String theory was originally proposed as a relatively modest attempt to explain some features of strongly-interacting particles, but before too long developed into an ambitious attempt to unite all the forces of nature into a single theory. The great thing about physics is that your theories don’t always go where you want them to, and string theory has had some twists and turns along the way. One major challenge facing the theory is the fact that there are many different ways to connect the deep principles of the theory to the specifics of a four-dimensional world; all of these may actually exist out there in the world, in the form of a cosmological multiverse. Brian Greene is an accomplished string theorist as well as one of the world’s most successful popularizers and advocates for science. We talk about string theory, its cosmological puzzles and promises, and what the future might hold. (For more general string theory background, check out Episode 18 with Clifford Johnson.) Support Mindscape on Patreon or Paypal. Brian Greene received his doctorate from Oxford University, and is currently a professor of Physics and Mathematics at Columbia University. His research includes foundational work on topology change, mirror symmetry, and the compactification of extra dimensions. He is the author of several best-selling books, including The Elegant Universe and The Fabric of the Cosmos, both of which were made into TV specials for NOVA. He and Tracy Day are co-founders of the World Science Festival. Web site

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0:00:00 Sean Carroll: Hello everyone, and welcome to The Mindscape Podcast. I’m your host, Sean Carroll. Those of you who have been regular listeners are of course experts on what we call, string theory, the physicists’ way of thinking about, some physicists anyway, way of thinking about replacing point particles and particle physics with little loops of string. String theory purports to be a theory of everything, including quantum, gravity and all the other forces of nature. And in a previous episode with Clifford Johnson, we explored the basic ideas of string theory and why physicists like it so much. There are, of course, problems in string theory, especially with connecting it to observations. One of these problems is that string theory naturally lives in a 10 dimensional space time, and you can get rid of the extra six dimensions to make string theory look more like our four dimensional world, but there’s more than one way to do that. The collection of all the ways of compactifying these extra dimensions is called the, string theory landscape, and every single compactification might lead to different apparent laws of physics in our observable world. Now scientists are very good at being given lemons and turning them into lemonade, so string theorists have said, “Well, maybe they’re all real. Maybe this landscape of different possible ways to get down from 10 dimensions to four dimensions, all take place somewhere out there in some large cosmological multiverse. Click above to close.0:00:00 Sean Carroll: Hello everyone, and welcome to The Mindscape Podcast. I’m your host, Sean Carroll. Those of you who have been regular listeners are of course experts on what we call, string theory, the physicists’ way of thinking about, some physicists anyway, way of thinking about replacing point particles and particle physics with little loops of string. String theory purports to be a theory of everything, including quantum, gravity and all the other forces of nature. And in a previous episode with Clifford Johnson, we explored the basic ideas of string theory and why physicists like it so much. There are, of course, problems in string theory, especially with connecting it to observations. One of these problems is that string theory naturally lives in a 10 dimensional space time, and you can get rid of the extra six dimensions to make string theory look more like our four dimensional world, but there’s more than one way to do that. The collection of all the ways of compactifying these extra dimensions is called the, string theory landscape, and every single compactification might lead to different apparent laws of physics in our observable world. Now scientists are very good at being given lemons and turning them into lemonade, so string theorists have said, “Well, maybe they’re all real. Maybe this landscape of different possible ways to get down from 10 dimensions to four dimensions, all take place somewhere out there in some large cosmological multiverse. 