Approaches to Quantum Gravity

In their famous paper on quantum electrodynamics from 1929, Heisenberg and Pauli wrote that they expect the quantization of gravity, which they believed to be necessary for physical reasons, to proceed along the same lines without difficulties. In fact, Pauli asked his assistant, Rosenfeld in Zurich, to do this job. Rosenfeld published two pioneering papers in 1929 and 1930, but the problem of quantizing gravity remains unsolved up to now. This volume is devoted to this problem. Its purpose is to give an overview of some of the existing approaches to quantum gravity. Its actual content is perhaps better expressed by its subtitle: `Toward a new understanding of space, time and matter'. Concepts of space and time form the main theme of the book, and the discussion focuses on both classical and quantum aspects. One can recognize in it the old dichotomy between discrete and continuous, that is, between the alternatives of using either discrete concepts such as graphs or continuous concepts such as differentiable manifolds at the most fundamental level. Much emphasis is put in both cases on the notion of background independence as a necessary requirement for the construction of any quantum theory of gravity; one can no longer quantize on a given spacetime as in electrodynamics, but must seek an ab initio quantization of everything, without any background being left. Daniele Oriti, the editor, is well known for his work on group-field theory and spin-foam models. He has collected 28 articles written by 33 contributors, most of them being competent scientists and specialists in their field. The articles are grouped into five parts. After a presentation of some fundamental ideas and general formalisms, three contributions circle around string and M-theory. Not surprisingly, they put much emphasis on the important concepts of gauge–gravity duality and holograpic principle. More space is devoted in Part III to loop quantum gravity and spin-foam models. While this part already invokes a discussion of discrete structures, the next part focuses entirely on discrete quantum gravity; it includes articles on Regge calculus, dynamical triangulation, and causal sets. The final Part V introduces the field of quantum-gravity phenomenology, but also presents new formal insight into spacetime models from non-commutative geometry and possible violations of Lorentz invariance. Except for some parts of Part V, the emphasis in this book is definitely on formal developments and mathematical concepts rather than (potential) physical applications. In its collection of topics, it can perhaps best be compared with the volume `Quantum Gravity' 2006 ed B Fauser et al (Basel:Birkhauser Verlag). In both volumes, the discussion of discrete structures as the starting point for a quantum theory of gravity plays a decisive role. Each of the five parts is supplemented by a section on `Questions and Answers', where authors and editor ask questions to other authors after having read their contributions. These sections are indeed very helpful, and it occurred more than once that I myself had a question which I found answered there. A person who is already well versed in quantum gravity research might even wish to read these sections by themselves in order to get an impression on the various existing opinions in this field. As the editor emphasizes in his preface, this volume can by no means give a complete account of this field. It is thus not surprising that many topics are either omitted or only briefly mentioned. Among them are quantum geometrodynamics (Wheeler–DeWitt equation), quantum cosmology (including loop quantum cosmology), semiclassical gravity, quantum black holes, affine quantization, and the relevance for the interpretation of quantum theory (e.g. Everett versus collapse interpretation). The selection naturally reflects the taste of the editor. The content of this book is certainly suitable as an introduction for theoretical physicists and mathematicians who seek an overview of current ideas on the formal developments of quantum gravity. It is, in my opinion, not suitable for students because most of the articles are rather condensed and assume some prior knowledge. This book is definitely highly recommendable for the readers of Classical and Quantum Gravity.