General relativity and quantum mechanics are the two most successful conceptual breakthroughs of modern physics, but Einstein’s description of gravity as a curvature in space-time doesn’t easily mesh with a universe made up of quantum wavefunctions. Recent work that tries to bring those theories together is revealing some mind-bending truths. In this episode, the physicist and author Sean Carroll talks with host Steven Strogatz about how space and time might be emergent properties of quantum reality, not fundamental parts of it..
Steven Strogatz (00:03): I’m Steve Strogatz, and this is The Joy of Why, a podcast from Quanta Magazine that takes you into some of the biggest unanswered questions in science and math today. In this episode, we’re going to be discussing the mysteries of space and time, and gravity, too. What’s so mysterious about them?
Well, it turns out they get really weird when we look at them at their deepest levels, at a super subatomic scale, where the quantum nature of gravity starts to kick in and become crucial. Of course, none of us have any direct experience with space and time and gravity at this unbelievably small scale. Up here, at the scale of everyday life, space and time seem perfectly smooth and continuous. And gravity is very well described by Isaac Newton’s classic theory, a theory that’s been around for over 300 years now.
(00:53) But then, about 100 years ago, things started to get strange. Albert Einstein taught us that space and time could warp and bend like a piece of fabric. This warping of the space-time continuum is what we experience as gravity. But Einstein’s theory is mainly concerned with the largest scales of nature, the scale of stars, galaxies and the whole universe. It doesn’t really have much to say about space and time at the very smallest scales.
And that’s where the trouble really starts. Down there, nature is governed by quantum mechanics. This amazingly powerful theory has been shown to account for all the forces of nature, except gravity. When physicists try to apply quantum theory to gravity, they find that space and time become almost unrecognizable. They seem to start fluctuating wildly. It’s almost like space and time fall apart. Their smoothness breaks down completely, and that’s totally incompatible with the picture in Einstein’s theory.
(01:54) As physicists try to make sense of all of this, some of them are coming to the conclusion that space and time may not be as fundamental as we always imagined. They’re starting to seem more like byproducts of something even deeper, something unfamiliar and quantum mechanical. But what could that something be? Joining me now to discuss all this is Sean Carroll, a theoretical physicist who hosts his own podcast, Mindscape. Sean spent years as a research professor of physics at Caltech [California Institute of Technology], but he is now moving to Johns Hopkins as the Homewood Professor of Natural Philosophy. He’s also an external professor at the Santa Fe Institute. But no matter where he is, Sean studies deep questions about quantum mechanics, gravity, time and cosmology. He’s the author of several books, including his most recent, Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime. Sean, thank you so much for joining us today.
Sean Carroll (02:54): Thanks very much for having me, Steve.
Strogatz (02:56): It’s very exciting to me to be talking with the master of emergent space-time. Really mind-boggling stuff, I enjoyed your book very much. I hope you can help us make some sense of these really thorny and fascinating issues in, I’d say, at the frontiers of physics today.
Why are you guys, you physicists, worrying so much about space and time again? I thought Einstein took care of that for us a long time ago. What’s really missing?
Carroll (03:21): Yeah, you know, we think of relativity, the birth of relativity in the early 20th century, as a giant revolution in physics. But it was nothing compared to the quantum revolution that happened a few years later. Einstein helped the beginning of special relativity, which is the theory that says you can’t move faster than the speed of light, everything is measured relative to everything else in terms of velocities and positions and so forth. But still, there was no gravity in special relativity. That was 1905. And then 10 years later, after a lot of skull sweat and heavy lifting, Einstein came up with general relativity, where, he had been trying to put in gravity to special relativity, and he realized he needed a whole new approach, which was to let space-time be curved, to have a geometry, to be dynamical. It’s the fabric of space-time itself that responds to energy and mass, and that’s what we perceive as gravity.
(04:14) And as revolutionary as all that was, sort of replacing fundamental ideas that had come from Isaac Newton, both special relativity and general relativity were still fundamentally classical theories. You know, we sometimes prevaricate about the word “classical,” but usually what physicists mean is, the basic framework set down by Isaac Newton in which you have stuff, whether it’s particles or fields, or whatever. And that stuff is characterized by what it is, where it is, and then how it’s moving. So for a particle, that would be its position and its velocity, right? And then, from that, you can predict everything, and you can observe everything and it’s precise and it’s deterministic, and this gives us what we call the clockwork universe, right? You can predict everything. If you knew perfect information about the whole world, you would be what we call “Laplace’s demon,” and you’d be able to precisely predict the future and the past.
