Sean Carroll explains why spacetime might not be fundamental. Attempts to quantize general relativity fail as an ordinary field theory, black hole information suggests locality breaks down, and holography shows how information can be encoded non-locally on horizons.
The emergence of space time.
That's right.
Okay, so I thought space time was fundamental.
Yeah, I know.
So this sort of dream that Einstein had, that everybody had and everybody has of, you know, the theory of everything. So how do we build up from many worlds, from quantum mechanics a model of space time, model of gravity?
Well, yeah. I mean, let me first mention very quickly why we think it's necessary. You know, we've had gravity in the form that Einstein bequeathed to us for over 100 years now, like 1915 or 1916. He put General relativity in the final form. So gravity is the curvature of space time. And there's a field that pervades all the universe that tells us how curved spacetime is.
And that's a fundamentally classical.
That's totally classical, right? Exactly. But we also have a formalism, an algorithm for taking a classical theory and quantizing it. This is how we get quantum electrodynamics, for example. And it could be tricky. I mean, you think you're quantizing something, so that means taking a classical theory and promoting it to a quantum mechanical theory. But you can run into problems. So they ran into problems, and they did that with electromagnetism, namely that certain quantities were infinity. And you don't like infinity. Right. So Feynman and Tomonaga and Schwinger won the Nobel Prize for teaching us how to deal with the infinities. And then Ken Wilson won another Nobel Prize for saying you shouldn't have been worried about those infinities after all. But still, it's always the thought that that's how you will make a good quantum theory. You'll start with a classical theory and quantize it. So if we have a classical theory, general relativity, we can quantize it, or we can try to, but we run into even bigger problems with gravity than we ran into with electromagnetism. And so far those problems are insurmountable. We have not been able to get a successful theory of gravity, quantum gravity, by starting with classical general relativity and quantizing it. And there's evidence that there's a good reason why this is true, that whatever the quantum theory of gravity is, it's not a field theory. It's something that has weird non local features built into it somehow that we don't understand. We get this idea from black holes and Hawking radiation and information conservation and a whole bunch of other ideas I talk about in the book. So if that's true, if the fundamental theory isn't even local in the sense that an ordinary quantum Field theory would be, then we just don't know where to start in terms of getting a classical precursor and quantizing it. So the only sensible thing, or at least the next obvious sensible thing to me would be to say, okay, let's just start intrinsically quantum and work backwards, see if we can find a classical limit.
So the idea of locality, the fact that locality is not fundamental to the nature of our existence, sort of, you know, I guess in that sense, modeling everything as a field makes sense to me. Stuff that's close by interacts. Stuff that's far away doesn't. So what's, what's locality and why is it not fundamental? And how is that even possible?
Yeah, I mean, locality is the answer to the question that Isaac Newton was worried about back at the beginning of our conversation. Right? I mean, how can the, the Earth know what the gravitational field of the sun is? And the answer, as spelled out by Laplace and Einstein and others, is that there's a field in between. And the way a field works is that what's happening to the field at this point in space only depends directly on what's happening at points right next to it. But what's happening at those points depends on what's happening right next to those. Right? And so you can build up an influence across space through only local interactions. That's what locality means. What happens here is only affected by what's happening right next to it. That's local locality. The idea of locality is built into every field theory, including general relativity. As a classical theory, it seems to break down when we talk about black holes. And, you know, Hawking taught us in the 1970s that black holes radiate, they give off, they will eventually evaporate away. They're not completely black. Once we take quantum mechanics into account and we think, we don't know for sure, but most of us think that if you make a black hole out of certain stuff, then like Laplace's demon taught us, you should be able to predict what that black hole will turn into if it's just obeying the Schrodinger equation. And if that's true, there are good arguments that can't happen while preserving locality at the same time. It's just that the information seems to be spread out non locally in interesting ways.
And people, should you talk about holography with the Leonard Susskind on your Mindscape podcast, People?
Oh, yes, I have a podcast. I didn't even mention that. I'm terrible at.
No, I'm gonna, I'm gonna ask you questions about that too. And I've been not shutting up about. It's my favorite science podcast, so. Or not. It's. It's not even a science podcast. It's like it's a scientist doing a podcast.
That's right. That's what it is. Absolutely, yes.
Yeah.
Anyway, yeah, so holography is this idea when you have a black hole and black hole is a region of space inside of which gravity is so strong that you can't escape. And there's this weird feature of black holes that again, is a totally thought experiment feature because we haven't gone and probed any yet. But there seems to be one way of thinking about what happens inside a black hole as seen by an observer who's falling in, which is actually pretty normal. Like everything looks pretty normal until you hit the singularity and you die. But from the point of view of the outside observer, it seems like all the information that that fell in is actually smeared over the horizon in a non local way. And that's puzzling. And that's so holography, because that's a two dimensional surface that is encapsulating the whole three dimensional thing inside. Right. Still trying to deal with that. Still trying to figure out how to get there. But it's an indication that we need to think a little bit more subtly when we quantize gravity.
So because you can describe everything that's going on in the. In three dimensional space by looking at the two dimensional projection of it means that locality is not necessary?
Well, it means that somehow it's only a good approximation. It's not really what's going on.
How are we supposed to feel about that?
Supposed to feel liberated? You know, space is just a good approximation. And this was always going to be true once you started quantizing gravity. So we're just beginning now to face up to the dramatic implications of quantizing gravity.
