Exploring the quantum gravity regime

我们所知道的宇宙中的所有物质都是由各种相互作用粘合在一起的原子组成的。当演员在舞台上移动时，物质在空间和时间上移动。但是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，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理解为引力的表现，从而使舞台和演员相互作用。找到对这种时空原子的一致的理论描述是理论物理学最大的挑战之一。我的研究计划的目标是：1-改进循环量子引力(LQG)框架所建议的时空原子的理论描述，2-探索此类时空原子的物理。我的计划的一个关键特征是专注于3D时空，即只有2个空间维度的时空。然后重力变成了拓扑，这意味着没有局部自由度，因此也就没有引力波。这可以被视为一个可解决的玩具模型，摆脱了4d物理理论的一些困难方面，同时保留了它的显著特征。我尤其打算在将我的不同理论建议扩展到现实的4d案例之前，对它们进行测试。黑洞是纯粹的引力物体，也存在于3D中。它们的性质和命运(它们会蒸发吗？)取决于它们的基本量子性质，既迷住了专家研究人员，也迷住了热切的公众。我的研究将极大地促进对3D情况下这些物体的量子性质的理解，使用我所介绍的LQG形式主义和技术工具。例如，我将精确计算这种黑洞量子态是否能隧穿到白洞量子态，有效地探索Rovelli等人最近引入的普朗克恒星的概念。不幸的是，设计实验来探索量子引力机制的希望微乎其微，因为这相当于重现宇宙起源时的条件。有趣的是，3D引力具有拓扑性，与凝聚态甚至量子信息论中的模型有许多相似之处，目的是为了建立量子计算机。我提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，以在一些原则上可以在实验室实现的实验中模拟量子重力效应。这一提议将创建一个新的研究领域--模拟量子引力，它将绕过获得有关量子引力的实验事实的一些困难。量子引力为拓展和吸引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出色的培训，提高加拿大的竞争力。

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.