How far are we from the quantum theory of gravity?

TL;DR

This paper reviews the progress of major quantum gravity approaches, especially loop quantum gravity and string theory, assessing their achievements, open questions, and potential for experimental validation in the near future.

Contribution

It provides a comprehensive comparison of results and open conjectures across various quantum gravity theories, highlighting recent advances and unresolved issues.

Findings

Significant progress in multiple quantum gravity approaches.

Unresolved issues remain in loop quantum gravity and string theory.

Potential for experimental tests at Planck scales to rule out some theories.

Abstract

An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other approaches are discussed, including dynamical triangulation models (euclidean and lorentzian) regge calculus models, causal sets, twistor theory, non-commutative geometry and models based on analogies to condensed matter systems. We proceed by listing the questions the theories are expected to be able to answer. We then compile two lists: the first details the actual results so far achieved in each theory, while the second lists conjectures which remain open. By comparing them we can evaluate how far each theory has progressed, and what must still be done before each theory can be considered a satisfactory quantum theory of gravity. We find there has been impressive recent progress on several fronts. At the same time, important issues about loop quantum gravity are so far unresolved, as are key conjectures of string theory. However, there is a reasonable expectation that experimental tests of lorentz invariance at Planck scales may in the near future make it possible to rule out one or more candidate quantum theories of gravity.