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, 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.PACS numbers: 04.60.-m * This article is to be published in International Journal of Modern Physics D and also in the book "One HundredYears of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity," edited by Wei-Tou Ni (World Scientific, Singapore, 2015 Quantum gravity is the research that seeks a consistent unification of the two foundational pillars of modern physics -quantum theory and Einstein's theory of general relativity. It is commonly considered as the paramount open problem of theoretical physics, and many fundamental issues -such as the microscopic structure of space and time, the origin of the universe, the resolution to spacetime singularities, etc. -relies on a better understanding of quantum gravity.The quest for a satisfactory quantum description of gravity began very early. Einstein after proposing general relativity thought that quantum effects must modify general relativity in his first paper on gravitational waves in 1916 [1] (although he switched to a different point of view working on the unification of electromagnetism and gravitation in the 1930s). Klein argued that the quantum theory must ultimately modify the role of spatio-temporal concepts in fundamental physics [2][3][4] and his ideas were developed by Deser [5]. With the interests and developments of Rosenfeld, Pauli, Blokhintsev, Heisenberg, Gal'perin, Bronstein, Frenkel, van Dantzig, Solomon, Fierz, and many other researchers, three approaches to quantum gravity after World War II had already been enunciated in 1930s pre-World War II as summarized by Stachel [6]:1. Quantum gravity should be formulated by analogy with quantum electrodynamics (Rosenfeld, Pauli, Fierz).2. The unique features of gravitation will require special treatment -the full theory with its nonlinear field equations must be quantized and generalized as to be applicable in the absence of a background metric (Bronstein, Solomon).3. General relativity is essentially a macroscopic theory, e.g. a sort of thermodynamics limit of a deeper, underlying theory of interactions between particles (Frenkel, van Dantzig).Many ideas of the early time continue to provide valuable insight about the nature of quantum gravity even today. For example, the 1939 work on linearized general relativity as spin-2 field by Fierz and Pauli [7] inspired a recent development on massive gravity, bimetric gravity, etc.Modern work on quantum gravity, however, did not really start off until the development of a canonical formalism in 1959-1961 by Arnowitt, Deser, and Misner (ADM) for the case of asymptotically flat boundary conditions [8][9][10][11][12][13][14][1...

Monte Carlo simulation of cosmologies with dust

“…These include Causal Dynamical Triangulations (CDT), Causal Sets, Loop Quantum Gravity (LQG), Asymptotic Safety, Euclidean Quantum Gravity and String Theory (-see e.g. [2] for an overview of some of these approaches).…”