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。然而，它们似乎是互不相容的。量子引力（QG）的候选理论，如超弦理论（ST）和环量子引力（LQG）旨在统一两者，并取得了重大进展。然而，没有一个实验或观察能够支持或反驳任何理论。我的主要研究重点是寻找QG的实验特征。所有量子引力理论都预测了最小可测量长度。我和我的合作者的研究表明，这意味着所有量子系统中都存在普遍的量子效应（Das, Vagenas, PRL101,221301(2008)）。这使人们相当乐观地认为，尽管普朗克能量尺度（约1016 TeV）很大，随着测量灵敏度的不断提高，QG的特征可能在低能实验室中被观测到。广义相对论最重要的应用之一是宇宙学，它使我们对宇宙大尺度结构的理解取得了显著进展。这一领域的两个主要未解决的问题是理解暗物质和暗能量的真实本质，它们共同构成了我们宇宙的95%。我们最近表明，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可行候选者。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。综上所述，基于我的专业知识，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：制定最小长度的洛伦兹协变描述和相关的QG广义不确定性原理（GUP）。将此应用于计算低能系统中的QG校正。在光力学实验室测量GUP效应。2：定量预测宇宙BEC的密度分布，并与现有数据进行比较。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一个可行的降维模型，并研究它对QG的影响。我的研究将为现有的QG理论、时空的基本维度以及暗物质和暗能量的BEC模型提供支持或反对的证据。从长远来看，它将对什么是正确的量子引力理论以及如何提取其实验特征提供重要的见解。这将有助于排除一些理论。它还将揭示时空的本质——它从根本上是离散的还是连续的。它将通过有关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，我将对各级HQP进行培训，并在国内和国际上开展合作。

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.