*The fact that a theory of quantum gravity hasn't been found reflects a crisis in physics. If we have a clearer understanding of the question “what is quantum gravity”, we will be better equipped to find our answer, writes Karen Crowther.*

We are all familiar with gravity. We observe its effects in the drooping of our bodies, the falling of sand through an hourglass, and the passing of the years as the Earth orbits the Sun. Our best description of gravity is Einstein's theory of general relativity, which tells us that the effects we observe are due to the interaction of objects with spacetime. While this theory is remarkably successful at describing the universe, physicists have long wanted to do away with it. For more than 70 years, they have been trying to find its successor: a theory of quantum gravity.

The fact that a theory of quantum gravity hasn't been found reflects a crisis in physics. But it is not obvious what the crisis is. How might we "diagnose" it? Here, I explore this question, and suggest that the answer is connected to another question—what is quantum gravity?

The reason that physicists want a theory of quantum gravity is not that there are any anomalous observations or unexplained experimental results that indicate a need to replace general relativity. Indeed, until recently, there were no observational results agreed to be evidence of quantum gravitational effects, and none of the attempts at a theory made any testable predictions. Although the empirical situation is no longer so bleak, the data available is still unlikely to be sufficient to lead to a new theory or strongly support any of the current attempts at finding one. And now, some physicists are starting to dissent.

Dissenting physicists argue that there are flaws in the formalism and methodology of some of the approaches to quantum gravity, particularly string theory. The underlying causes of the crisis, according to these physicists, range from psychosocial factors such as academic groupthink on the one hand to philosophical and scientific factors on the other.

“Although the empirical situation is no longer so bleak, the data available is still unlikely to be sufficient to lead to a new theory or strongly support any of the current attempts at finding one.”

**What is the Problem? We Don't Know the Problem**

Here, I would like to present one way of diagnosing the crisis that may be useful in eventually helping resolve it. My suggestion is that the problem is that we don't know what quantum gravity is. Or, put another way, the reason we haven't found a theory is because we don't know what we are looking for.

So, what is quantum gravity? Quantum gravity is whatever satisfies the constraints, or criteria of acceptance, we take to define quantum gravity.

A constraint is a principle, or feature, that physicists assume the new theory must satisfy. Physicists impose these in their search in order to narrow down the space of possible theories so that they're not left groping around completely in the dark.

So, what are the constraints on quantum gravity?

**Constraining the Search**

The constraints on quantum gravity are both empirical (coming from observational and experimental data) and non-empirical. The empirical constraints usually take precedence over the non-empirical ones in confirming or disconfirming a theory. The non-empirical constraints, however, are of great relevance to the current crisis.

Non-empirical constraints play various crucial roles in the construction and evaluation of scientific theories. For instance, they can be used as guiding principles which help us look for the theory yet may not end up featuring in the theory. They can also be used in a stronger role, as criteria of theory acceptance, where a new theory should not be accepted if it is incompatible with the principle.

Getting a better handle on these non-empirical constraints is, I claim, a potentially useful way of diagnosing, and perhaps eventually resolving, the current crisis in physics. This means examining which constraints are being used, how they are being used, and asking whether or not they should be used in these roles.

**Different Constraints, Different Theories**

Although we have no theory of quantum gravity, we have several approaches to finding one. These have different starting points, different methodologies, and different non-empirical constraints. In other words, the different approaches to quantum gravity have different goals: they are looking for different things. There is currently no single answer to the question of "what is quantum gravity?"

So, what is common to the different research programs? Is there some minimally agreed-upon set of constraints that they adopt?

The main motivation for seeking a theory of quantum gravity is that there are some domains—"regions" or "features" of the universe—that require both general relativity and quantum theory for their description, including the universe at extremely short length-scales, black holes, and the beginning of the universe. So a minimal definition of quantum gravity would be any theory that describes these domains. This looks like an empirical constraint since it concerns how the theory would describe and predict certain phenomena in the universe, however, we cannot directly observe or experiment in these domains.

This driving motivation is often framed as the non-empirical constraint of unification: we require a theory that describes quantum and gravitational effects as originating from the same source, e.g., from some basic entity or interaction. But unification is not necessary in order to satisfy the requirement of describing those particular domains.

String theory is one approach that takes unification as a constraint: it is promoted as a theory that has gravity and the three other fundamental forces all coming from the same origin, namely, the excitations of one-dimensional strings.

Other approaches do not share this constraint (at least in the strong form described). For instance, causal set theory and loop quantum gravity are approaches that instead prioritise the constraint of background independence. This principle is inspired by a central insight of general relativity and states that quantum gravity should not feature a fixed, or background, spacetime. There are different senses in which a spacetime can be said to be fixed, for instance, it may be one that doesn't change in the theory, or may be one that is used in the theory, but not itself described by the theory.

Background independence had not historically been taken as a constraint on string theory: the theory describes strings moving around in a background spacetime. Yet, thanks to philosophical criticism, background independence has come to be recognised as being of importance even in string theory, and there have been new developments in this area, for instance by showing that it's possible that the background spacetime is itself made up of strings.

Recently, a number of constraints labelled as "beauty principles" have been put under philosophical scrutiny by Sabine Hossenfelder. These include symmetry, unification, and naturalness. Hossenfelder's own diagnosis of the crisis is that these particular constraints have been clung to for too long and are not useful—they have, she argues, led us astray.

Exposing these widespread assumptions and demonstrating the need to investigate them is a good start, but we need to go even further.

