Quantum gravity and hydrodynamics: a surprising partnership

量子引力和流体动力学：令人惊讶的合作关系

• 批准号: RGPIN-2021-02941
• 负责人: Jensen, Kristan
• 金额: $ 2.84万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=763013
• 关键词: Quantum; gravity; hydrodynamics; surprising; partnership

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.

该提案由两个看似无关的主题组成。第一个是量子引力的研究，其中时空的量子力学性质发挥着基础作用。第二个是流体动力学的新领域，即有限温度下许多量子系统的长波长描述。这些思路实际上是一致的。许多黑洞的长波长描述正是流体动力学的描述，从某种意义上说，爱因斯坦引力是对构建时空的基本自由度的低能“流体动力学”描述。事实上，我自己的研究帮助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。我建议在量子引力领域解决几个基本问​​题。其中之一涉及引力场量子力学涨落的作用，这种涨落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，似乎编码了有关黑洞可能的微观状态的信息。然而，我们有充分的理由相信，在弦理论等完整的量子引力模型中，这些配置是不稳定的。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精确联系，以及它们对可观测物理学的贡献。另一个主要目标是建立一个一致的宇宙学模型，其中量子力学得到充分考虑。这样的框架对于正确对待暴涨物理学当然很重要，在此期间宇宙的能量密度接近普朗克尺度，但现在对于理解宇宙的量子态与宇宙微波背景中可观测的涨落之间的关系也很重要。当谈到流体动力学时，我的主要目标是找到所谓的量子物质“分形”相的流体描述，这种相已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特的时空对称性，我将能够找到描述远距离守恒量流动的纳维-斯托克斯方程的类比。有充分的理由认为这些方程将暗示对输运的相当独特的预测，这将有助于发现自然界中的分形相。确认这些相的存在，并成功预测它们的基本性质，将是量子力学历史和对称性在物理定律中的作用的又一次胜利。我的工作总体上属于推进我们的物理学基础知识的范围，这种知识激励科学家和外行人对我们共同的宇宙感到惊叹。