Approaches to Quantum Gravity

Abstract

In their famous paper on quantum electrodynamics from 1929, Heisenbergand Pauli wrote that they expect the quantization of gravity, whichthey believed to be necessary for physical reasons, to proceedalong the same lines without difficulties. In fact, Pauli asked hisassistant, Rosenfeld in Zürich, to do this job. Rosenfeld published twopioneering papers in 1929 and 1930, but the problem of quantizinggravity remains unsolved up to now.This volume is devoted to this problem.Its purpose is to give an overview of some ofthe existing approaches to quantum gravity. Its actual content is perhapsbetter expressed by its subtitle: `Toward a new understanding ofspace, time and matter'. Concepts of space and time form the maintheme of the book, and the discussion focuses on both classical andquantum aspects. One can recognize in it the old dichotomy between discrete and continuous, that is, between the alternatives ofusing either discrete concepts such as graphs or continuous conceptssuch as differentiable manifolds at the most fundamental level. Much emphasis is put in both cases on thenotion of background independence as a necessary requirement forthe construction of any quantum theory of gravity; one can no longerquantize on a given spacetime as in electrodynamics, but must seek an ab initio quantization of everything, without any backgroundbeing left.Daniele Oriti, the editor, is well known for his work on group-fieldtheory and spin-foam models. He has collected 28 articles written by33 contributors, most of them being competent scientists andspecialists in their field. The articles are grouped into fiveparts. After a presentation of some fundamental ideas and generalformalisms, three contributions circle around string and M-theory. Notsurprisingly, they put much emphasis on the important concepts ofgauge–gravity duality and holograpic principle. More space is devotedin Part III to loop quantum gravity and spin-foam models. While thispart already invokes a discussion of discrete structures, the nextpart focuses entirely on discrete quantum gravity; it includesarticles on Regge calculus, dynamical triangulation, and causalsets. The final Part V introduces the field of quantum-gravityphenomenology, but also presents new formal insight into spacetime models fromnon-commutative geometry and possible violations of Lorentzinvariance. Except for some parts of Part V,the emphasis in this book is definitely on formal developments and mathematicalconcepts rather than (potential) physical applications. In its collection of topics, it can perhaps best be comparedwith the volume `Quantum Gravity' 2006 ed B Fauser et al (Basel:Birkhäuser Verlag). In both volumes, the discussion ofdiscrete structures as the starting point for a quantum theory ofgravity 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.