How far are we from the quantum theory of gravity?
Lee Smolin
TL;DR
Smolin evaluates the progress toward a complete quantum theory of gravity by methodically comparing the leading programs, especially loop quantum gravity and string theory, against a comprehensive set of questions spanning quantum gravity, cosmology, unification, and foundational issues. He aggregates tangible results and open conjectures for each approach, highlighting impressive advances (such as discrete quantum geometry and horizon microphysics in LQG, and perturbative consistency and dualities in string theory) while also underscoring unresolved challenges (notably background independence in string theory and low-energy limits in LQG). The paper argues that Planck-scale tests of Lorentz invariance could soon rule out some candidates, offering near-term empirical leverage. Overall, LQG is presented as closer to a complete framework with a concrete program for completion, whereas string theory remains a broad, highly ambitious enterprise with significant open conjectures and a larger landscape of possible backgrounds. The work emphasizes the vitality of multiple approaches and the potential convergence of ideas, suggesting experimental guidance will soon help distinguish between competing quantum-gravity pictures.
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.