(05:08) But even general relativity, which says that space-time is curved, that still falls into that framework. It’s still a classical theory. And we all knew, once quantum mechanics came along, circa 1927, let’s say. It was bubbling up from 1900, and then sort of — it triumphed in 1927, at a famous conference, the fifth Solvay Conference, where Einstein and Bohr argued about what it all meant.
(05:32) But since then, we’ve accepted that quantum mechanics is a more fundamental version of how nature works. I know — you said this for all the right reasons, but it’s not that quantum mechanics happens at small scales. Quantum mechanics is the theory of how the world works. What happens at small scales is that classical mechanics fails. So you need quantum mechanics. Classical mechanics turns out to be a limit, an approximation, a little tiny baby version of quantum mechanics, but it’s not the fundamental one.
And since we discovered that, we have to take all of what we know about nature and fit it into this quantum mechanical framework. And we have been able to do that for literally everything we know about nature, except for gravity and curved space-time. We do not yet have a full, 100% reliable way of thinking about gravity from a quantum point of view.
Strogatz (06:24): I appreciate that correction. You’re right, I was being a little bit loose there in saying that quantum mechanics only applies at the smallest scales. I mean, there’s — on mathematical grounds, we can see how quantum mechanics becomes classical mechanics. It’s consistent with it, it’s — in fact, it implies classical mechanics, once the scale gets to be the more familiar one.
Carroll (06:45): Yeah, not only is that true, but it’s kind of crucially important, and I like to emphasize it even more than most people do, because we’re not born understanding quantum mechanics. We kind of have a much more intuitive grasp of classical mechanics. And we kind of tend to think of the world in classical terms. Classically, things have positions, and they have locations — positions and velocities. Quantum mechanically, that’s not true. And it’s really hard to wrap your brain around that. And so, we tend to speak in exactly the way that you said, like, classical mechanics works on large scales, quantum mechanics works on small scales, because we kind of don’t want to face the fact that quantum mechanics is everywhere in everything and we should learn to understand what’s going on.
Strogatz (07:28): But you say that gravity has been this kind of outlier, that it’s very hard — or at least it hasn’t been incorporated in a fully satisfactory way yet, into any kind of quantum mechanical framework. Is there a way to sum up what the nature of the difficulty is? Why is it so hard to come up with a theory that merges quantum theory and gravity?
Carroll (07:47): Yeah, there are kind of two sets of issues that come up. What you might call technical issues, and conceptual issues. We human beings start classically. When you’re a physics student as an undergraduate, and you’re learning quantum mechanics, what does that mean? That means that you’re taught the classical model for something, like a harmonic oscillator, or the hydrogen atom, or whatever. And then you’re given rules for quantizing that classical theory, okay? So there’s supposed to be, in some sense — you mathematicians out there in the audience will appreciate — a map from the space of classical theories to quantum theories, okay? The quantization procedure.
(08:26): This is all a complete fake. I mean, it sort of is a kludge that works sometimes, but this purported map from classical theories to quantum theories is not very well-defined. You can have the same classical theory that maps on to two different quantum theories. You can have two different classical theories mapping onto the same quantum theory. So, there’s no direct correspondence and after all, why should there be?
(08:46): But again, nevertheless, it has worked for electromagnetism, the nuclear forces and everything else. When you straightforwardly apply that quantization procedure to gravity — we have a classical theory, general relativity, we can quantize it. It just blows up. It just gives us infinite crazy answers.
(09:04) This has happened before in the history of trying to quantize classical theories. Richard Feynman and Julian Schwinger and Sin-Itiro Tomonaga famously won the Nobel Prize for showing how to get rid of the infinities in quantum electrodynamics. But the infinities you get in gravity are of a different character, they’re not get-rid-able, they’re not “renormalizable,” as we say. So, at a very fundamental mathy level, you know, the procedure that you were relying on all along just stalls and you don’t know what to do.
(09:35): But then there’s a whole set of more deep conceptual issues, not only do you not know what to do, you don’t know what you’re doing. Because, with everything else, every other theory other than gravity, it’s very clear what’s going on. You have stuff inside space-time. The stuff has a location, right? It has a point in space, it’s moving through time. Even if you have a field, it has a value at every point in space, etc.
