标题： 组合量子引力与涌现的三维量子行为 显示英文标题

标题： Combinatorial quantum gravity and emergent 3D quantum behaviour

摘要： 我们回顾了组合量子引力这一方法，它结合了爱因斯坦关于动态几何的思想和惠勒的“万物源于比特”假设，在一个由粗奥利维耶-里奇曲率支配的动力学图模型中展开。由于图上的环路凝聚，这导致从随机相到几何相的连续相变。在二维情况下，几何相描述了具有两个逆相关尺度的负曲率表面，一个是紫外（UV）普朗克长度，另一个是红外（IR）曲率半径。在普朗克尺度以下，随机比特特性得以保留：普朗克大小的随机比特块描述了由其超额曲率给出的激发能量的物质粒子。在普朗克长度和曲率半径之间，表面是平滑的，光谱和豪斯多夫维数为2；在大于曲率半径的尺度上，粒子将表面视为有效的洛伦兹de Sitter表面，光谱维数变为3，并且作为共动观察者所见的有效慢粒子动力学在欧几里得三维空间中表现为量子力学。由于三维距离继承自底层的二维de Sitter表面，我们在三维中也获得了围绕大质量粒子的弯曲轨迹，代表了大规模的引力相互作用。因此，我们将提出这个二维模型描述了一个适用于真实量子引力的通用全息屏幕。 显示英文摘要

摘要： We review combinatorial quantum gravity, an approach which combines Einstein's idea of dynamical geometry with Wheeler's "it from bit" hypothesis in a model of dynamical graphs governed by the coarse Ollivier-Ricci curvature. This drives a continuous phase transition from a random to a geometric phase, due to a condensation of loops on the graph. In the 2D case, the geometric phase describes negative-curvature surfaces with two inversely related scales, an ultraviolet (UV) Planck length and an infrared (IR) radius of curvature. Below the Planck scale the random bit character survives: chunks of random bits of the Planck size describe matter particles of excitation energy given by their excess curvature. Between the Planck length and the curvature radius, the surface is smooth, with spectral and Hausdorff dimension 2; at scales larger than the curvature radius, particles see the surface as an effective Lorentzian de Sitter surface, the spectral dimension becomes 3 and the effective slow dynamics of particles, as seen by co-moving observers, emerges as quantum mechanics in Euclidean 3D space. Since the 3D distances are inherited from the underlying 2D de Sitter surface, we obtain curved trajectories around massive particles also in 3D, representing the large-scale gravity interactions. We shall thus propose that this 2D model describes a generic holographic screen relevant for real quantum gravity.