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Graviton & Quantum Gravity · Acedra
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Graviton & Quantum Gravity
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0:02
Physics is this close to understanding the entire universe. And what lives in this gap? Many physicists think it’s the elusive graviton—the quantum particle of gravity—whose discovery will finally allow us to stitch together our two great theories of nature into a single master theory. But what is the graviton, and does it even exist?
1:31
- The quantum revolution started when we realized that light is made of particles—photons. Max Planck guessed it and Albert Einstein proved it. Light is a wave in the electromagnetic field, and so even from the beginning of modern physics we have this idea that a force—the electromagnetic force—is communicated by particles. As quantum mechanics evolved into quantum field theory, we also found the particles for the weak and the strong forces. That’s three
2:02
of the four fundamental forces, leaving only gravity lacking a mediating particle. So, if we could just figure out the graviton, we’d have unified all the forces of nature and be on track to a theory of everything. We’re now 100 years after the birth of quantum mechanics, and much of the past century of work towards this master that hinges on the existence of the graviton. But does it exist? If not, much of that work in unifying our theories has been in the wrong direction.
2:34
We can describe nearly the entire universe in terms of two theories—quantum mechanics and general relativity. Yet they look wildly different to each other. taOn the quantum side we have these fields filling all of space, whose oscillations give us all known particles of matter and three of the four fundamental forces. These quantum fields fracture into discrete shards as you zoom in, and whose properties and
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particles can never be pinned down precisely. On the relativity side we have space and time merging into a unified fabric of spacetime; a fabric that can expand and warp. It stretches in response to matter and energy, leading to what we experience as the force of gravity. It’s a pretty effective picture. Quantum theory gives us the stuff of the universe, relativity gives us the container. Matter in spacetime. Matter tells spacetime how to curve and
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spacetime tells matter how to move. So, if this picture works so well in describing the universe, why do we need to try to force gravity to work the same way as the quantum forces. Well, partly because the two theories are so different. We expect, or at least hope, that all the complexity we observe in the universe emerges from unified underlying laws. That proved to be true of all matter and most of the forces of nature—quantum fields all the way down. It
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would be weird if the most fundamental layer of reality was actually two unrelated things. And extra weird if the theories describing those things are profoundly different—fundamentally
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discrete and random for the quantum, fundamentally continuous and deterministic for relativity. But maybe that’s just how it is. Not very elegant, but does the universe care what we find pretty? There’s another reason besides aesthetics that we need quantum theory and relativity theory to connect. That’s because at a fundamental level, they actively contradict each other. Together they describe most of the universe,
4:45
but in certain places like the center of a black hole or at the big bang, they generate contradictions and paradoxes that, it seems, can only be solved by finding the master theory in which quantum mechanics and general relativity connect seamlessly. For various reasons, most physicists trying to solve this problem follow a particular path. The path of particles. They try to quantize gravity, just as they once
5:14
quantized electromagnetism. And the search for this theory of quantum gravity implies a particle that mediates gravity. That’s the graviton. If the graviton exists, then gravity has to be quantum, and vice versa. Let’s see why that’s the case. To get a photon, we start with the classical electromagnetic field—the one described by Maxwell’s equations. A field in that sense is just something that extends through space
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and has some value at each point in space. That value can be a simple number. Like, the density or temperature of the air in the room, giving a density or temperature field. Or it can be a vector—a number and direction. The EM field is like that—a strength of the force and a direction at every point in space. Fields can support waves—oscillations in field strength that move through space. The
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density field in air supports sound waves. The EM field supports EM waves, which we know as light. So, when Planck and Einstein showed that light is made up of indivisible particles, we were set on the path to quantizing the EM field itself. This process of “quantization” followed the development of quantum mechanics in the mid 20s and quantum field theory in the following couple of decades. Through quantization, the EM field is broken down into countless modes of
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all different frequencies. In this new description, even the empty or vacuum-state of the EM field is made of those modes—made of infinite electromagnetic waves stacked and canceled into nothing. And those “virtual” modes are made of discrete packets, just as “real” EM waves—so the EM field is made of virtual photons. In quantum field theory, we describe the quantum electromagnetic force in terms of particles
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exchanging these virtual photons. They take momentum from one particle and give it to another, causing the push and pull that we see as a smooth EM force. Photons mediate electromagnetism. We’ve talked about whether these virtual photons can be thought of as “real” before. But what IS real is the fact that the EM field is extremely well described as being made up of quantized chunks. If we use basically the exact same process to quantize slightly more
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complicated fields we get the other quantum forces and their mediating particles—the gluons for the strong force and the W and Z bosons for the weak. It should not be taken lightly that this stuff works so incredibly well. We take a classical field, make some symmetry arguments to guess what other fields might exist, apply quantization rules, and boom, we figure out almost all of the particles and forces that
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make up our universe. The standard model of particle physics is arguably the most successful theory in physics, and perhaps science. It’s not surprising that we’d want to envelop gravity and spacetime into the explanatory magnificence of quantum field theory. So, how do we proceed? Well, we need to identify the field that we’re trying to quantize and then apply the quantization rules just like we did with the other forces.
