Black holes and cosmology in quantum gravity

在原子和核现象的尺度上，小的物理是由量子理论描述的。我们现在有了广泛成功的量子理论，描述了自然界中观察到的四种基本力中的三种：电磁、弱和强核相互作用。另一方面，大尺度的物理学，包括对太阳系、星系和整个宇宙学的研究，是由引力理论描述的，其中最成功的是爱因斯坦的广义相对论。这个理论把重力想象成空间和时间的几何曲率，焊接成一个实体：时空。量子理论在涉及高度致密物体（如黑洞和非常早期的宇宙）的非常强的引力场的引力现象中预计是重要的。将引力与量子理论相结合被广泛认为是理论物理学的前沿问题，并将揭示物质的“量子几何”。这项研究的目的是探索一种发展量子引力理论的方法。这需要使用时钟作为描述几何和物质的一部分，并帮助我们澄清“宇宙能量”的含义。我将使用这种被称为哈密顿理论的描述，通过计算机模拟来研究大爆炸前早期宇宙的特性，以及黑洞的形成。这些模拟将使用一种被称为蒙特卡洛方法的重力和物质状态的随机抽样方法。这是一项非常高效和发达的技术，有着广泛的应用，但到目前为止，它还没有被应用于完全量子环境下的物质和宇宙几何的研究。这种方法有望揭示被称为相变的特性，这种特性在物质的固体、液体和气相中都很常见。但是，如果物理系统是重力和物质，重力被描述为时空弯曲的几何形状，那么这些阶段可能会变得不寻常且具有启发性。一个有趣的特征是相关长度。这是测量空间中物理效应相互关联的距离。如果这个距离非常大，这意味着非常遥远的物理现象是相关的，或者是步调一致的。无限的相关长度表示相变。我希望在这个提议中采用的思想和方法将为量子引力问题提供新的见解。这些见解可以指导未来的理论发展，并提供对宇宙学问题的更好理解，例如暗物质和能量。所使用的模拟方法具有从预测民意调查到分析大数据集的多种适用性，因此为HQP培训提供了重要的多学科工具。****** ************ *** **

The physics of the small, at the scale of atomic and nuclear phenomena, is described by quantum theory. We now have broadly successful quantum theories that describe three of the four observed fundamental forces in nature: electromagnetic, weak and strong nuclear interactions. On the other hand, physics on large scales, encompassing the study of solar systems, galaxies and cosmology as a whole, is described by a gravitational theory, the most successful of which is Einstein's theory of general relativity. This theory envisions gravity as a curvature of the geometry of space and time, welded together as one entity: spacetime.*** Quantum theory is expected to be important in gravitational phenomena involving very strong gravitational fields of highly compact objects, such as black holes and the very early Universe. Combining gravitation with quantum theory is widely considered to be the frontier problem in theoretical physics, and would reveal a "quantum geometry" with matter.*** The purpose of the proposed research is to explore one approach to developing a quantum theory of gravity. This requires the use of a clock as a part of the description of geometry and matter, and helps us to clarify what is meant by "energy of the Universe." I will use this description, called the Hamiltonian theory, to study the properties of the early Universe very close to the Big Bang, and the formation of black holes, using computer simulations.*** These simulations will use a method of random sampling of the state of gravity and matter known as the Monte Carlo method. This is a very efficient and well-developed technology that has wide ranging applications, but it has so far not been applied to the study of matter and the geometry of the Universe in a fully quantum setting. This method is expected to reveal properties called phase transitions, that are familiar in solid, liquid and gas phases of matter. But if the physical system is gravity and matter, with gravity described as a spacetime curved geometry, the phases could turn out to be unusual and revealing. One interesting feature is the correlation length. This is a measure of how far apart in space physical effects are correlated. If this distance is very large, it means that very distant physical phenomena are related, or march in step. An infinite correlation length signals a phase transition.*** I expect the ideas and methods to be employed in this proposal will provide new insights into the problem of quantum gravity. These insights could guide future theoretical developments, and provide a better understanding of cosmological problems, such as dark matter and energy. The simulation methods to be used have diverse applicability, from forecasting polls to analyzing big data sets, and therefore provide important multi-disciplinary tools for training HQP. ****** ************ *** **