Any theory of quantum gravity will (likely) have these three properties
We know more about quantum gravity than you think.
I was playing around with an AI copywriter. I wasn’t expecting much from it. AI isn’t very creative and whatever AI produces whether art or writing tends to be derivative. I used rytr, a free tool, and gave it a few prompts about how AI might help solve quantum gravity. This is what it generated:
Quantum gravity is a fundamental problem in physics. It is the field of study that seeks to unify quantum mechanics and general relativity. The word “quantum” refers to the smallest possible unit of energy, or quanta. The word “gravity” refers to the force that keeps us on Earth and causes things to fall towards Earth’s surface.
The two theories are incompatible with one another because they describe two different aspects of reality: quantum mechanics describes how matter behaves at an atomic level, and general relativity describes how space-time curves as a result of matter’s presence in it.
In order for these two theories to be reconciled, there needs to be a way for them to work together without contradicting each other. AI may be able to help solve this problem by
The writing is not bad, but you can tell the content is derivative because it doesn’t really tell you anything useful or interesting about the topic. It isn’t written like someone who knows what they are talking about. Maybe that’s why people read my articles (at least the ones about physics). I can’t claim to be an expert in theology or political theory or history, but I have spent over 20 years studying physics. I have read hundreds if not thousands of academic papers on dozens of topics, and I have a good idea of the common misconceptions that appear in the media.
Now, it is true that quantum physics describes what happens on the atomic level, and it is true that the best theory of gravity we now have describes how matter curves or warps spacetime. These facts are not in dispute. What is in dispute is whether quantum gravity has anything to do with these things.
Using the word “atomic level” loosely to talk about anything as big as or smaller than an atom, most theories of quantum gravity propose to explain how the theory of gravity differs from Einstein’s theory of curved spacetime we know and love.
String theory does so by explaining that gravity is the result of a gravitational field appearing from the vibrations of strings in a higher dimensional spacetime. This theory does little to try to merge the Riemannian geometry of general relativity with quantum theory. Instead, it attempts to unify gravity with all other forces as string modes acting against a fixed background spacetime.
Loop quantum gravity is less ambitious and tries to explain how spacetime can be emergent from loops on graphs. It utilizes a special formulation of general relativity to achieve this called Ashtekar variables and then proposes a discrete spacetime where only connections between points matters.
There are a few other approaches to quantum gravity worth mentioning: quadratic gravity, classical gravity (the idea that gravity is fundamentally classical), as well as asymptotic safety. One might also include Entropic Gravity since it assumes that spacetime and gravity don’t exist at a small enough scale. Each of these has their own problems.
Most authors, if they get down into the details at all, explain that the big problem with quantum gravity has to do with a mathematical technique called “renormalization”. We use renormalization to make quantum theories give sensible results, but those quantum theories have to have a particular mathematical form in order to be renormalizable.
It’s hard to overemphasize how important renormalization is. Without it no realistic quantum theory produces sensible results. They just predict infinite values. Ken Wilson won the Nobel Prize partly for making sense out of it.
Wilson taught us that renormalization is not just a mathematical technique. It is a theory for describing how quantum theories change with scale, either increasing energy scale or decreasing length scale. (Energy and distance in quantum physics are inversely proportional.) Quantum theories tend to change subtly as we probe higher and higher energies and smaller and smaller scales until, at some magical scale, they change radically to become new theories.
For example, Fermi’s theory describes the weak force that explains radioactive decay. Fermi’s theory, however, could not be correctly “quantized” because it was not “renormalizable”. In other words, it broke down at a certain energy scale around 293 GeV (Giga electronVolts). At that point, Fermi’s theory actually merges with electromagnetism and becomes electroweak theory producing W and Z bosons. This radical change means that Fermi’s theory is an effective theory or approximation to the more fundamental electroweak theory.
Fermi’s theory is like a description of liquid water. The changes in how the water behaves are subtle as the temperature increases until, at 100 degrees Celsius (212 Fahrenheit) at 1 atmosphere of pressure, theories that apply to liquid water rapidly break down as the water boils and becomes a gas. Electroweak theory is like a description of water molecules. It explains the gas but also how we get from gas to liquid (via spontaneous symmetry breaking and the Higgs mechanism in the case of electroweak).
Theoretical particle physicists infer that a general principle of quantum physics is that theories tend to merge with other theories at higher energies. This suggests that all theories should merge at some very high energy called the Grand Unification Energy.