But in gravity, you’re sort of combining a whole bunch of different possible geometries of space-time. And what that means is, you’re not really sure what time is, for one thing, and you’re not really sure where things are in space, because if you don’t know the geometry of space, it is impossible to identify a point in space uniquely throughout all the possible quantum combinations of the geometry of space-time. So, we really, at a fundamental level, have difficulty knowing what we’re talking about, when it comes to quantum gravity.
Strogatz (10:33): It certainly does sound very thorny, that the arena itself, like in traditional thinking, physics, as you say, there’s stuff and fields and particles and things happening, moving around from place to place, from moment to moment inside this arena of space-time. But now it’s the arena itself. Einstein already took us a little bit in that direction by making the arena a dynamical thing where space and time could warp and have, as you say, dynamics. But it’s now, it seems like it’s getting much worse.
Carroll (11:02): Well, it is, because remember, I alluded to the idea that, classically, for a particle, you have a very clear notion of where it is, its location, and how fast it’s moving. And you could measure those things. The whole spookiness of quantum mechanics is that to define what you mean by quantum mechanics, you have to use words like “observation” and “measurement.” That was never true in classical mechanics, you just measure whatever you want, it was perfectly trivial and straightforward. Quantum mechanics is a little bit different from that.
(11:03) And so, one of the lurking things here, in this whole discussion, you know, there’s many, many theoretical physicists who would say, yes, quantum gravity, very, very important, we should try to understand this. But we don’t understand quantum mechanics. Even though it’s been around for almost 100 years. We don’t agree on what quantum mechanics is saying, because of these weird words like measurement and observation. So, I tried to explain why quantum gravity is hard but I’m going to reveal my prejudices, because I can’t do that without explaining what I think quantum mechanics is. Or at least, referring to what I think quantum mechanics is.
Strogatz (11:32): So I think that segues very nicely into the next thing I was going to ask you. We’re hoping, by the end of this episode, to give people a feeling of what it means for space-time to be emergent. But what would it mean for you, or anybody studying space and time, for them to be emergent?
Carroll (12:05): So I don’t think that there is any such thing as a position or a velocity of a particle. I think those are things you observe, when you measure it, they’re possible observational outcomes, but they’re not what is — okay, they’re not what truly exists. And if you extend that to gravity, you’re saying that what we call the geometry of space-time, or things like location in space, they don’t exist. They are some approximation that you get at the classical level in the right circumstances. And that’s a very deep conceptual shift that people kind of lose their way in very quickly.
(12:58) It’s a tricky word. We have to think about it. Emergence is kind of like morality. Sometimes we agree on it when we see it. But other times, we don’t even agree on what the word is supposed to mean. So, the physicists, and mathematicians, and other natural scientists tend to — but not always — rely on what a philosopher would call weak emergence. And weak emergence is basically a convenience, in some sense. The idea is that you have a comprehensive theory, you have a theory that works at some deep level. Let’s say, the standard example is gas in a box, okay? You have a box full of some gaseous substance, and it’s made of atoms and molecules, right? And that’s the microscopic theory. And you say that, okay, I could — in principle, I could be Laplace’s demon, I could predict whatever I want, I know exactly what’s going on.
(13:47) But, we human beings, when we look at the gas in the box with our eyeballs, or our thermometers, or whatever, we don’t see each individual atom or molecule, and its position and its velocity, we see what we call coarse-grained features of the system. So we see its temperature, its density, its velocity, its pressure, things like that. And the happy news — which is not at all obvious or necessary, it’s kind of mysterious when it happens and when it doesn’t — but the happy news is that we can invent a predictive theory of what the gas is going to do just based on those coarse-grained macroscopic observables. We have fluid mechanics, right? We can model things without knowing what every atom is doing. That’s emergence, when you have a set of properties that are only approximate and coarse-grained, that you can observe at the macroscopic level, and yet you can predict with them. And weak emergence just means, there’s nothing new that happened along the way. You didn’t say that, oh, when you go to the larger scales and you zoom out, fundamentally new essences or dynamics are coming in. It’s just sort of the collective behavior of the microscopic stuff. That’s weak emergence.
(15:01) There’s also strong emergence where spooky new stuff does come in. And people talk about the necessity of that when they think about consciousness or something like that. I’m not a believer in strong emergence at the fundamental level. So, to me, what the emergence of space-time means is that space-time itself is like, the fluid mechanics. It’s like gas temperature and pressure and things like that. It’s just a coarse-grained, high-level way of thinking about something more fundamental, which we’re trying to put our finger on.
