Phenomenological and Theoretical Aspects of Quantum Gravity

量子力学和广义相对论是两个最成功的物理理论。量子引力(QG)的候选理论，如超弦理论(ST)和圈量子引力(LQG)，旨在将两者统一起来，并取得了重大进展。然而，还没有一个实验或观察来支持或驳斥任何理论。我的主要研究重点是寻找QG的实验签名。所有的QG理论都预测了一个最小可测量长度。我和我的合作者的研究表明，这意味着在所有量子系统中都存在普遍的QG效应(Das，Vagenas，PRL101,221301(2008))。这引起了相当大的乐观情绪，尽管普朗克能量标度巨大，约1016TeV，随着测量灵敏度的不断提高，QG的特征可能在低能量实验室中被观察到。广义相对论最重要的应用之一是宇宙学，它在我们理解宇宙大尺度结构方面取得了显著进展。这一领域的两个主要悬而未决的问题是对暗物质和暗能量的真实本质的理解，这两种物质加起来占我们宇宙的95%。我们最近已经证明，超轻玻色子的玻色-爱因斯坦凝聚体(BEC)是暗物质和暗能量的一个可行的候选者。BEC的密度解释了暗物质，它产生的负压量子势解释了暗能量。基于上述原因，并以我的专业知识为基础，我的研究目标是调查上述领域的三个关键问题。在短期(1-2年)和中期(3-5年)，我将：1：在QG中制定最小长度的洛伦兹协变描述和相关的广义不确定原理(GUP)。将其应用于计算低能系统中的QG校正。在光机械实验室测量GUP效应。步骤2：做出定量预测，如宇宙BEC的密度分布，并与现有数据进行比较。步骤3：在我的团队最近工作的基础上，研究引力希格斯机制作为可行的降维模型，并研究其对QG的影响。我的研究将提供证据，支持或反对现有的QG理论，关于时空的基本维度，以及暗物质和暗能量的BEC模型。从长远来看，它将为什么是正确的量子引力理论以及如何提取其实验签名提供重要的见解。这将有助于排除一些理论。它还将阐明时空的本质--无论它是从根本上是离散的还是连续的。它将通过关于宇宙内容和支配宇宙的引力理论的详细信息，帮助我们了解宇宙的起源和演化。为了实现这些目标，我将培训各级HQP，并在国内和国际上进行合作。

Quantum Mechanics and General Relativity are two of the most successful physical theories. Yet they appear to be mutually incompatible. Candidate theories of Quantum Gravity (QG) such as Superstring Theory (ST) and Loop Quantum Gravity (LQG) aim to unify the two, and have made significant progress. However, there has not been a single experiment or observation which supports or refutes any theory. The main focus of my research is to find experimental signatures of QG. All QG theories predict a minimum measurable length. The research of my collaborators and I have shown that this implies universal QG effects in all quantum systems (Das, Vagenas, PRL101,221301(2008)). This has given rise to considerable optimism that despite the immensity of the Planck energy scale, about 1016 TeV, with continual improvement in measurement sensitivities, signatures of QG may be observable in the low energy laboratory. One of the most important applications of General Relativity is cosmology, which has made remarkable progress in our understanding of the large scale structure of the universe. Two main unresolved problems in this area are understanding of the true nature of dark matter and dark energy, which together make up 95% of our universe. We have recently shown that a Bose-Einstein condensate (BEC) of ultralight bosons is a viable candidate for both dark matter and dark energy. The density of the BEC accounts for the dark matter and the quantum potential with negative pressure that it generates accounts for the dark energy. Motivated by the above, and building on my expertise, the objective of my research is to investigate three key problems in the aforementioned areas. In the short (1-2 years) and medium term (3-5 years), I will:  1: Formulate a Lorentz covariant description of minimum length and the related Generalized Uncertainty Principle (GUP) in QG. Apply this to compute QG corrections in low energy systems. Measure GUP effects in the optomechanical laboratory.   2: Make quantitative predictions such as density profiles of the cosmic BEC and compare with available data.  3: Building on my team's recent work, study gravitational Higgs mechanism as a viable model of dimensional reduction and study its implications for QG.  My research will provide evidence for or against the existing theories of QG, on the fundamental dimension of spacetime and the BEC model of dark matter and dark energy. In the long term, it will give important insights into what the correct theory of quantum gravity is and how to extract its experimental signatures. It will help rule out some theories. It will also shed light on the nature of spacetime - whether it is fundamentally discrete or continuum. It will help us understand the origin and evolution of the universe via detailed information about its contents and the theory of gravity which governs it.  In order to accomplish these objectives, I will train HQP at all levels and collaborate nationally and internationally.