Quantum gravity and hydrodynamics: a surprising partnership

这一建议由两个看似无关的主题组成。第一个是量子引力的研究，时空的量子力学性质在其中起着基础性的作用。第二个是流体力学的新领域，即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，在某种意义上，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，一个竞技场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。一个是引力场量子力学涨落的作用，它导致了虫洞的几何形状。这些贡献出现在普通的爱因斯坦引力中，似乎编码了关于黑洞可能微观状态的信息。然而，我们有充分的理由相信，在弦理论这样的量子引力完整模型中，这些组态是不稳定的。我的研究计划的一个主要目标是解开这些虫洞和黑洞之间的精确联系，以及它们可能对可观测物理学做出贡献的意义。另一个主要目标是制定一个宇宙学的一致性模型，其中量子力学是完全占。这样一个框架对于正确处理暴胀物理学当然很重要，在暴胀物理学中，宇宙的能量密度接近普朗克尺度，但是现在理解宇宙的量子态和宇宙微波背景中可观测到的波动之间的关系也很重要。在流体力学方面，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，这种相已经被假设，但尚未在实验室中发现。利用这些理论材料中有些奇异的时空对称性，我将能够找到描述长距离守恒量流动的纳维尔-斯托克斯方程的类似物。有充分的理由认为，这些方程将意味着相当独特的预测输运，这将有助于发现自然界中的分形相。确认这种相的存在，并成功预测它们的基本性质，将是量子力学史上的又一次胜利，也是对称性在物理定律中的作用。我的工作大致上属于福尔斯的名义下，推进我们的物理学基础知识，那种激励科学家和外行人都惊叹于我们共享的宇宙。

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.