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移动，就像演员在舞台上移动一样。那么舞台是由什么组成的呢？什么是空间和时间的原子？爱因斯坦证明了空间和时间可以统一为一个概念——时空。他还意识到，这个时空的几何特征可以理解为引力的一种表现，使舞台和演员相互作用。为这些时空原子找到一个一致的理论描述是理论物理学的最大挑战之一。***我的研究项目有以下目标：***1——改进环量子引力（LQG）框架提出的时空原子的理论描述；***2——探索时空原子的物理性质。***我的程序的一个关键特点是关注3d时空，即只有2个空间维度的时空。重力就变成了拓扑这意味着没有局部自由度，因此没有引力波。这可以看作是一个可解的玩具模型，在保留其显著特征的同时，摆脱了4d物理理论中一些困难的方面。在将我的不同理论建议推广到现实的4d案例之前，我打算特别检验一下它们。黑洞是纯粹的引力物体，同样存在于三维空间中。它们的性质和命运（它们会蒸发吗？）取决于它们基本的量子性质，这让专家研究人员和热切的公众都着迷。我的研究将使用我所介绍的LQG形式主义和技术工具，显著推进对这些物体在3d情况下的量子性质的理解。例如，我将精确地计算这种黑洞量子态是否可以隧穿到白洞量子态，有效地探测最近由Rovelli等人引入的普朗克恒星的概念。***不幸的是，设计实验来探测量子引力制度的希望很小，因为这将相当于重现宇宙起源的条件。有趣的是，三维引力是拓扑学的，为了构建量子计算机，它与凝聚态物质甚至量子信息理论中研究的模型有许多相同的特征。我建议使用这些相似性来识别凝聚态物质模型中三维量子引力的特征，以模拟量子引力效应在一些原则上可以在实验室中实现的实验中。这一提议将创建一个新的研究领域“模拟量子引力”，这将规避一些困难，以获得有关量子引力的实验事实。***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分支，它为将来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.