**Questioning the Unquestionable**

Not all constraints adopted are done so explicitly. Many are assumed without being noticed by physicists or are so ingrained that no one questions them. It may be that they are indeed necessary or useful but we do not know that until we have examined them.

One is the cherished principle of generalised correspondence (physicists also call this reduction). The new theory must "link up" with the theory it's replacing in the domains where the older theory is known to be successful, via various mathematical relations that connect the two theories.

Correspondence is taken as an unquestionable constraint for empirical reasons: it's supposed to be a shortcut for showing that the new theory does not conflict with currently known observational data. It's an invaluable shortcut because there is so much existing data that doing all the necessary calculations to check it using the new theory simply isn't feasible. But correspondence is a mathematical relation between two theories, and, as such, is certainly a non-empirical constraint.

This principle may seem natural, or even obvious, but it's also a bit strange—we are seeking a replacement for a particular theory because we believe that theory is incorrect. Yet, we are relying on this older theory as an essential means of confirming the newer theory, as a substitute for direct empirical testing. In the case of quantum gravity, this means showing how both quantum field theory and general relativity, in their respective domains, are entailed by any new theory of quantum gravity. The newer theory (through the correspondence relations) is supposed to explain why the older theories were successful, in spite of their being incorrect. We know that general relativity works to describe our massive bodies as they fall towards the ground; quantum gravity cannot make this untrue, but it should offer deeper insight into why.

String theory, for instance, should be well-approximated by quantum field theory in the domains where we know that quantum field theory works, and should also be well-approximated by general relativity in the domains where general relativity works. For other approaches, including loop quantum gravity and causal set theory, the focus has predominately been on showing how we can "recover" particular aspects of spacetime from a non-spatiotemporal theory—arguably, this has been the primary goal of such approaches. These theories say that spacetime does not exist at the level of quantum gravity, yet they are still tasked to explain how it is that we successfully use the idea of spacetime in general relativity.

Why should we question the use of the generalised correspondence principle in quantum gravity? Because correspondence is relied upon very heavily in all approaches, we need to be assured of its soundness and be aware of its implications. It is a non-empirical constraint that is being used in the ways that empirical constraints are. For example, it is widely adopted as a criterion of acceptance, meaning that a theory of quantum gravity will not be accepted unless it links up with general relativity in a particular way. And, depending on what we mean by quantum gravity, it must also link up to quantum field theory in a particular way. (Again, we see how the non-empirical constraints serve to define what the question of quantum gravity is).

Questioning the generalised correspondence principle may mean asking whether the principle should be used as a criterion of acceptance—after all, if the principle is just a shortcut to establishing that the theory doesn't conflict with existing data, then it is not strictly necessary. Taking it as necessary might be too restrictive, and serve to exclude some theories that may be otherwise viable.

“We are seeking a replacement for a particular theory because we believe that theory is incorrect. Yet, we are relying on this older theory as an essential means of confirming the newer theory.”

There are, however, other reasons for imposing correspondence as a constraint: for instance, if we define quantum gravity as a theory that is more fundamental than general relativity and quantum field theory, then correspondence is a way of demonstrating this.

Quantum gravity is understood as a theory that is not only more fundamental than our current theories but absolutely fundamental—meaning that there is no deeper theory beyond. This is another constraint that we can question. Must quantum gravity be fundamental? Why should we assume it is? Could it be detrimental to the search for the theory to assume that it must be fundamental? I suggest that these types of questions might help us in better understanding the problem of quantum gravity.

For a theory to be fundamental in this sense, it must be UV-complete. This is another non-empirical constraint and states that the theory should give predictions at all short distance scales, or, equivalently, all possible high energy scales. ("UV" refers to ultraviolet frequencies, meaning short wavelengths, and "complete" means that the theory covers these. Note that being UV-complete is a necessary condition for fundamentality, but not a sufficient one.)

General relativity, like Newtonian mechanics before it, is a UV-complete theory: it gives predictions at all distance scales. Yet, we know that Newtonian mechanics is not correct at short distance scales, since it gets replaced by quantum theory. And now we are assuming that general relativity is not correct at all short distance scales—though there is no empirical evidence that suggests general relativity fails here—we are assuming that it gets replaced by quantum gravity. UV-completeness has standardly been taken as a constraint on quantum gravity: but again, we can, and should, question this (along with a related constraint, of mathematical consistency).

These are just some examples intended to give an indication of the sheer variety and pervasiveness of non-empirical constraints, as well as the essential role they play in framing the problem of quantum gravity.

**A Firm Foundation**

We do not need to tear everything down in order to build it back up. Nevertheless, if we take the crisis of quantum gravity seriously, then radical action is needed.

I have suggested one way of framing the crisis of quantum gravity is we do not know what quantum gravity is — we do not know the constraints that help to define the theory we are looking for. And we do not know which non-empirical guides can help us find it.

The radical action I advocate involves critically examining all of the principles we use, or could use, in searching for the theory—no matter how essential, fruitful, or convenient these might appear. This even, or perhaps especially, includes the most basic assumptions, without which we can hardly imagine physics at all. Here, we draw inspiration from the responses to previous crises, where physics turned to philosophy: questioning its foundational principles in order to diagnose the problems and move forward. Most clearly, this occurred at the turn of 20th century, with the crises in physics that eventually resulted in the development of relativity and quantum mechanics.

If we have a clearer understanding of the question “what is quantum gravity”, we will be better equipped to find our answer. The aim is not to do away with our non-empirical constraints, but rather to establish their validity and to ensure we have a firm foundation for future inquiry.

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