Nontrivial small-scale structure of spacetime and consequences for particle propagation

洛伦兹不变性是我们理解亚原子物理学的基石。与此同时，我们知道目前的理论是不完整的，量子引力将极大地改变这幅图景，也许包括在非常小的长度尺度上破坏洛伦兹不变性。但是，目前还没有可行的量子引力理论可以预测或排除这种崩溃。因此，如果人们能在普朗克能量尺度上通过实验检测或排除洛伦兹不变性破缺，这将极大地增强我们对空间和时间的理解，并有助于寻找正确的理论。像HESS或俄歇这样的天文台可以探测到可以探测普朗克尺度物理的超高能粒子。事实上，这些观测已经排除了某些特殊形式的洛伦兹不变性破缺。然而，这样的结果需要一个理论框架。只有当理论框架不是纯粹的唯象学的，而是基于（量子）时空模型时，观测才能告诉我们关于最小长度尺度下时空结构的具体情况。本项目的目标是建立这样一个框架。我们希望在小尺度上建立简单可靠的时空模型，推导出它们的唯象结果，并通过与观测结果的比较，了解一些关于空间和时间的本质。为了做到这一点，我们将发展时空缺陷的理论，并提出新的方法来研究圈量子引力。

Lorentz invariance is the cornerstone of our understanding of subatomic physics. At the same time, we know that the present theory is incomplete and that quantum gravity will change the picture dramatically, perhaps including a breakdown of Lorentz invariance at very small length scales. But there is, at present, no viable theory of quantum gravity which would predict or rule out such a breakdown. Thus, if one could experimentally detect or rule out Lorentz invariance breaking at the Planck energy scale, it would vastly enhance our understanding of space and time and aid in the search of the correct theory. Observatories such as HESS or Auger detect ultrahigh-energy particles which can probe Planck-scale physics. In fact, certain special forms of Lorentz-invariance breaking have already been ruled out by these observations. However, results such as these require a theoretical framework. Only if the theoretical framework is not purely phenomenological but based on a model of (quantum) spacetime, can the observations tell us something concrete about the structure of spacetime at the smallest length scales. The goal of the present project is to build such a framework. We want to develop simple and reliable models of spacetime at small length scales, derive their phenomenological consequences, and, by comparison with observations, learn something about the nature of space and time. To do this, we will develop theories of spacetime defects and also bring new methods to bear on loop quantum gravity.