Quantum gravity: A brief history of ideas and some prospects

Abstract

We present a bird's-eye survey on the development of fundamental ideas of quantum gravity, placing emphasis on perturbative approaches, string theory, loop quantum gravity (LQG) and black hole thermodynamics. The early ideas at the dawn of quantum gravity as well as the possible observations of quantum gravitational effects in the foreseeable future are also briefly discussed. Int. J. Mod. Phys. D Downloaded from www.worldscientific.com by CAMBRIDGE UNIVERSITY on 08/11/15. For personal use only. S. Carlip et al. 1530028-2 Int. J. Mod. Phys. D Downloaded from www.worldscientific.com by CAMBRIDGE UNIVERSITY on 08/11/15. For personal use only. Quantum gravity: A brief history of ideas and some prospectsNinety-nine years passed since the very first conception of Einstein. Today, quantum gravity has grown into a vast area of research in many different (both perturbative and nonperturbative) approaches. Many directions have led to significant advances with various appealing and ingenious ideas; these include causal sets, dynamical triangulation, emergent gravity, H-space theory, LQG, noncommutative geometry, string theory, supergravity, thermogravity, twistor theory and much more. (For surveys and references on various approaches of quantum gravity, see Refs. 22-25; for detailed accounts of the history and development, see Refs. 6 and 26; for a popular science account of quantum gravity, see the book Ref. 27.) Perturbative Quantum GravityThe quantization of general relativity on the perturbative level (with or without matter) was the life work of DeWitt, for which he was awarded the 1987 Dirac Medal and the 2005 Einstein Prize. 28-30 His program eventually succeeded -against the expectation of most expert opinion during the 1960s -in generalizing Feynman's covariant quantization of quantum electrodynamics so that it could be applied as well to theories such as general relativity and Yang-Mills that are based on non-Abelian gauge symmetries. There were three key steps:

Reduction of gravity-matter and dS gravity to hypersurface

“…This is based on the mathematically well known fact that ∞ remains as the "same" ∞ even after a finite number is added to it; ∞ is not a fixed number but a "state" of increasing numbers 9. The equivalence between the usual formulation and ADM formulation of general relativity was questioned in[36].…”

Correlated worldline theory: Structure and consistency

“…The effort to find a consistent theory of quantum gravity, which incorporates key features of both quantum mechanics and general relativity, has been going on now for many decades [1][2][3][4]. Roughly speaking, one can discern two points of view on how to do this:…”

Spacetime as a Quantum Many-Body System

“…The construction of a complete theory of quantum gravity remains an open issue, despite decades of activities and important progress [1]. These have led to a number of approaches [2] and many fascinating suggestions for a radically new basis for understanding the world, which remain, however, still incomplete and not directly tested by observations.…”

“…The main attitude towards the problem of quantum gravity has been for many years [1] (and still is, in many corners) the straightforward one applied to all other fundamental interactions: start from the best classical description we have of the interaction and quantize it, i.e. apply to the corresponding classical theory well-tested techniques for turning it into a quantum theory.…”