Sean Carroll

I'm not just making this up. There is a standard understanding that there are two kinds of problems with quantizing gravity. There are technical problems and there are conceptual problems. The technical problems are just that, according to the ordinary ways we have of doing quantum field theory, which is what you should need to do in gravity since gravity

Einstein's general theory of relativity is a classical field theory. In quantum field theory, we have rules for taking a classical field theory and quantizing it. And in the case of gravity, these rules don't work. The straightforward way of saying this is that it's not a renormalizable theory, which is to say that if you try to extend your quantum field theory version of gravity,

Einstein's general theory of relativity is a classical field theory. In quantum field theory, we have rules for taking a classical field theory and quantizing it. And in the case of gravity, these rules don't work. The straightforward way of saying this is that it's not a renormalizable theory, which is to say that if you try to extend your quantum field theory version of gravity,

to arbitrarily high energies, you kind of get nonsense. You lose the ability to predict what is actually going to happen, okay? I'm sort of hesitating because there's a technical way of saying this. I'm not sure if it's worth saying, but essentially to make any one prediction requires an infinite number of input parameters in the theory. That's the consequence of non-renormalizability.

to arbitrarily high energies, you kind of get nonsense. You lose the ability to predict what is actually going to happen, okay? I'm sort of hesitating because there's a technical way of saying this. I'm not sure if it's worth saying, but essentially to make any one prediction requires an infinite number of input parameters in the theory. That's the consequence of non-renormalizability.

Now, you may have heard me say that we have this thing called effective field theories, right? If you don't want to extend your field theory to arbitrarily high energies, then we can just say we have a cutoff, we have an energy scale above which we don't care, and make a theory about what happens below that scale. And that you can do for gravity, and it works in a wide variety of circumstances. But

Now, you may have heard me say that we have this thing called effective field theories, right? If you don't want to extend your field theory to arbitrarily high energies, then we can just say we have a cutoff, we have an energy scale above which we don't care, and make a theory about what happens below that scale. And that you can do for gravity, and it works in a wide variety of circumstances. But

If you think that what we're actually after, at some point, you care about what does happen even at arbitrarily high energies. So the effective field theory technique lets you have a functioning theory, an effective theory, below a certain energy scale. But that doesn't mean you don't care what happens above the energy scale.

If you think that what we're actually after, at some point, you care about what does happen even at arbitrarily high energies. So the effective field theory technique lets you have a functioning theory, an effective theory, below a certain energy scale. But that doesn't mean you don't care what happens above the energy scale.

And when you start including gravity, maybe you do care what happens at energy scale. So gravity is just sort of not a successful quantum field theory by the standard measures. So in other cases where we had like the Fermi theory of the weak interactions, Enrico Fermi came up with this theory where neutrons could decay into protons, electrons, and antineutrinos, right?

And when you start including gravity, maybe you do care what happens at energy scale. So gravity is just sort of not a successful quantum field theory by the standard measures. So in other cases where we had like the Fermi theory of the weak interactions, Enrico Fermi came up with this theory where neutrons could decay into protons, electrons, and antineutrinos, right?

That's a non-renormalizable theory also, just like gravity is. But it turns out it wasn't the right theory. It was only a theory that works below a certain energy scale. And above that energy scale, you have to invoke W bosons and the weak interactions and things like that. and you get the standard model of particle physics, which is a renormalizable theory.

That's a non-renormalizable theory also, just like gravity is. But it turns out it wasn't the right theory. It was only a theory that works below a certain energy scale. And above that energy scale, you have to invoke W bosons and the weak interactions and things like that. and you get the standard model of particle physics, which is a renormalizable theory.

So you might hope to find a renormalizable theory that reduces to gravity at low energies. No one has been able to do that. They tried. Okay. Well, actually, sorry, that's not true. String theory is exactly an example of this. In fact, maybe it's worth saying that, you know, to a lot of people who wonder why string theory is so popular, this is really the reason. At the end of the day,

So you might hope to find a renormalizable theory that reduces to gravity at low energies. No one has been able to do that. They tried. Okay. Well, actually, sorry, that's not true. String theory is exactly an example of this. In fact, maybe it's worth saying that, you know, to a lot of people who wonder why string theory is so popular, this is really the reason. At the end of the day,

That's why string theory is so popular because you think that you really are looking for a theory that is complete. Indeed, the phrase that is used is an ultraviolet complete theory, a theory that works up to arbitrarily high energy scales. And I'm even underselling the problem with gravity because it's not just that gravity itself is non-renormalizable and gives you infinities at high energies.

That's why string theory is so popular because you think that you really are looking for a theory that is complete. Indeed, the phrase that is used is an ultraviolet complete theory, a theory that works up to arbitrarily high energy scales. And I'm even underselling the problem with gravity because it's not just that gravity itself is non-renormalizable and gives you infinities at high energies.

But the infinities depend super sensitively on not just how gravity operates but how every other field in the world operates because everything couples to gravity.

But the infinities depend super sensitively on not just how gravity operates but how every other field in the world operates because everything couples to gravity.

So the naive feeling is if you just try to come up with a quantum theory of gravity that's well-defined, you need an infinite conspiracy between what the gravitational field is doing at high energies and what all the other fields are doing at high energies. It turns out string theory gives you that infinite conspiracy because it's just one thing, a string, that's vibrating in different ways.