Strogatz (15:34): Wow, as you’re describing the gas in a box, I happen to be sitting in a box. I’m in a studio that is kind of box-shaped. There is a gas in here, which is the air that I’m breathing.
So anyway, yeah, very vivid to me, the example you’re talking about. And it is amazing, isn’t it? That there are laws at that collective or emergent scale that work, that don’t — you know, like thermodynamics was oblivious to statistical physics. In fact, was discovered first, and only later, the microscopic picture came out. And so, I guess you’re saying something like that would be happening now with space and time and gravity, that we have the macroscopic theory that’s Einstein’s.
Carroll (16:14): When I’m not spending my research time studying quantum mechanics and gravity, I’m studying emergence. I think that there’s a lot to be done here, to be sort of cleaned up and better understood, in a set of questions that spans from philosophy to physics to politics and economics, not to mention biology and the origin of life. So, I think that these are deep questions that we’ve been kind of messy and sloppy about addressing, but I don’t think that the emergence of space-time is difficult for that reason.
(16:45) So, when you talk about, is the United States emergent from its citizens? Or is Apple Computer Company emergent from something? Those are hard questions. Those are like, tricky, like “where do you draw the boundary?”, etc. But for space-time, I think it’s actually pretty straightforward. The lesson, the important take-home point for the podcast is, you don’t start with space-time and quantize it, okay? Just like when you have the gas in the box, you’re trying to get a better and better theory of the gas in the box, but you realize that it’s made of something fundamentally different. And I think that’s what I’m proposing, and other people are proposing for space-time as well, that the whole thing that used to work for electromagnetism and particles and the Higgs boson and the Standard Model, where you started with some stuff and quantized it, that’s not going to be the way it’s going to happen for gravity and space-time. You’re going to have something fundamentally different at the deep micro-level, and then you’re going to emerge into what we know of as space-time.
Strogatz (17:46): Shouldn’t we start talking about entanglement, at this point, maybe?
Carroll (17:49): Never too early to start talking about entanglement.
Strogatz (17:51): Let’s talk about it. What is it? I hear it a lot. I hear quantum people talking about it. Nowadays, especially, with quantum computing, we keep hearing about entanglement. Why don’t you just start with telling us what it means, where the idea came from?
Carroll (18:04): Yeah, I mean, let’s think about the Higgs boson. We discovered it a few years ago, it’s a real particle, and I wrote a book about it, The Particle at the End of the Universe. The Higgs boson — one of the reasons why it’s hard to detect is that it decays. It has a very, very short lifetime, right? So, you can imagine if someone put a Higgs boson right in front of you, it would generally decay into other particles in about one zeptosecond. That’s 10-21 seconds. Very, very quickly.
(18:31) One thing it can do, it can decay into an electron and a positron, an antielectron. So it can decay into two particles, electron and positron. Now remember quantum mechanics. So, you can predict roughly how long it will take the Higgs boson to decay, but when it spits out that electron and positron, you can’t predict the direction in which they’re going to move.
(18:54) I mean, that makes perfect sense because the Higgs boson itself is just a point. It has no directionality in space. So there’s some probability of seeing the electron, in a cloud chamber or whatever, moving in whatever direction you want. Likewise, for the positron, there’s some probability, seeing it moving in whatever direction you want. But you want momentum to be conserved. So you don’t want the Higgs boson sitting there, stationary, to decay into an electron and a positron both moving rapidly in the same direction. That would be a shift in the momentum, right?
(19:26) So, even though you don’t know what direction the electron is going to move in, and you don’t know what direction the positron is going to move in — sorry, I’m already, I’m being, I’m being the person who I make fun of, I’m speaking as if these are real. Even though you don’t know what direction you will measure the electron to be moving in, and you don’t know what direction you will measure the positron to be moving in, you know that if you measure them both, they will be back to back. Because they need to have equal and opposite momentum, for those to cancel out.
(19:54) So what that means is, if you believe all those things, right away, this is why we believe there’s only one wavefunction for the combined system of the electron and the positron. It’s not an independent question, what direction are you going to measure the electron in? What direction are you going to measure the positron in? It’s a statement you need to ask at the same time. That’s entanglement, right there. Entanglement is the fact that you cannot separately and independently predict what the observational outcome is going to be for the electron and the positron.