But gravity isn’t like Fermi’s theory in some important ways. It isn’t just a force theory. It is a theory of space and time. It is not only a theory of how matter attracts. It is a theory that includes such strange beasts as black holes, describes the universe as a whole, and has some counterintuitive things to say about temperature and entropy.
Yet, we can make educated guesses and infer more about quantum gravity than much of the literature and certainly the AI authored snippet above seem to imply.
Resolving Planck Scale Physics
If you try to make an analogy between Fermi’s theory and gravity, you quickly run into problems when you approach small scales.
The Planck length is the smallest measureable distance because any smaller distance, if energy existed at that wavelength, would form a black hole. It is so small that if an atom were the size of the Earth, the Planck length would be smaller than an atom. We have never come close to detecting anything at this scale.
The problem with forming black holes at the Planck length scale is that it doesn’t stop there. Einstein’s theory interacts with itself so strongly at these scales that it runs away generating nonsense results that are insurmountable. In other words, we can’t discount physics going on below the Planck length because we can’t get the theory to behave “nicely” at that scale, for example, becoming a non-interacting theory.
Einstein’s physics never stops interacting with decreasing scale, so smaller scales, such as those below the Planck scale, can’t be thrown out to force the theory to make sense.
All other theories stop changing with scale at some point, called a conformal UV fixed point. As far as we know, Einstein’s relativity has no such point although it does have a conformal fixed point at large scales, called a conformal IR fixed point. In other words, Einstein’s theory stops interacting with itself at very large scales.
This makes Einstein’s relativity an ill-defined quantum field theory or half-ill defined since it has the one required fixed point at cosmic scales but lacks the other one. All well-defined quantum field theories that explain electromagnetism and the behavior of atoms, quarks, and so on have two fixed points one at the scale of the very large and one at the scale of the very small. The theories run between these two scale points, perturbing them but ultimately running back to them.
If Einstein’s relativity were an approximation that only works at large scales and some other theory explains what’s going on at small scales, then we could solve this problem. If this were the case, we would call Einstein’s an “effective” field theory because it is effectively true at large scales even though it breaks down at small. Indeed, the problems with Einstein’s theory at small scales cry out for it to be merely effective, spontaneously broken, just as Fermi’s was, because otherwise the universe would seem to be impossible.
Using the AdS/CFT Correspondence
If we go by the other forces, gravity should be a perturbation of a conformal field theory, not just curved spacetime at the Planck length, and this would make it radically different at small scales from the theory we know.
A conformal field theoretic gravity only appears however when you take a specific kind of solution of the Einstein field equations called an Anti-deSitter spacetime and project it onto a hypersurface (just the boundary of a higher dimensional volume) in one less dimension. This is called the AdS/CFT correspondence.
Despite the jargon in the previous paragraph, it isn’t that complicated a concept, at least to picture in the usual three dimensions if you’ve ever seen a hologram, especially if you’ve made one with lasers and holographic film.
Holography is the idea that all the information in a space is contained in a lower dimensional surface and projected into that space. Holograms do exactly this by encoding enough information about light, color, intensity, and, most importantly, direction, and projecting it from a two dimensional plate or film into a three dimensional space. The projection of the image, although originating from a two dimensional film, creates the appearance of a three dimensional object.
The AdS/CFT correspondence is an example of holography or the holographic principle because it says that all the information in a quantum theory in an AdS space can be encoded by a conformal field theory, meaning a scale invariant one, in one less dimension.
What does that really mean? Well, it means that you can relate a theory of quantum gravity to a conformal quantum field theory in one less dimension which is an interesting and useful result. It says that you don’t have to worry about quantum gravity in the world in which we live, where it might not make sense as a quantum field theory, because it only has to make sense as a conformal field theory on some (potentially infinitely distant) boundary. But that doesn’t solve the fundamental problem because our theory is incomplete.
All AdS/CFT tells us is that any complete theory of quantum gravity on an AdS will be precisely a CFT. It also works in the other direction, so that, by studying CFTs and making general statements about them, we can say things about all possible theories of quantum gravity.
Unfortunately, it does not tell us what that theory is.
While usually presented in the context of string theory, AdS/CFT actually explains even elementary results in quantum mechanics such as free particles and energy levels of wavefunctions in terms of holography, so it is a powerful concept all by itself.
The AdS/CFT is a non-trivial but incomplete and sometimes baffling theory, especially because we seem to live in a universe that is deSitter rather than anti deSitter.
An anti-deSitter universe can be thought of as being a hypersurface embedded in a universe with two time dimensions and several space dimensions. Particles travel along this surface through time and when you quantize them they map to CFTs.
