanics and gravity. How did our universe begin? How will it end? What is dark energy? What is inside a black hole? Each of these questions is fundamental to our understanding of nature, but none of them can be answered in a framework that does not include both gravity and quantum physics. Recent developments in string theory have brought us closer than ever before to answering questions like these. Twenty years ago, researchers in string theory discovered a stunning connection between the physics of quantum gravity and the physics of quantum field theories, the well-understood mathematical models that physicists use to understand elementary particles and their interactions. Through this connection, known as the AdS/CFT correspondence, quantum gravity questions that were previously impossible to answer can be translated into much simpler questions that can be answered by quantum field theory. A very basic question about AdS/CFT is to understand how the physics of dynamical spacetime (the key feature of Einstein's theory of gravity) can be seen to emerge from the physics of ordinary quantum field theories. Recently, there has been a great deal of exciting progress suggesting that the answer to this question lies in the emerging field of quantum information theory (the theory behind quantum computers). According to work by our group and others, the phenomenon of quantum entanglement plays a central role in understanding nature of spacetime and gravity; this observation is leading the way to a better understanding of how gravity works at a fundamental level. For example, it is now understood that certain measures of entanglement in quantum field theory correspond directly to measures of geometry in the corresponding gravitational theory. Using this, we have shown that in some situations, the Einstein equations which govern the dynamics of spacetime and its interactions with matter can be deduced directly from the physics of quantum entanglement in the corresponding field theory. In the proposed research, I plan to exploit these emerging connections between gravity and quantum information theory in various ways. I would like to extend our derivation of Einstein's equations to a wider class of field theory states and investigate possible quantum corrections to these equations. I plan to extend some earlier work to investigate the gravitational implications of various constraints of entanglement coming from quantum information theory. Finally, I plan to explore a scenario that we have recently proposed by which the AdS/CFT correspondence might be used to provide a model of cosmology and help us to better understand our universe's beginning, its accelerating expansion through dark energy, and its end.