Quantum information theoretic approach to quantum gravity

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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.