0:01:26 SC: Maybe this is a good thing, the story goes along to say, because maybe certain things that are surprising about our observed world becomes less surprising if our world is just one of many universes in this large ensemble. Now, not everyone agrees. This is controversial stuff. But before we can have an opinion about it, one way or the other, we have to understand what’s going on. Today’s guest Brian Greene has done very influential work on string theory in general, but especially on the problem of compactifying those extra dimensions in the many ways that we think we can do it and exploring their cosmological implications. You might know Brian better as a best-selling author. His books include, “The Elegant Universe” and “The Fabric of the Cosmos”, among others. He’s also been the host of specials on Nova on PBS that explain some of these esoteric ideas, and he’s also the co-founder of the World Science Festival. So, I think it’s safe to say that Brian Greene is one of the most effective and respected popularizers of science, especially of high-level, theoretical physics that we have in the world today. Brian really has a true gift for explaining very difficult concepts, and that’s what we have in front of us. 0:02:34 SC: And the Mindscape philosophy, I’m not gonna tell you what’s right or wrong, we’re gonna give you the ideas and you can decide for yourself. Let me give my occasional note that we love it when people pledge to Mindscape on Patreon or PayPal. You can see the links on the webpage. And, of course, leaving nice reviews on iTunes and elsewhere is always a good thing. So this is gonna be both a fun and enlightening episode. I hope you enjoy it. Let’s go. [music] 0:03:19 SC: So Brian Greene, welcome to the Mindscape Podcast. 0:03:21 Brian Greene: Thank you. Good to be here. 0:03:22 SC: This is a special event for a few reasons. For one thing, it’s the first live show that we’re doing… 0:03:27 BG: Look at that. 0:03:27 SC: On the Mindscape Podcast. It’s not technically. It’s supposed to be a live show, but we’re sitting here in Columbia University in Brian’s office and several of his students are hanging around listening to what we have to say. So, maybe there’ll be laughter or jokes, applause? 0:03:40 BG: That’s what we’re shooting for guys. [laughter] 0:03:43 SC: Alright, so I actually did an interview with Clifford Johnson fairly recently, where we did the history and motivation of string theory. So I’m going to proceed under the assumption that all the listeners here have absorbed all of that, and they know what string theory is. But just to be safe, why don’t we give the basic story of the particular feature of extra dimensions in string theory and what we’re supposed to do about them? 0:04:08 BG: Yeah, sure. So again, not to cover ground that you already covered with Clifford, but the basic idea is that Einstein had this dream of a unified theory that would put our understanding of everything in some sense together into a single theoretical framework and he died without finding that unified theory. But then in the late ’60s and ’70s, this idea of string theory came along, which suggested a possible way of putting all of nature’s forces together in a quantum mechanical framework, which is actually even beyond what Einstein actually had in mind. And when people studied the equations of the theory, they found somewhat surprisingly that the math only was internally consistent if the universe had more than three dimensions of space, and depending on exactly when you look at the theory in the timeline of unfolding the exact number of dimensions that the math required has changed for reasons that we completely understand. It’s not as though there’s someone throwing some dice around to figure out what the number of dimensions is, but the question that you ask is, what in the world do you do with a theory that says that there are more than three dimensions of space? 0:05:19 SC: People of weaker constitutions would say, “Well, there are three dimensions of space. String theory predicts there are nine or whatever therefore the theory is wrong.” [chuckle] 0:05:27 BG: They may not only have a weaker constitutions, they may be much smarter than generations of physicists who perhaps have been wasting their time on the possibility that there really are these extra dimensions. But the reason why we’re not willing to so quickly discard these theories that suggest that there are other dimensions, is that, A, we believe that there are ways to make sense of them, that is to make them compatible with all known observations. And B, the mathematics that yields this possibility of more than three dimensions achieves some, at least on paper, spectacular things. 0:06:03 SC: Right. 0:06:04 BG: So with the pay-off being huge, namely, the possibility of a unified theory of gravity and quantum mechanics and the other forces of nature, and with the possibility that the extra dimensions could actually be real and around us right at this very moment, we’re willing to entertain that possibility. 0:06:20 SC: Can I just ask? Maybe this is not a fair question, but, what is the percentage chance you would put on string theory being a correct description of nature. 0:06:27 BG: Physics by probability. Yes. 0:06:29 SC: Bayesian inference. 0:06:30 BG: A very quantum mechanics… 0:06:31 SC: No, just being Bayesian. 