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We do know that gravity behaves like electromagnetism in important ways. It has a strength at all points in space. It also supports waves—gravitational waves—that also travel at the speed of light. There are differences, however. According to general relativity, the gravitational field is not a field on top of spacetime, like electromagnetism, but rather in a very real sense it’s the fabric of spacetime itself. This tangling of the field
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and its .. is going to be a problem as we’ll see, but for now let’s proceed. Let’s get a little more precise. In the Einstein field equations, the field we’re interested in is encapsulated in something called the metric tensor—a 10-valued object made up of scalars and vectors with a value at every point in space. It’s a field, albeit a very complicated one. Where the EM field can be thought of as a thing lying on top of the
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background grid of spacetime, this tensor field of GR in a real sense IS the grid of spacetime. In electromagnetism, the field changes with respect to the grid. In general relativity, the grid itself changes. This is going to prove complicated, but nonetheless, this grid, this spacetime, this tensor field is the thing we need to quantize. So let’s do that. We’ll start with an approach that hopefully won’t break anything. We’re going to treat the gravitational field as a
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small fluctuation – or perturbation – to an imaginary flat and static background. We poke flat spacetime very lightly and see what comes out. Hopefully a graviton. This is a very standard approach in physics. It’s called perturbation theory. Rather than completely changing our model, we just make a tiny adjustment to what we understand and see what happens. The result is a good approximation to reality, assuming the perturbation is very
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small. Take for example electromagnetism—we can understand its quantum behavior by taking account of the exchange of different nudges to the electromagnetic field as represented by the exchange of virtual photons in different ways. For a weak interaction, only the most obvious exchanges matter—like the exchange of a single virtual photon. Stronger interactions require us to account for more complex exchanges, but it all works out beautifully.
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When we do this to the gravitational field everything is … also fine! Not only can we do a sort of gentle quantization of a weak gravitational field, we get a glimpse of the quantum of that field that mediates the gravitational force—the graviton. What does it look like? Well, it inherits all of its properties in a pretty non-negotiable way from the field it comes from. It’s a massless, spin-2 boson. Massless means it travels at the speed of light. Spin 2 means it has a
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180 degree rotational symmetry that reflects the sort of stretch-squish action on space, just like the gravitational waves that should be built from these gravitons. And boson means you can stack infinite gravitons together, to make gravitational waves. And just as virtual photons make the quantum EM field, we can build the fabric of spacetime out of virtual gravitons. Cool cool. In a sense we just succeeded in quantizing gravity. This approach of
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perturbative quantum gravity, and it actually works. We can use it to recover classical gravity. We can even use it to make predictions, like Stephen Hawking’s prediction of Hawking radiation—leaky black holes. So why don’t we just stitch this quantum gravity to the rest of quantum field theory and say we have a theory of everything? Why not add the graviton to the standard model library and move on with our lives?
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Not so fast. We want our final theory to explain the whole universe, but our perturbative quantum gravity only works in the case of very weak gravity. It doesn’t work for places with extreme spacetime curvature, like the centers of black holes. We also want to actually verify our quantum gravity theory with experiment, and our perturbative theory works only in situations where it’s essentially impossible
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to differentiate it from regular Einsteinian gravity with a human-buildable experiment. We really need the full theory. So, to finish the job of quantizing gravity we have to see if we can generalize this to a theory that works everywhere, including where gravity is extreme. As gravity gets stronger, our perturbations get bigger and the corrections we need to make to our classical theory get larger. More technically,
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we need higher-order corrections, represented by more complex interactions via virtual gravitons. Remember how we do this for the quantum electromagnetic interactions. We calculate our quantum EM force by summing over all the possible virtual interactions that could have occurred. For weak EM fields it’s enough to include only the most probable such interactions, and that means the simplest ones. Like, the exchange of a virtual photon or two. For stronger EM fields,
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more complex interactions become important. That includes so-called self-energy terms, which result from the feedback between the different fields. These higher-order terms involve loops that appear in the many Feynman diagrams that we sum together to compute a strong interaction. In a previous episode we talked about the connection between these loops and the mass of the electron, and how they appear to make that mass infinite.
