Sean Carroll

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.

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.

And you can show that not only are there no infinities, sorry, not only is it renormalizable, but it's finite. There's not even an infinity you have to remove in string theory. You just get a finite answer. No other approach to quantum gravity that anyone has been working on has that nice property.

And you can show that not only are there no infinities, sorry, not only is it renormalizable, but it's finite. There's not even an infinity you have to remove in string theory. You just get a finite answer. No other approach to quantum gravity that anyone has been working on has that nice property.

So as many other problems as string theory has, as long as it has that nice property, it's going to be a popular approach to quantizing gravity. The other set of problems are the conceptual problems. When we're quantizing gravity, we don't even know what it is we're quantizing because space-time itself is on the table.

So as many other problems as string theory has, as long as it has that nice property, it's going to be a popular approach to quantizing gravity. The other set of problems are the conceptual problems. When we're quantizing gravity, we don't even know what it is we're quantizing because space-time itself is on the table.

Among one—one among a large number of avatars of this particular problem is what is called the problem of time. This is what we were talking about in the solo episode recently. If you naively plug away, treat general relativity like a field theory, quantize it, you get an equation called the Wheeler-DeWitt equation, which says that the wave function of the universe doesn't evolve with time.

Among one—one among a large number of avatars of this particular problem is what is called the problem of time. This is what we were talking about in the solo episode recently. If you naively plug away, treat general relativity like a field theory, quantize it, you get an equation called the Wheeler-DeWitt equation, which says that the wave function of the universe doesn't evolve with time.

But it does evolve with time. I'm looking around. My immediate environment is evolving with time. So what's up with that? So these are conceptual problems, not just technical problems. It's not just I hit infinity. It's just that I'm getting nonsensical answers to the questions because I don't have any firm ground to stand on. In ordinary quantum field theory, at least I have space-time.

But it does evolve with time. I'm looking around. My immediate environment is evolving with time. So what's up with that? So these are conceptual problems, not just technical problems. It's not just I hit infinity. It's just that I'm getting nonsensical answers to the questions because I don't have any firm ground to stand on. In ordinary quantum field theory, at least I have space-time.

It's there. It's sitting there. It's rigid, and I know what it is, and I have some fields vibrating on it. In quantum gravity, space-time itself, is part of the quantum description and it's much harder to know where to start because that's a unique situation. There's no other versions of physics theories in which space-time itself is part of the dynamical playground.

It's there. It's sitting there. It's rigid, and I know what it is, and I have some fields vibrating on it. In quantum gravity, space-time itself, is part of the quantum description and it's much harder to know where to start because that's a unique situation. There's no other versions of physics theories in which space-time itself is part of the dynamical playground.

So yeah, we don't know what time is. We don't know how Lorentz invariance evolves. We don't know what it is we're supposed to be predicting. You have the wave function of the universe. Okay, what does it mean? How do you turn it into a prediction for something? No one knows. the once and for all answers to any of these questions. So yeah, gravity is special.

So yeah, we don't know what time is. We don't know how Lorentz invariance evolves. We don't know what it is we're supposed to be predicting. You have the wave function of the universe. Okay, what does it mean? How do you turn it into a prediction for something? No one knows. the once and for all answers to any of these questions. So yeah, gravity is special.

Gravity is different as far as we can tell. Nate Wadoops says, the volume of a sphere is proportional to radius cubed. And the area of a sphere is proportional to radius squared. So it seems intuitively obvious that there are too few Planck squared units on the surface of a sphere to capture all the information contained in the much more numerous Planck cubed units of volume within the sphere.

Gravity is different as far as we can tell. Nate Wadoops says, the volume of a sphere is proportional to radius cubed. And the area of a sphere is proportional to radius squared. So it seems intuitively obvious that there are too few Planck squared units on the surface of a sphere to capture all the information contained in the much more numerous Planck cubed units of volume within the sphere.