0:06:31 BG: Bayesian, I agree, I agree, yeah. It’s a somewhat unfair question because I don’t feel at the moment that we have enough to go on, we’ve had the possibility, a long shot possibility, of finding extra dimensions say, at the Large Hadron Collider, and nothing turned up, but we knew that that was the most likely outcome by virtue of the fact that the extra dimensions are likely to be so small that the energies required to access them is so high that the Large Hadron Collider simply wouldn’t have enough power to do so. So, I would say 50/50 would be the gut reaction on whether or not these theories are relevant to the world. And if you ask me a slightly different question, which is, how strongly do I feel about the beauty of the world if there are extra dimensions? Is I think it’s spectacular. What a wonderful idea that the way you unify the laws of physics is by stepping beyond the dimensions that we know about, allowing for a new perspective, so to speak. 0:07:46 BG: And the analogy that people sometimes use is, if you look at planet Earth with all of the complexity of the geography and the topography, if you’re walking around, it looks like it’s a haphazard collection of things, but yet, if you pull out, you see this beautiful, spherical, Earth floating in the black void, and how beautiful is that unified theory of earth that only becomes apparent when you go off into another dimension, that is, the dimension of altitude; of height. So, in the same way, if we go beyond the three dimensions that we know about of space, and have these other dimensions, then all of a sudden, it all clicks together into a unified theory; that’s deeply satisfying. 0:08:28 SC: You’re just asking the Flat Earth contingent to flood my YouTube comments. You’re just poking the bear right there. 0:08:34 BG: That’s right. 0:08:34 SC: But even though physicists don’t like to attach probabilities to their theories, you do vote with your feet, you decide what you think is most worth working on. And is it fair to call yourself a String Theorist at this stage of your career? 0:08:46 BG: Yeah, I would say so, it’s certainly been a dominant theme in the work that I’ve done. But at the same time, I would say this, sometimes I’m described because… You’ve written books too, so you know how you can get pigeon-holed by virtue of the things that you do in that domain. I’ve sometimes been described as a proponent of string theory. 0:09:08 SC: Oh yeah. 0:09:08 BG: And I don’t consider myself a proponent of string theory. I consider myself as someone who is excited about the possibility that string theory is the right description of the world. But I reserve judgement to ultimately base my assessment on observation and experiment. 0:09:21 SC: Sure. 0:09:22 BG: And so from that perspective, if tomorrow someone came along with evidence that showed us that string theory was wrong, maybe some mathematical inconsistency of the theory, or some quality of the world that was fundamentally impossible to incorporate within the theory, and could prove that mathematically for instance, I would happily, and I don’t mean this in some pejorative way or even some dismissive way or a sarcastic way, I would truly, happily move on, because I’d like to consider myself, as you and everybody else I suspect would say, we’re all after truth, and I don’t care what flavor truth is. 0:10:00 SC: Right. 0:10:00 BG: I just don’t wanna be wasting my time on something that’s demonstrably not true, and if string theory falls into that category, I’d let it go like a hot potato. 0:10:07 SC: But so far it hasn’t, and in part because we have clever ways to hide the extra dimensions from our view. So what are some of those clever ways? 0:10:15 BG: Well, there are two dominant ways. The one that was studied most intensively, even going way back, long before string theory to the early decades of the 20th century, is that the world could have two kinds of dimensions, big and obvious dimensions that are easy to see with the naked eye, and those are the ones that we obviously know about, left-right, back-forth, up-down. But there could be other dimensions of space that are tightly curled up, crumpled up into a very small shape, so small as the theory goes, that we can’t detect such shapes with the naked eye or even with today’s most powerful equipment. So that’s one way. They’re all around us and they’re just too small for us to see and too small for today’s technology to even access. 0:10:56 BG: The other possibility is that the dimensions in principle could actually be quite big, but we’re unable to probe into those extra dimensions because of the way that we access the world. So we see things with our eyes, which are sensitive to photons. Imagine that photons can’t penetrate into those extra dimensions, even though they’re big and even though they’re all around us, photons absolutely are unable to penetrate. Then again, we won’t see those extra dimensions because of that probe being unable to go into that additional, spatial part of the world that is there but we’re unable to access. 