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But these sorts of infinites can’t be real or we wouldn’t have a universe. In regular quantum field theory we have a way to remove them called renormalization. It lets us sort of divide them out by grounding them in measured values, for example by measuring the true mass of the electron. This is possible with the regular quantum fields because the perturbative expansion—the sum of Feynman diagrams—”only” generate a finite number of infinities. It’s
15:44
still possible to absorb these into a finite number of additional terms in our equations. Even if “absorbing infinities” sounds a bit hokey, it works incredibly well. By grounding our otherwise-infinite predictions in a few finite measurements of the real universe, quantum field theory is able to make stunningly precise predictions of many, many things. Not a bad trade-off. Depicting the EM field as being made of virtual photons is incredibly successful,
16:15
which forces us to take seriously this picture of a quantized field. At some level we believe that the EM and other quantum forces are mediated by particles. If we can do for gravity what we just did for electromagnetism then we can make the same argument for the reality of the graviton. So, we’re ramping up the strength of our quantum gravity, increasing the complexity of our perturbative approximation, and hoping we can renormalize any infinities to get a sensible
16:45
theory. And this is where everything goes catastrophically wrong. The problem is that gravitons interact gravitationally. They interact with themselves. The photon, on the other hand, does not interact electromagnetically—at least not directly. It interacts with, say, the electron field, which feeds back on the EM field. That extra step limits the complexity of the photon self-interaction and limits the number of self-energy loops, making renormalization possible.
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But a graviton can directly spawn other virtual gravitons which can spawn more virtual gravitons, ad infinitum. Instead of a finite number of self-energy loops we get an infinite number. An infinite number of terms in our perturbative approximation that can’t be renormalized—canceled out—with a finite number of real measurements. In cases of strong gravity, our quantum gravity theory becomes meaningless. We say that perturbative quantum gravity is
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non-renormalizable. We can also think of this in terms of the strength of the gravitational coupling—the gravitational constant—getting stronger as the field getting stronger, ultimately sending the field strength to infinity. This straightforward approach at quantizing gravity leads to nonsense. So maybe it follows that we can’t build the gravitational field out of gravitons after all. Does this mean that the
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graviton doesn’t exist? Not really. What it means is that this simple picture of quantum gravity that we get by applying the same quantization methods as the other forces isn’t right. There may be a theory of quantum gravity that just can’t be got to by the simple perturbative approach. Interestingly, it’s the graviton itself that may lead us to the final answer. Even though the standard approach didn’t get us all the way, the picture of the graviton we got from it is
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almost certainly right—if the graviton exists at all, it has to be a massless, spin-2 boson. Nothing else can generate the Einstein field equations in the classical limit. And that’s why, when we find a theory that predicts a massless, spin-2 boson our ears prick up and we wonder if we’ve found a potential for quantum gravity. And that’s happened once before, giving us string theory. This was originally meant
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to be a theory for quark interactions, but a graviton-like particle popped out of the math in such a profound way that it sparked a many-decade quest to find a stringy theory of everything. You can’t avoid the graviton in string theory, and in string theory you also avoid the rampant infinities because. At the smallest scales where gravity can be strongest, the graviton field is smeared out over the vibrating strings at the theory’s core.
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There are other approaches to quantum gravity, like loop quantum gravity and others. All of them have a graviton, because without the graviton there’s no path to classical gravity. It’s again sounding like the graviton is inevitable. But again, no. It’s only inevitable if gravity is fundamentally quantum in the first place. If the final theory looks more like quantum mechanics than general relativity. What’s the alternative? Well,
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it’s that the fabric of spacetime doesn’t have discrete chunks—it’s not made of gravitons. Maybe a smooth, continuous spacetime is fundamental in some way. A number theories favour this option. Even Roger Penrose is a proponent, encouraging us to “gravitize the quantum” rather than quantizing gravity. Fit quantum mechanics into general relativity rather than the way around. Ultimately, finding evidence of the actual existence of the graviton will be critical to
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confirming the quantum nature of gravity and even which quantum gravity we have. As I hinted, that’s going to be really, really hard to do directly because we’d need to build solar-system-sized particle accelerators. Fortunately there are brilliant methods to observe the indirect effects of the interactions of a quantum graviton that we can do now. For example, spotting the mediation of quantum entanglement by a gravitational field or a Cavendish experiment, but with exceptionally
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tiny masses. One of these methods may pan out very soon, or we may have to start astroengineering our mega-collider. Nature has set a last gigantic hurdle to understanding her deepest laws. We need to understand and then find the graviton, and then we’ll hold the building block of spacetime.
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