LEAPS-MPS: Investigating Emergent Gravity in Combinatorial Quantum Systems

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。该奖项资助圣何塞州立大学卡萨洪·贝特雷教授的研究活动。空间和时间可能是物理现实最基本的方面。然而，对它们的本质的更深层次的解释仍然是一个谜。近年来，人们寻求了许多可能的方法来解决这个问题；这些方法通常被归类为弦理论、循环量子引力和因果动态三角剖分等名称。作为该项目的一部分，贝特雷教授将采用一种名为浮现背景独立量子引力(EBIQG)的补充方法。这一方法假定，空间和时间的积木是某些量子力学关系，可以用图形的形式表示。在这种方法下，空间和时间只能以宏观平均值的形式出现。贝特雷教授将构建数值工具，模拟图论量子系统的统计和热力学性质，并构建二维量子引力中维度和几何的出现模型。预计该项目还将产生更广泛的重大影响。圣何塞州立大学是一所为少数群体服务的机构，参与这一研究项目的本科生和硕士学生将不仅培养分析研究技能，还将培养进行数值模拟的实践技能。该项目还将为这些学生提供在STEM领域取得成功的经验和信心。更严格地说，这项研究将为EBIQG领域带来两个重要的新方向。首先，它强调了作为起点的空间本身的统一维度的出现。将欧几里得空间的维度的图论推广称为归纳维度，作为图的微态的动态量，使其演化为光滑流形的出现维度。其次，这个研究项目使用所有几何图-表面三角剖分的图论类似物-而不仅仅是规则格子和规则图形来建模离散空间。通过这种方法，图模型中量子引力的出现看起来像是简并的零温度基态。因此，这些研究将有助于为从非几何图论希尔伯特空间走向新兴整数维和几何的具体模型铺平道路。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).This award funds the research activities of Professor Kassahun Betre at San Jose State University. Space and time are perhaps the most fundamental aspects of physical reality. However, a deeper explanation of their nature is still a mystery. Many possible approaches toward addressing this issue have been pursued in recent years; these are usually grouped under names such as String Theory, Loop Quantum Gravity, and Causal Dynamical Triangulation. As part of this project, Professor Betre will pursue a complementary approach called Emergent Background-Independent Quantum Gravity (EBIQG). This approach posits that the building blocks of space and time are certain quantum-mechanical relationships that can be expressed in the form of graphs. Within such an approach, space and time emerge only as macroscopic averages. Professor Betre will build numerical tools that simulate the statistical and thermodynamic properties of the graph-theoretic quantum systems, and construct a model for the emergence of dimension and geometry in a two-dimensional quantum gravity. This project is also envisioned to have significant broader impacts. San Jose State University is a minority-serving institution, and undergraduate and masters students participating in this research project will develop not only analytical research skills but also practical skills in conducting numerical simulations. This project will also provide these students the experience and confidence to succeed in STEM fields. More technically, this research will bring two important new directions to the field of EBIQG. First, it highlights the emergence of the uniform dimension of space itself as a starting point. A graph-theoretic generalization of the dimension of Euclidean space called inductive dimension is used as a dynamical quantity of the graph microstates that course-grains into the emergent dimension of smooth manifolds. Second, this research project models discretized space using all geometric graphs --- graph-theoretic analogues of triangulations of surfaces --- rather than just regular lattices and regular graphs. With this approach, the emergence of quantum gravity from the graph models appears as a degenerate zero- temperature ground state. Such research will therefore help to pave the way towards a concrete model for emergent integer dimension and geometry from a non-geometric graph-theoretic Hilbert space.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.