(20:26) And this is completely generic and everywhere in quantum mechanics. It’s not a rare, special thing. Many things are entangled with many other things. It’s the unique and fun and very useful time when things are not entangled with each other. It took a long time — like, Einstein and his friends — Einstein, Podolsky and Rosen, EPR — published a paper in 1935 that really pointed out the significance of entanglement. Because it was sort of there, already, implicit in the equations, but no one had really shone a flashlight on it, and that’s what Einstein did. And the reason why it bothered him is because when that Higgs boson decays and the positron and the electron move off in opposite directions, you can wait a long time, let’s say you wait a few years before you measure what direction the electron is moving in.
(21:14) So, both particles are very, very far away from each other. And now when you measure the location of one, supposedly the location of the other one is instantly determined. And there’s no limit of the speed of light or anything like that. So for obvious reasons, Einstein, very fond at the speed of light as a limit on things, he didn’t like that. He never really quite thought that that was the final answer, he was always searching for something better.
Strogatz (21:39): And the argument goes nowadays that it’s okay, it’s no violation of special relativity, because you can’t use this to transfer any information or something? Is that the statement?
Carroll (21:39): Yeah, well, you know, there’s, there’s a whole bunch of statements that one can make. But the one that we absolutely think is true, is the one that you just made. If you imagine these two particles moving back-to-back, and one person detects one, and there’s another one, you know, a light-year away, who’s going to detect the other one, the point is that they don’t know what your measurement outcome is, you would have to tell them.
So even though in the global point of view, now, the location where the other particle is going to be detected is known to God, or to the universe, it is not known to any particular person sitting at any location within the universe. It takes the speed of light time to take a signal that would let you know that there is some now new fact about the matter, where you’re going to observe the positron. So, you cannot actually use this for signaling, you just don’t know what has happened when your other observer has measured something. And you can actually prove that, under reasonable assumptions, in the theory as we know it.
(22:43) So it seems as if this is the tension, that the way the universe works involves correlations that travel faster than the speed of light, but in some well-defined sense, information does not travel faster than the speed of light. That should worry you, that we didn’t define any of these words. So you know, what does that mean? You’re not going to build a transporter beam or anything like that out of this stuff.
(23:09) But — but let me just add one other thought, which I think, again, is a result of my quirky way of thinking about these things, which is not entirely standard, which is, people really like locality. Like, locality is a central thing. Locality is just the idea that if I poke the universe at one point in space-time, the effects of that poke will happen at that point, and then they will ripple out. But they will ripple out to other points no faster than the speed of light, okay? There’s nothing I can do to poke the universe here that will change the state of the universe in a tangible way very, very far away. And you can see how this entanglement thing is kind of on the boundary of that, like, the description of the universe changes instantly far away, but no information is traveling.
(23:51) So then, if you believe that locality is fundamental like that, then you’re sort of asking this question, why does the universe almost violate that but seem to not quite? That’s the puzzle that we have. And this is — a lot of ink has been spilled in the foundations of quantum mechanics.
(24:06) I think about it entirely the other way around, because I think of the wavefunction as the fundamental thing, right? I think that’s what exists in reality. And the wavefunction, like the wavefunction of this positron and electron is utterly nonlocal. It just exists all — it’s a, it’s a feature of the universe as a whole right from the start. So, I also have a mystery to be explained, but my mystery is the opposite way. It’s not “why is locality approximately or, you know, seemingly violated by entanglement?” It’s “why is there locality at all?” Like, that’s the puzzle to me.
Strogatz (24:41): Okay, so with talking about entanglement and its discontents or its wonders, what does all this have to do with what we were saying earlier about space as emergent? Because there is some connection, right?
Carroll (24:52): That’s right. The aspiration is to say that we start with this abstract quantum wavefunction. So, what I mean by abstract is, it’s not a wavefunction of anything. The usual way of talking, because we’re human beings that start classically, is to say we have the wavefunction of the electron, of the harmonic oscillator, of the Standard Model of particle physics or whatever. No, that’s cheating. We don’t allow ourselves that. We just have an abstract quantum wavefunction and we’re asking, can we extract reality as we know it from the wavefunction? Space-time, quantum fields, all of those things, okay. So we don’t have a lot to work with.
(25:30) But what we can do is, we’re able to use clues from physics as we understand it in the real world. So, in the real world, we have, to a very good approximation, the world is run by what we call quantum field theory. Okay, so, the stuff of the world, the particles and the, you know, the forces, etc., all come from fields that spread all throughout space and time and have a quantum mechanical nature.
(25:55) So, there’s a field for the electron, there’s a field for the photon, a field for the gluon, a field for the Higgs boson, etc. A field for gravity. All of these things are quantum mechanical fields. Now, again, this is not what I’m proposing, this is just our current best approximation, right? This is what seems to fit the data. And you can ask questions about what that looks like in practice.