0:11:33 SC: And how big could these dimensions be? 0:11:35 BG: Well, because gravity is a force that’s highly sensitive to the geometry of space and time, in almost all of these theories, gravity can penetrate in some way, shape or form into these extra dimensions, and that places a constraint on how big those dimensions can be. So, in conventional approaches maybe the dimensions might be, oh, a millionth of a millimeter across, or something of that sort. So that still sounds small, but it’s actually enormous. [chuckle] 0:12:08 SC: To you and me it’s small but to the quark it’s big. 0:12:09 BG: But it’s actually enormous compared to the… Yeah, to the Planck scale, which is say, 10 to the minus 33 centimeters. So that’s the typical size when we look at the equations of string theory, the Planck scale as the size of the extra dimensions. But there’s a great deal of flexibility that comes with this other way of hiding them from common view. 0:12:31 SC: Yeah, and so one of the things that I say sometimes, I tell a story, and a historical story and correct me if this is wrong. But in 1998, we discovered that the universe is accelerating, and the simplest explanation we have for that is that there is energy in empty space itself, right? That there is vacuum energy or Einstein’s cosmological constant. And the story I tell is, that this empirical database finding changed the course of string theory. Is that a fair assessment? 0:13:03 BG: I think it’s a fair assessment. Initially, when that discovery was made, there was a concern that it might actually rule string theory out, because the energy that you’re referring to, people had great difficulty incorporating it into the models of the world that were emerging from the equations of string theory. And that definitely was a strong motivation for people to try to find some new, clever, mathematical way of making the equations of string theory align with the observations of the accelerated expansion of the universe. And groups of physicists claimed that they achieved that goal, and the community by and large agreed with them, that they had succeeded in incorporating this dark energy, this accelerated expansion, into the mathematics of string theory. As of today, there’s grumblings… 0:14:00 SC: Yeah. 0:14:01 BG: That perhaps that was accepted too quickly. 0:14:04 SC: Too hasty, yeah. 0:14:04 BG: Yeah, and that… So people are now, and this is a sign of a healthy field, re-evaluating the state of the theory relative to the observations that may impact it. So you’re right, it did have a significant influence on the course of string theory, and even today is again influencing people’s thinking for a second round, if you will, to try to make sure that the theory is actually compatible with the observations. 0:14:33 SC: Yeah, and just in saying that actually I realize I’m skipping ahead, ’cause I’m too excited about talking about cosmology, and so forth, but we need to get on the table the idea that there’s more than one way to hide the extra dimensions, and those different ways show up in our visible, low energy world, right? 0:14:50 BG: Yes. The beauty of string theory is that it’s not merely a matter of hiding away an embarrassing quality that the theory says that there should be more than three dimensions of space. If it was merely a matter of hiding it away, I don’t think that people would have been all that excited about this prospect. Certainly as a graduate student in the Dark Ages, which is… 0:15:12 SC: Mumbledy mumble years ago. 0:15:13 BG: Yeah, yeah. A very long time ago. When I learned that string theory required extra dimensions, and that the precise shape of those extra dimensions could impact the low energy physics that we can observe say at a particle accelerator, I thought that was the most spectacular collection of ideas that I had ever encountered. 0:15:31 SC: Yeah. 0:15:31 BG: So my thesis, my dissertation, was among the first calculations to take specific shapes for the extra dimensions and extract from them predictions, which you can’t see my air quotes with my fingers here on the podcast, but to try to see whether we could extract some predictions for qualities of the world that we might be able to observe, like the number of particles that are around us, and even in principle how they interact in their masses. So yes, there is, in principle, a wonderful link between the way you hide the extra dimensions and the physics that you actually observe. 0:16:06 SC: And I remember the specific thing that I thought it was always fascinating was the claim that string theory could explain why there are three generations of matter particles of, there’s the electron, the muon, the tau. 0:16:16 BG: Yeah. 0:16:17 SC: Who ordered that? Why, in fact, Columbia is the home of… 0:16:20 BG: I. Rabi. 0:16:20 SC: I. Rabi, who wondered who ordered the muon. Are there other things like that, that people should know about. And actually, could you even explain that? How can the shape of the extra dimensions give us three copies of the electron? 