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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=742288
• 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.

该提议是两个看似无关的主题的组成。首先是对量子重力的研究，其中时空的量子机械性质起着基本作用。第二个是用于流体动力学的新型领域，这是有限温度下许多量子系统的长波长描述。这些思想实际上是协调的。许多黑洞的长波长描述恰恰是流体动力学的，从某种意义上说，爱因斯坦重力是对建立时空的基本自由度的低能“流体动力”描述。的确，我自己的研究帮助将这些链编织在一起，其中一个竞技场的发展为另一个领域提供了新的想法。我建议在量子重力领域提出几个基本问​​题。一种涉及导致虫洞几何形状的重力场的量子机械波动的作用。这些贡献出现在普通的爱因斯坦重力中，似乎编码有关黑洞可能的微骨的信息。然而，有充分的理由相信，在像字符串理论这样的量子重力的完整模型中，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，以及它们可能有助于可观察到的物理学的意义。另一个主要目的是制定一个一致的宇宙学模型，其中量子力学被充分考虑了。这样的框架对于正确处理通货膨胀物理学肯定很重要，在此期间，宇宙的能量密度接近普朗克量表，但是当理解宇宙微波背景中宇宙量子状态和可观察到的波动之间的关系时，现在也很重要。在流体动力学方面，我的主要目标是找到量子物质的所谓“分裂”阶段的流体描述，这些阶段已经假定，但尚未在实验室中发现。使用这些理论材料的某种异国情调的时空对称性，我将能够找到长途描述保守量的流量的Navier-Stokes方程的类似物。有充分的理由认为这些方程将暗示运输的独特预测，这将有助于发现自然界中的分布族阶段。证实这种阶段的存在，以及对其基本特性的成功预测，将是量子力学史和对称性在物理定律中的作用中的另一个胜利。我的作品广泛地属于促进我们对物理学的基本知识的途径，这激发了科学家和外行人，以惊叹于我们分享的宇宙。