And so, the important thing about field theory is that even in empty space, there are still fields there. Space is not completely empty, it’s not just like, an empty vessel. There are fields that, as we say, are in their ground state. They’re in their lowest-energy state. So they’re — classically, you just say the field has value zero. Like you could say, there’s something called the magnetic field, but at this particular point in space, it’s zero. It’s still — there is a field, but its value is zero. Quantum mechanically, it’s more complicated than that, but you can still say it’s in its lowest-energy state. That’s something you’re allowed to say.
(26:49) And then what you can do is take two different points of space-time, at some distance between them, and because there’s still things there, because there still are fields even in empty space, you can say, is there entanglement between these two points of space? Because of the fields there. Are the — is the quantum state of the fields at these two points in space, is it entangled? And the answer is yes, it is always going to be entangled.
And in fact, more than that, if the points are nearby, the fields will be highly entangled with each other. And if the fields are far away, the entanglement will be very, very low. Not zero, but very, very low. So in other words, there is a relationship between the distance between two points and their amount of entanglement in the lowest-energy state of a conventional quantum field theory.
(27:38) And what we say is, look, we start with an abstract quantum wavefunction. We don’t have any such words like distance, or fields, for that matter, right? But we do have the word “entanglement.” We can figure out, if you divide up the wavefunction into this bit and this bit, are those two bits entangled? There’s mathematical ways to measure them using the mutual information, etc. So you can quantify the amount of entanglement between different pieces of the wavefunction. And then, rather than saying “the more distance, the less entanglement,” you turn that on its head. You say, “Look, I know what the entanglement is.” Let me assume, let me put out there as an ansatz [a mathematical assumption], that when the entanglement is strong, the distance is short. And I’m going to define something called the distance. And it’s a small number when the entanglement is large, it’s a big number when the entanglement is small.
(28:26) So what you’re doing is, in this big space in which the wavefunction lives, you’re dividing it up into little bits, you’re relating them — Steve, you will be happy about this. You’re drawing a network, a graph. You have different parts of Hilbert space. Those are nodes in the graph, and then they have edges, and the edges are the amount of entanglement. And there’s a function of those amount of entanglement which says, invert it, roughly speaking, and get a distance. So now you have a graph of nodes with distances between them. And you can ask, do those nodes fit together to approximate a smooth manifold? And if you pick the right kind of laws of physics, they will.
(29:06) And then you can ask, if I perturb it a little bit, so I poke it, so it’s not in its lowest-energy state, it has a little bit of energy in it. Well, that’s going to be dynamical. That’s going to stretch space-time, that’s going to change the amount of entanglement. We can interpret that as a change in the geometry of space. Is there an equation that that obeys?
And the answer is, you know, under many assumptions that are not entirely solid yet, but seem completely plausible, the geometry of that emergent space obeys Einstein’s equation of general relativity. Not completely as surprising and dramatic as it sounds, because there’s not a lot of equations it could have obeyed. But the point is that if we follow our nose, if we say we start not with space, but with entanglement, how should it behave? How should it interact? We get to a place where it’s not at all surprising that it has dynamics, that it changes, that it responds to what you and I would notice as energy, and the kind of response is the kind that Einstein had there in general relativity.
(30:03) So, you can imagine an alternative theory of physics — history of physics. Where Einstein did not invent general relativity. Where we invented quantum mechanics first, and we understood it. And we really thought about it very deeply, and at some point, someone said, you know, if you really take this seriously, the emergent geometry of space should be dynamical and curved, I’m going to call it general relativity. That’s not what happened. But that’s what we’re hoping to work out when we’re all done.
Strogatz (30:28): There’s this big story about this awful acronym, AdS/CFT correspondence, that some people may have heard of. Some of our listeners may know that there’s some — some work that has a similar spirit to what you’re describing, where you derive gravity — not you, Juan Maldacena, I guess, and Lenny Susskind and other people — are trying to derive gravity from quantum field theories that don’t have gravity in them. Can you tell us about some of that and explain it to us?
Carroll (30:35): Right. It is very much close in spirit. And the idea is that you have this principle, called the holographic principle. It doesn’t really deserve the name of a principle because it’s a little bit vague. But the idea is that for a black hole, all of the information, all the quantum mechanical information inside a black hole, can in certain circumstances be thought of as spread out on the boundary of the black hole.
