Quantum gravity and hydrodynamics: a surprising partnership

这个提案是由两个看似无关的主题组成的。第一个是对量子引力的研究，其中时空的量子力学性质起着根本性的作用。第二个是流体力学的新领域，有限温度下许多量子系统的长波长描述。这些思路实际上是协调一致的。许多黑洞的长波描述正是流体力学的描述，从某种意义上说，爱因斯坦引力是对构成时空的基本自由度的低能“流体力学”描述。事实上，我自己的研究有助于将这些线索编织在一起，一个领域的发展为另一个领域提供了新的想法。在量子引力领域，我提出了几个基本问题。一个是引力场的量子力学涨落的作用，它导致虫洞几何形状。这些贡献出现在普通的爱因斯坦引力中，似乎编码了有关黑洞可能微观状态的信息。然而，我们有充分的理由相信，在像弦理论这样的完整量子引力模型中，这些构型是不稳定的。我的研究计划的一个主要目标是揭示这些虫洞和黑洞之间的确切联系，以及它们可能对可观测物理学做出的贡献。另一个主要目标是建立一个完全考虑量子力学的一致的宇宙学模型。在暴胀物理学中，宇宙的能量密度接近普朗克尺度，这样的框架对于正确处理暴胀物理学当然很重要，但现在在理解宇宙的量子态与宇宙微波背景中可观测的波动之间的关系时，它也很重要。谈到流体力学，我的主要目标是为量子物质的所谓“分形”相找到一种流体描述，这种描述已经被假设，但尚未在实验室中发现。利用这些理论材料的奇特时空对称性，我将能够找到描述长距离守恒量流动的纳维-斯托克斯方程的类似物。有充分的理由认为，这些方程将意味着对输运的相当独特的预测，这将有助于发现自然界中的分相。这些相存在的证实，以及对其基本性质的成功预测，将是量子力学史上的又一次胜利，也是对称在物理定律中所起作用的又一次胜利。我的工作主要是推进我们的物理学基础知识，激发科学家和外行人对我们共同拥有的宇宙的惊叹。

This proposal is a composition of two seemingly unrelated themes. The first is the study of quantum gravity, where the quantum mechanical nature of spacetime plays a fundamental role. The second is novel arenas for hydrodynamics, the long-wavelength description of many quantum systems at finite temperature. These lines of thought in fact harmonize. The long-wavelength description of many black holes is precisely that of hydrodynamics, and in a sense, Einstein gravity is the low-energy "hydrodynamic" description of the fundamental degrees of freedom that build up spacetime. Indeed, my own research has helped weave these strands together, with developments in one arena informing new ideas for the other. There are several fundamental questions I propose to address in the realm of quantum gravity. One concerns the role of quantum mechanical fluctuations of the gravitational field that lead to wormhole geometries. These contributions appear in ordinary Einstein gravity and seem to encode information about the possible microstates of black holes. Yet there is good reason to believe that, in complete models of quantum gravity like string theory, these configurations are unstable. A major goal of my research program is to unravel the precise connection between these wormholes and black holes, and the sense in which they might contribute to observable physics. Another major objective is to formulate a consistent model of cosmology in which quantum mechanics is fully accounted for. Such a framework is certainly important to properly treat inflationary physics, during which the energy density of the universe was close to the Planck scale, but it is also important now when understanding the relation between the quantum state of the universe and observable fluctuations in the cosmic microwave background. When it comes to hydrodynamics, my main goal is to find a fluid description for so-called "fracton" phases of quantum matter, which have been postulated but yet to be discovered in the lab. Using the somewhat exotic spacetime symmetries of these theoretical materials, I will be able to find the analogue of the Navier-Stokes equations describing flows of conserved quantities at long distance. There is good reason to think that these equations will imply rather unique predictions for transport, which will assist in the discovery of fracton phases in Nature. The confirmation that such phases exist, and successful predictions of their basic properties, will be yet another triumph in the history of quantum mechanics and the role of symmetries in physical laws. My work broadly falls under the byline of advancing our fundamental knowledge of physics, of the sort that inspires scientists and laypeople alike to marvel at the universe we share.