Continuum limit, dynamics and holography in quantum gravity

量子引力中的连续极限、动力学和全息术

• 批准号: RGPIN-2017-04224
• 负责人: Dittrich, Bianca
• 金额: $ 6.34万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=710937
• 关键词: Continuum; limit; dynamics; holography; quantum

“What is the nature of space and time?” This is a question that has advanced the development of physics through the centuries. Physics was revolutionized at the beginning of the 20th century by two separate paradigm shifts: On the one hand, Einstein's vision of space and time as a unified and dynamical object that describes the gravitational force; on the other, the invention of quantum theory that prescribes an inherent fuzziness to fundamental matter. By the end of the 20th century, it became clear that both theories, taken separately, predict their own demise: Einstein's theory of gravitation predicts the collapse of matter to black holes, that crash more and more matter into a spacetime singularity. Quantum theory, describing the fundamental matter interactions, leads to infinities and therefore inconsistencies at very small distances. We need therefore a theory of quantum gravity that replaces smooth space time, on which 20th century physics is based, with a truly quantum space time. With space time itself becoming a fuzzy object, such a theory will again revolutionize our understanding of space and time. Currently, we have a number of approaches to a quantum theory of gravity, but they all face a key challenge: to show that quantum space time does lead to smooth space time, as we experience it in our everyday world. Only then can we accept a given approach as a theory of quantum gravity. This will be the main issue tackled by this research program. It is a very difficult task as it requires the bridging of an unprecedented number of magnitudes. It can be compared to deriving the hydrodynamics of water from the interactions between the hydrogen and oxygen atoms. There have been, however, a number of exciting developments which bring this task into reach. Most importantly, these allowed me to develop a framework of renormalization, applicable to non-perturbative quantum gravity approaches, which led to the construction of first numerical algorithms to tackle the continuum limit. This research program will expand the current analytical and numerical tools and use these to extract the continuum limit of quantum gravity models. This research will significantly advance our grasp on the dynamics encoded in quantum gravity models. Instead of being focussed on building particular models of quantum gravity, the methods that will be developed will allow a unified treatment and the derivation of universal as well as model dependent predictions. This will be key to derive physical predictions and to construct improved models, which will help us to unravel the notion of quantum space time. Quantum gravity research attracts excellent students and provides outreach efforts with exciting material. This will increase students choosing STEM subjects and keeps them motivated, which will, in turn help Canada to keep and expand its edge in the research and development sector.

“空间和时间的本质是什么？”这个问题几个世纪以来推动了物理学的发展。物理学在世纪初被两个独立的范式转变所革命：一方面，爱因斯坦将空间和时间视为描述引力的统一和动态对象;另一方面，量子理论的发明规定了基本物质的固有特性。 到了世纪末，很明显，这两个理论，单独来看，预测自己的灭亡：爱因斯坦的引力理论预测物质坍缩成黑洞，越来越多的物质撞进时空奇点。描述基本物质相互作用的量子理论导致无穷大，因此在非常小的距离上不一致。因此，我们需要一种量子引力理论，用一种真正的量子时空来取代世纪物理学所基于的光滑时空。随着时空本身成为一个模糊的对象，这样的理论将再次彻底改变我们对空间和时间的理解。 目前，我们有许多方法来研究引力的量子理论，但它们都面临着一个关键的挑战：证明量子时空确实会导致平滑的时空，就像我们在日常世界中所经历的那样。只有这样，我们才能接受一个给定的方法作为量子引力理论。这将是本研究计划要解决的主要问题。 这是一项非常艰巨的任务，因为它需要连接数量空前的规模。它可以与从氢原子和氧原子之间的相互作用中推导出水的流体动力学相比较。然而，已经出现了一些令人兴奋的事态发展，使这一任务得以实现。最重要的是，这些使我能够开发一个重整化框架，适用于非微扰量子引力方法，这导致了第一个数值算法的构建，以解决连续极限。该研究计划将扩展当前的分析和数值工具，并使用这些工具来提取量子引力模型的连续极限。 这项研究将大大推进我们对量子引力模型中编码的动力学的掌握。而不是专注于建立量子引力的特定模型，将开发的方法将允许统一的治疗和推导的普遍以及模型依赖的预测。 这将是导出物理预测和构建改进模型的关键，这将有助于我们解开量子时空的概念。 量子引力研究吸引了优秀的学生，并为推广工作提供了令人兴奋的材料。这将增加选择STEM科目的学生，并保持他们的积极性，这反过来将有助于加拿大保持和扩大其在研发领域的优势。