So if you think of the interior of the black hole as a three-dimensional region of space, and the boundary, the event horizon, as a two-dimensional boundary, somehow, you could think of all the information of the black hole as being located on the boundary. So that’s holography, because there’s only a two-dimensional boundary that is filling in the three-dimensional inside, much like shining a light on a two-dimensional hologram gives you a three-dimensional image.
(31:45) What Maldacena did was applied that not to black holes, but to a certain kind of cosmological space-time called anti-de Sitter space. So, in general relativity, in Einstein’s theory of gravity, if there’s nothing going on, if there’s no energy, no stuff, or anything like that, you can solve the equation, Einstein’s equation, and you find flat space-time, which we call Minkowski space-time, this is just the arena where special relativity lives.
(32:12) The next simplest thing you can do is add energy to it, but add only vacuum energy, energy of empty space itself. So there’s no particles or photons or anything like that. There’s just empty space, it has energy. We think that space does have energy now, we discovered this with the accelerating universe, in 1998. And the equations were solved back in 1917 by Willem de Sitter, a Dutch astrophysicist. So, if you have a positive amount of energy in empty space, you get a cosmological solution called de Sitter space. And that is basically where our real universe is evolving to, as we expand and the galaxies move further and further away.
(32:52) If you just flip the sign to make the vacuum energy have a negative amount, you’re allowed to do that. And it’s called anti-de Sitter space. It’s just a flip of the sign in the math. And the great news is that this anti-de Sitter space — again, it’s a pure — all that should drive home to you that this is not the real world. Not only is it empty, but the vacuum energy is negative rather than positive. It’s a completely thought-experiment kind of thing. But what Maldacena showed is that gravity, quantum gravity, string theory he was thinking of in particular, inside anti-de Sitter space can be related to a theory of quantum field theory without gravity, that you can think of as living on the boundary infinitely far away.
(33:36) So if there’s a boundary to anti-de Sitter space infinitely far away, it’s one dimension less. Because it’s kind of like, you know, the event horizon of a black hole, it’s wrapped around the anti-de Sitter space. It is itself flat space-time. There’s no gravity there, you can define quantum field theory on it, you have no conceptual issues with quantizing it. It’s good old, well-defined quantum field theory. And Maldacena argued that it is the same theory as quantum gravity in the interior, in what we call the bulk of anti-de Sitter space. There’s a relationship between these two theories that is a one-to-one correspondence. And it’s hard to prove that. But there’s an enormous amount of evidence that it’s true.
(34:14) And then, subsequent to that, people like Mark Van Raamsdonk and Brian Swingle and others pointed out that if you take the theory on the boundary, the theory that we understand, the quantum field theory without gravity, and all you do is you twiddle the amount of entanglement between different parts of the quantum field theory on the boundary, the geometry of the anti-de Sitter space inside responds. It changes in response to that. In some sense, the geometry of that emergent anti-de Sitter space, holographically emergent, is very sensitive to the amount of entanglement on the boundary. So this is the sense in which, in this case, geometry is emerging from entanglement.
(34:57) So, to compare that to what I’m doing, I am not in anti-de Sitter space. I’m here on Earth, both literally and conceptually. I am in the limit where space-time is almost flat, right, where gravity is weak. Like the solar system, even though the sun is very big, gravity is still weak, it’s nowhere near being a black hole. So there’s no holography, everything is pretty local, as we were talking about before, everything is, you know, bumping up against other things right next to each other, right here in space.
(35:24) The holographic limit, that’s kind of the opposite. Holography kicks in where gravity is strong, where you either have a black hole or a cosmological horizon or something like that. And that’s when the information seems like it’s in one dimension less. What you need in the full theory, which nobody has, is both at once.
(35:47) There’s a huge number of people working on AdS/CFT. CFT because the particular kind of field theory you have on the boundary is what is called a conformal field theory. So C-F-T, conformal field theory. So, there’s a huge number of people working on that. And it’s fun, and it’s well-defined, there’s a lot of math, there’s a lot of physics, full employment, whereas what I’m doing is much less well-defined, because we don’t have this well-defined boundary where everything doesn’t involve gravity, and therefore you can solve all your equations.
(36:16) But, you know, I think that you’re going to need both at the end of the day. I think that the AdS/CFT approach doesn’t really illuminate what goes on in the solar system very well. It illuminates what goes on cosmologically pretty well. So I think that they’re compatible ways of sort of coming at the problem from different approaches.
