Quantum information theoretic approach to quantum gravity

这个研究项目涉及数学物理中最深奥的问题之一：将广义相对论和量子理论扩展成一个包含两者的统一理论。在这里，主要的挑战之一是，广义相对论和量子理论在非常小的长度尺度上给出了明显矛盾的时空本质指示。广义相对论指出，时空应该是连续的，而量子理论指出，时空应该拥有子结构，最终可能是离散的，尽管间隔极小。（从字面上看，“量化”一词的意思是离散化）。在此背景下，本研究项目开发并应用了信息论领域的新方法。在那里，人们发现，在某些情况下（有限带宽），连续信号，如音乐或图像，如果以一定的最小速率进行采集，可以完全从离散样本中重建出来。每个CD播放机都使用所谓的香农采样技术。这个研究项目的目的是推广香农抽样理论，使物理场可以被描述为生活在连续的时空上，完全等价地，生活在任何具有足够紧密间隔的离散时空上——从而克服广义相对论和量子理论之间的表面矛盾。此外，研究宇宙学的分支也是这个研究计划的一部分。一方面，目的是研究真空能量（即暗能量）的起源，以及在什么条件下它会或不会产生引力。另一方面，宇宙微波背景辐射可能有可测量的含义，这将是量子引力效应的第一次测量。通过这项研究开发的信息理论方法很可能会为实际的信息技术带来有用的结果——已经有一种专利数据压缩方法从这项研究中出现了。

This research program is concerned with one of the deepest problems in mathematical physics: to extend general relativity and quantum theory into one unified theory that encompasses both. Here, one of the main challenges is that general relativity and quantum theory give apparently contradictory indications about the nature of space-time at very small length scales. General relativity indicates that space-time should be a continuum while  quantum theory indicates that space-time should possess a substructure and might ultimately be discrete, albeit with an extremely small spacing. (Literally, the term ``quantization" means discretization). In this context, the present research program develops and applies new methods  taken from the field of information theory. There, it was found that under certain circumstances (a finite bandwidth) continuous signals, such as music or images, can be completely reconstructed from discrete samples if they are taken at a certain minimum rate. Every CD player uses these so-called Shannon sampling techniques. The aim of this research program is to generalize Shannon sampling theory so that physical fields can be described as living on continuous space-time and, entirely equivalently, on any discretization of space-time with sufficiently tight spacing - thereby  overcoming that seeming contradiction between general relativity and quantum theory. In addition, it is part of this research program to study the ramifications in cosmology. On the one hand, the aim is to investigate the origin of vacuum energy (i.e. dark energy) and the conditions under which it does or does not gravitate. On the other hand, there could be measurable implications for the cosmic microwave background radiation, which would be the first measurements of quantum gravity effects. The information theoretic methods developed through this research may well lead to useful side results also for practical information technology - already, a patented data compression method emerged from this research.