The only downside is that such a universe has a negative cosmological constant! And we know, because our universe’s expansion is accelerating, that ours has a positive cosmological constant, so-called Dark Energy. Our universe seems to be deSitter, not anti deSitter. A deSitter space can be thought of as a hypersurface embedded in a space with one time and several space dimensions.
While some particle theorists would like gravity to somehow flip from AdS to dS at a particular length scale, neatly solving the problem, others have attempted to build the dS/CFT correspondence with mixed results.
The dS/CFT correspondence has, unfortunately, run into some problems. One is that quantum field theories on dS spaces are subject to “bubble nucleation”, meaning that the vacuum is unstable and forms bubbles of true vacuum which may threaten the existence of a correspondence to CFTs on the boundary.
Using the Holographic Principle and Black Hole Thermodynamics
One of the most famous formulas in physics, due to Hawking and Bekenstein, is that the entropy of a black hole is proportional to the surface area of its event horizon. This fact is another example of the holographic principle because it means that all the information contained within a black hole only grows relative to its surface area. This means that anything that falls into a black hole, which lends its entropy and information to said hole, only contributes in proportion to how much it expands the black hole’s event horizon.
Thus, we have to infer from this that the entire universe is a hologram, projected from two dimensions into three. But this fact also has implications on quantum gravity.
Think about it like this: if information is stored on surfaces instead of in volumes, then that includes the information stored in gravity itself which produces space and time. That means that space itself must be a holographic projection and must cease to exist at some small scale. Conversely, everything in the universe can be represented as information and energy living on its boundary. What is inside the universe, what physicists call its “bulk” contains only the information that exists on the boundary, projected in from “infinity”, meaning arbitrarily far away or most likely a very large but finite horizon of some kind in our case.
That means that we can define quantum gravity as a theory living, not in the universe, but on its boundary with degrees of freedom that also live on the boundary. Einstein’s theory then emerges as an approximation.
In fact, by this, the holographic principle resolves one of the worst predictions in the history of physics, the prediction that the cosmological constant should be 120 orders of magnitude (1 with 120 zeros) times what we measure it to be. That prediction assumes every point in space has something called vacuum energy, basically that Planck scale black holes are popping into and out of existence all the time everywhere. Each of those black holes, however, would have an associated amount of information. But, if it is true that information exists only on the boundary of the universe, the problem is resolved. There are no Planck scale black holes because the boundary of the universe can’t hold as much information as the bulk interior and hence can’t support all those tiny black holes and their associated info.
One proposed boundary is what is called the future horizon, which is not at infinity but is rather the farthest we will ever be able to see in the expanding universe. There is some indication that you can arrive at the cosmological constant using the size of this horizon and the holographic principle.
The Unknown Theory of Quantum Gravity
From all the above, we can make educated guesses about the theory of quantum gravity:
It must be a conformal field theory to cut off or resolve physics below the Planck scale.
It will be expressed in terms of the AdS/CFT or, if we can make it work, dS/CFT correspondence.
It will make use of the holographic principle.
String theory mostly falls into this paradigm (not surprisingly many of the inventors of these principles are string theorists). They predict the existence of many compact dimensions that we can’t see as well, but none of these three principles actually requires string theory.
Loop quantum gravity has also made some steps to relating itself to AdS/CFT and holography.
There are also some theories that fall outside this program like asymptotic safety which has largely rejected the holographic principle in favor of gravity being a local quantum field theory in bulk spacetime.
There may yet be another theory that perfectly explains all of these without necessarily being a theory of everything or needing to describe spacetime as emerging from small scale local degrees of freedom. If spacetime is projected, then it emerges from a projector on the boundary and is not emergent in the bulk of spacetime itself. This likely applies to everything and so a theory of everything would also be holographic in every respect.
While none of these principles have to be in a theory of quantum gravity, it would be surprising if they were not given that we can infer them from either Einstein’s theory, quantum field theory, or some combination of the two.
The ultimate unknown theory of quantum gravity, however, continues to elude us, mired in theoretical problems and a lack of evidence to boot. Will any of us live to see it resolved?
Kaplan, Jared. “Lectures on AdS/CFT from the bottom up.” (2016).
Harlow, Daniel, and Douglas Stanford. “Operator dictionaries and wave functions in AdS/CFT and dS/CFT.” arXiv preprint arXiv:1104.2621 (2011).
S. R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys.Rev. D 21 (1980) 3305