Strogatz (36:32): You know, I’m glad you mentioned Van Raamsdonk and Swingle, because that’s another very seminal paper in this whole, I want to say “space” of emergent space-time. Thinking, you know, looking ahead, these ideas of emergent space-time, do you think they’ll have impact on our current models in physics?
Carroll (36:50): Well, I think there’s still, certainly, a lot to do just in terms of understanding the proposal, right? I mean, really going from these incomplete ideas about entanglement and emergent geometry to a full theory like, “Oh, this is why things have three dimensions of space. This is the kind of laws of physics that let this happen in the first place,” you know, and so on. And so there’s just, like, a lot of very basic groundwork remaining to be done. The ideal thing, the wonderful thing that would be amazing, is to make an experimental prediction from all this.
(37:25) And it’s not completely wacky to imagine that is possible. For the following reason: You know, it goes back to what we said about space and time not being quite on an equal footing. We’re using them in different ways. So the technical term for this is we’re violating Lorentz invariance. It’s this symmetry that was handed down by Lorentz, a famous Dutch physicist, a mentor of Einstein’s, that says it doesn’t matter how you look at space and time, everyone’s perspective is equal.
That’s not quite right, in our point of view. It might not be right. So, it’s possible that there is an experimental prediction for a tiny violation of Lorentz invariance. And this might show up in, you know, how photons propagate across the universe or something like that, or some very delicate, precise laboratory experiment we can do here on Earth. We don’t know. I don’t have that prediction yet for you. But I think that is something that is plausible within this framework.
Strogatz (38:21): That’s a wild idea. Because a lot of people think of the Lorentz invariance, basically, this principle of relativity, taken very seriously, as a deep inviolable principle in physics, and you’re saying it may be itself an emergent-like approximation. It’s almost like a spurious symmetry that comes out from looking at the emergent theory rather than the fundamental theory.
Carroll (38:43): Yeah, that’s exactly right. And again, maybe, as we have both been saying. It’s a low-probability, high-impact question to ask. So I think — it’s worth spending some of your time on questions like that.
Strogatz (38:55): I feel like you’ve been a very brave and generous person in sharing these speculations with us. I mean, you’ve been so honest about the tentative nature of science, which for all of us who actually do science and math, know that that’s how it really is. But I think it’s, it’s very healthy for our listeners to appreciate this, that we’re all sticking our necks out all the time and we kind of like it, and it’s what makes it such an adventure.
Carroll (39:20): Well, I do think that and, you know, I think that there’s a school of thought that says that scientists should not talk about their results until they’re completely established and refereed and everyone agrees they’re right. And not only do I think that that’s implausible, because even results that are refereed and published could be wrong, I think it’s very antithetical to the spirit of how science is, you know, and I want to emphasize that science is not just a set of results that are handed down from on high, it’s a process. We could be wrong. We’re making suppositions and hypotheses and guesses, and we’re going to figure out whether or not they work. And that’s not a bug, it’s a feature. That’s, that’s how science works. So I’m very willing to talk about tentative things as long as I try to emphasize that they are tentative things.
Strogatz (40:09): Yep. Thank you and bravo. And that we are trying to be rational. We’re looking for evidence, we’re willing to admit when we’re wrong, when we are wrong.
Carroll (40:17): Yeah, actually, I think that it would increase trust in science if we were more honest about the fact that we can be wrong all the time. Because we are going to be wrong some of the time, and if we pretend that we’re never wrong, then it’s going to hurt our credibility when we’re wrong.
Strogatz (40:32): Okay, amen, Sean. Thank you so much for joining us in a really delightful conversation today.
Carroll (40:37): It’s my pleasure. Thanks very much for having me on.
Announcer (40:43): If you like The Joy of Why, check out the Quanta Magazine Science Podcast, hosted by me, Susan Valot, one of the producers of this show. Also, tell your friends about this podcast and give us a like or a follow where you listen. It helps people find The Joy of Why podcast.
Strogatz (41:05): The Joy of Why is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests, or other editorial decisions in this podcast or in Quanta Magazine. The Joy of Why is produced by Susan Valot and Polly Stryker. Our editors are John Rennie and Thomas Lin, with support by Matt Carlstrom, Annie Melchor, and Leila Sloman. Our theme music was composed by Richie Johnson. Our logo is by Jackie King, and artwork for the episodes is by Michael Driver and Samuel Velasco. I’m your host, Steve Strogatz. If you have any questions or comments for us, please email us at [email protected] Thanks for listening.