Exploring the quantum gravity regime

我们所知道的宇宙中的所有物质都是由原子通过各种相互作用粘在一起组成的。 物质在空间和时间中的运动就像演员在舞台上的运动一样。那么舞台是由什么组成的呢？空间和时间的原子是什么？爱因斯坦证明了空间和时间可以统一在一个单一的概念中，即时空。他还意识到，这个时空的几何特征可以被理解为引力的表现，因此舞台和演员相互作用。找到一个一致的时空原子的理论描述是理论物理学的最大挑战之一。 我的研究计划的目标是： 1- 改进了环圈量子引力（LQG）框架对时空原子的理论描述， 2- 探索这种时空原子的物理学。 我的程序的一个关键特征是关注3d时空，即，只有两个空间维度的。引力于是变成拓扑的，这意味着没有局部自由度，因此没有引力波。这可以被看作是一个可解的玩具模型，摆脱了4d物理理论的一些困难方面，同时保留了其显着特征。我特别打算在把我的不同理论方案推广到现实的四维情况之前，先检验一下它们。 黑洞是纯粹的引力物体，也存在于三维空间中。他们的本性和命运（他们会蒸发吗？），这些量子力学依赖于它们的基本量子性质，吸引了专家研究人员和热切的公众。我的研究将大大推进对这些物体在3D情况下的量子性质的理解，使用我介绍的LQG形式主义和技术工具。例如，我将精确地计算这样的黑洞量子态是否可以隧穿到白色空穴量子态，有效地探索了最近由Rovelli等人提出的普朗克星的概念。 不幸的是，设计实验来探测量子引力机制的希望很小，因为这相当于重现宇宙起源时的条件。有趣的是，3d引力的拓扑性与凝聚态甚至量子信息理论中的模型有许多相似之处，这些模型都是为了建造量子计算机而研究的。我建议利用这些相似性来识别凝聚态模型中3d量子引力的特征，从而在一些原则上可以在实验室中实现的实验中模拟量子引力效应。这一提议将创建一个新的研究领域“模拟量子引力”，它将绕过一些困难，获得有关量子引力的实验事实。 量子引力为推广和吸引STEM学生提供了很好的手段。作为数学物理的一个子领域，它为能够在私营或公共部门工作的学生提供了良好的培训，提高了加拿大的竞争力。

All of the matter we know of in the universe is composed of atoms glued together by various interactions. The matter moves in space and time as actors move on a stage. But then what is the stage composed of? What are the atoms of space and time? Einstein showed that space and time can be unified in a single concept, space-time. He also realized that the geometric features of this space-time can be understood as a manifestation of the gravitational force, so that the stage and the actors interact with one another. Finding a consistent theoretical description of such atoms of space-time is one of the greatest challenges of theoretical physics. My research program has as its aims: 1- improving the theoretical description of the atoms of space-time suggested by the loop quantum gravity (LQG) framework, 2- probing the physics of such atoms of space-time. One key feature in my program is to focus on 3d space-times, i.e., those with only 2 spatial dimensions. Gravity then becomes topological which means that there are no local degrees of freedom, hence no gravitational waves. This can be viewed as a solvable toy model, getting rid of some difficult aspects of the 4d physical theory while retaining its salient features. I intend in particular to test my different theoretical proposals before extending them to the realistic 4d case. Black holes are purely gravitational objects, also existing in 3d. Their nature and fate (will they evaporate?), which depend on their fundamental quantum nature, mesmerizes both expert researchers and an eager public. My research will advance significantly the understanding of the quantum nature of these objects in the 3d case, using the LQG formalism and technical tools I have introduced. For example, I will precisely calculate whether such black hole quantum state could tunnel to a white hole quantum state, probing effectively the concept of Planck stars introduced recently by Rovelli et al. There is unfortunately little hope of devising experiments to probe the quantum gravity regime since it would amount to recreating the conditions at the origin of the Universe. Interestingly, 3d gravity being topological shares many features with models studied in condensed matter and even in quantum information theory in order to build quantum computers. I am proposing to use these similarities to identify features of 3d quantum gravity in condensed matter models to mimic quantum gravity effects in some experiments that could in principle be implemented in a lab. This proposal would create a new research area “analogue quantum gravity”, which would circumvent some of the difficulties to have access to experimental facts about quantum gravity. Quantum gravity provides great means for outreach and for attracting STEM students. As a subfield of mathematical physics, it provides excellent training for students who will be able to work in the private or public sectors, improving Canadian competitiveness.