0:16:32 BG: Yeah. So the idea is, you are studying the equations of string theory as they manifest in a world that has extra dimensions of a very specific shape. And the number of solutions to the equations dictates the number of particles that you’d see in the world around you. And while it might be a little bit hard to picture, if you’re not used to solving equations on curved shapes, the precise way that the shape curves on itself has a direct impact on the number of solutions of your equations. And it was found that there is a quality of the shape, which mathematicians had long known about it, it has a technical name, it’s called The Euler characteristic of the Euler number, but the details of the name don’t really matter, but that quality of the shape dictates the number of solutions. So you could go to a mathematician in principle and say, “Hey, we’re looking for a shape, a six-dimensional shape, that has such and such mathematical features and the Euler number is such that it gives rise to three generations, three collections of solutions to these equations.” And that sent mathematicians scurrying about, in some sense at the service of physicists… 0:17:42 SC: Yeah. 0:17:42 BG: Which is sort of a curious state of affairs, to come up with these shapes, and Shing-Tung Yau, who was actually my post-doctoral advisor, came up with a couple of examples that had the right Euler number to agree with the number of particles that experimenters had long found. So my dissertation was taking one of those shapes. 0:18:03 SC: Yeah. 0:18:03 BG: And then going further, and trying to say, “Okay, it gives the right number of particles, but it doesn’t give the interactions of those particles? Does it give the masses of those particles?” And those are very difficult calculations to carry out, but within a certain set of assumptions, we pushed it through and found it didn’t agree with what we saw in the world around us. But that was a sort of a proof of principle. 0:18:25 SC: Are you saying it’s a falsifiable theory? 0:18:27 BG: Well, I wish I was. I wish it was, because in the 1980s when we were doing this, there were only five known shapes. 0:18:33 SC: Right. 0:18:35 BG: Six known shapes or so for the extra dimensions. And then, if that were the sum total of allowed shapes, then it perhaps would be a falsifiable theory. You go, shape by shape by shape, compare it to observation, and if it agreed, fantastic, if not, you could throw the theory away and move on. The challenges, historical development through the ’90s and 2000s, people found more and more candidate shapes for the extra dimensions. It grew from five to 5000 to 10,000. And I like to say, 10,000 it’s still a double to analyze these shapes, because graduate students, like those who you guys will one day be, need projects, right? 0:19:12 SC: Yeah. 0:19:12 BG: So there you go. Just throw them one shape after another. 0:19:15 SC: 10 shapes each. 0:19:15 BG: And then just get it done. But when the thing grew from thousands into millions and billions, and depending precisely on how you count, a number that’s thrown around that’s not as meaningful as it might sound, but 10 to the 500 is a number that people throw around, and that’s just such a huge number of candidate shapes that you’re never gonna analyze them one by one. 0:19:35 SC: Yeah. 0:19:35 BG: And therefore, you don’t know if within there, there is the shape that would agree with all observations. And if it does exist, how would you even find it? 0:19:45 SC: Right. So the hope is… Let’s just summarize where we are. So, we have this theory that works really well in 10 dimensions, but we’ve known since the 19-teens that you can hide dimensions by curling them up, and if there are only a few… And the way that you call them up, tells you not only what particles you have, but their masses, and this is why string theory involves so much math, right? The geometry and the topology, the extra dimensions affect the particles we see. And we’ve been coming better and better at finding new shapes. And one of the things that gets affected is the energy of empty space. Is that right? 0:20:18 BG: Yeah, that’s right. So it’s not just, as you said, the masses of the particles, and the number of particles, but in principle, all physical qualities of the world would be encoded in these shapes for the extra dimensions and various ways that we can mathematically dress them up, if you will. But you can still think of it roughly as the shape. So, it’s not a bad image to think of the shape as sort of, it’s the DNA of the universe, right? 0:20:45 SC: Yeah. 0:20:45 BG: Just like the DNA sequence within our bodies encodes the detailed features of how we appear in the world, the precise shape of the extra dimensions determines the detailed properties of the universe itself. 0:21:00 SC: Yeah, and a DNA sequence that is as long as a human genome, there’s a huge number of possible DNA sequences, right? And evolution does not try every one of them but it lands on one that is pretty good, which is us. 0:21:11 BG: Yeah. Right. 0:21:11 SC: And maybe we’ll get there, but maybe the universe does something like that, but… 0:21:15 BG: Right. 