What do we want from quantum gravity?

To begin with, a theory of quantum gravity should tell us how quantum matter gravitates, especially if gravity is strong. As long as gravity is weak, we could get away with quantizing it in the same way that we quantize other interactions. But this weak-field quantization stops making sense when gravity is strong, such as when highly energetic particles collide at energies so high that the particles themselves have a strong gravitational interaction.
Quantum gravity should also tell us what happened in the very early universe. According to general relativity, our universe started in a singularity. This unphysical result indicates that we need a more fundamental description of space and time back then. Since gravity was strong in the early universe, quantum effects of gravity cannot be neglected when describing this phase.
General relativity also predicts singularities when matter collapses into black holes, which leads to what is known as the black hole information loss paradox. It concerns the fact that black holes emit thermal radiation because of quantum effects, not including quantum gravitational effects. But when the black hole has completely evaporated, all that is left is thermal radiation, regardless of what formed the black hole. Information is destroyed in this irreversible process, but since irreversible processes cannot happen in quantum mechanics as we know it, this represents an inconsistency. Quantum gravity should explain what happens to the information in black holes.
Along with solving these thorny problems, the successful theory of quantum gravity must also be able to reproduce all achievements of general relativity and the Standard Model of particle physics. And it must make testable predictions that give us confidence that we have the right description of nature.

What have we learned so far?

Physicists are working on several approaches to quantum gravity: string theory and loop quantum gravity; causal dynamical triangulation and asymptotically safe gravity; causal sets; group field theory; emergent and induced gravity; and a few other comparably small research agendas. String theory currently has the highest score in addressing the above requirements, followed by loop quantum gravity and asymptotically safe gravity.

Graphical artwork of blue and yellow spiralling lines on a black background
From the outside, research on any of these approaches to quantum gravity must be like watching the construction of a tunnel. For a long time, nothing much happens, except that occasionally a tool goes in and rubble comes out. But step inside and you will see a hive of activity. Recently, a lot of progress has been made in each of the approaches – progress that has considerably advanced our understanding of the problem. In the end though, a tunnel is only useful once a breakthrough is made.
While no breakthrough has yet been made, we are learning. We have learned that specific properties of quantum gravity appear in several of the approaches, if in different manifestations. The best known example may be holography – the encoding of information contained in a volume on the boundary of that volume. The existence of a minimal length scale is another such property that appears in different approaches. It seems that, ultimately, quantum gravitational fluctuations prevent us from resolving structures arbitrarily well. A more recent discovery is that the dimension of space–time seems to become smaller on short distances, a surprising behaviour that has also been found in different approaches.
I have little doubt that we will be able to unify quantum mechanics and gravity; some of my colleagues might even argue that we have already done so. But we are not looking for a theory of quantum gravity. We are looking for the theory of quantum gravity – the theory that describes the world around us. Making connections with observation is thus not only important, but also necessary for quantum gravity to be scientific.

What is next?

So far, we do not have any experimental evidence for quantum gravity. But during the last decade it has become clear that it is technologically possible, even in the absence of a fully fledged theory, to search for evidence of general properties expected of quantum gravity – like the ones named above, and more still, such as violations of certain symmetries. This can be done, and has been successfully done in some cases already, through the use of phenomenological models. Such models parameterize effects and make connections with observations. Observations can then be used to learn what properties the yet-to-be-found theory can have and which it cannot have. I think that this experimental guidance is essential to constructing the theory of quantum gravity, and is the route to making progress.
Since gravity is really a consequence of space–time being curved, we are looking for a theory of the quantum nature of space and time itself. It is the most fundamental of the currently open questions in the sense that it concerns the most basic ingredients of our theories. Next to revolutionizing our understanding of space, time and matter, quantum gravity will likely also significantly advance other areas. The nature of time and its uni-directional arrow are puzzles deeply interlinked with quantum gravity, and so is the physics of the early universe. Moreover, I believe we will learn a lesson about quantization that has the potential to improve our ability to manipulate quantum matter.
The tunnel's construction site might not look like much, but rest assured: once a breakthrough is made, you will see heavy traffic on the new route.