0:21:15 SC: Before we get there… Okay, so there’s this thing called, the energy of empty space. In string theory, where there are extra dimensions you compactify them. The shape and the size of the extra dimensions predicts the energy of empty space. But even before we knew about that there was this thing called the cosmological constant problem. We were worried about the energy of empty space, even though we weren’t string theorists. So why don’t you tell us about that? 0:21:39 BG: Well, the cosmological constant is a wonderfully interesting concept that’s had a twisted history. Beginning in 1917, Albert Einstein introduces this term into his equations of general relativity in order that he can have a universe that’s static. He had this philosophical prejudice that the universe shouldn’t be changing, at least in its large scale structure over time, things in the universe could exist and change and morph, but the universe as a whole, no, that always was and always would be. 0:22:12 SC: I think that’s also what the observations indicated at the time, to be fair. 0:22:15 BG: They did suggest it, that’s right. So it wasn’t just out of his head. You look up and it doesn’t seem like… 0:22:19 SC: You don’t see anything. Yeah. 0:22:21 BG: Not much is happening out there. So the problem though was, as others pointed out to Einstein as well, his equations seemed incompatible with that view of the universe, and Einstein had a clever way of making it compatible, which was changing the equations to include a term, that in some sense, would generate a repulsive gravitational push to counteract the usual attractive gravitational pull, and in that way, yield the universe that would be steady state; unchanging over time. Now, when the observations in 1929 revealed the universe is expanding, Einstein sort of smacked himself on the forehead and said, “I wish I hadn’t introduced this cosmological constant.” And he said, “Away with it. Away with the cosmological… “ 0:23:00 SC: He could have become famous. 0:23:00 BG: That’s right. Poor Einstein; smart guy, almost. And then, so he throws away the cosmological constant. But then, you fast forward to the observation that you talk about 1998, when it was recognized that the universe is not only expanding but speeding up in its expansion, you need something that’s pushing outward. What could that be? Cosmological constant is a natural possibility that then reappears in the equations, and people are fond of saying, even Einstein’s bad ideas turn out to be good. 0:23:29 SC: Right. 0:23:29 BG: You just have to wait long enough. So there’s the cosmological constant as a phenomenological tool for making our equations agree with what we observe. But the question you ask is a more theoretical one, which is, as particle physicists, as quantum field theorists using the tools of the trade, we’ve had a hard time finding a way within our mathematics to allow, to calculate the energy of the universe and find a sufficiently small number. The natural number for the energy of space that comes from the wild undulations of quantum uncertainty playing out in microscopic domains, particles popping into and out of existence, the fabric of space oscillating in wild ways, the energy that emerges is huge. So we have no trouble getting a cosmological constant out of our mathematics. We have trouble making it small enough. 0:24:22 SC: But more specifically, it’s a sum of huge things, some of which are positive and some which are negative, right? 0:24:28 BG: That’s right. And without very detailed cancellations between the positive and negative, the order of magnitude of that number would be about 10 to the 120. Whereas the number in the relevant units would be sort of on the order of one. 0:24:43 SC: Right. 0:24:43 BG: So we’re off by a factor of 10 to the 120 and people are fond of saying that’s the biggest mismatch between the theoretical calculation and observation in the history of science. So it’s a big, big mismatch. 0:24:54 SC: I’ve always felt challenged when I hear that to come up with a theoretical calculation that makes a worse prediction than that. 0:25:00 BG: That’s worse. 0:25:00 SC: Then I could become famous to you. Yeah. 0:25:00 BG: There you go. So it’s an interesting state of affairs, where now the observations are saying that it’s a non-zero value, in order to explain the accelerated expansion of space, and the challenge for us is to come up with some theoretical calculation that yields a number that’s not huge, that’s small enough to be compatible with observations, and that is something that people still struggle with in a mighty way today. 0:25:27 SC: And there was this belief before 1998, before we found the universe was accelerating, that the empirically determined value of the vacuum energy, the cosmological constant, is clearly really small, much smaller than it should be, therefore, it’s probably zero. 0:25:42 BG: Yeah. It’s much easier to explain the number zero than a number that’s very, very close to zero. 0:25:47 SC: Yeah. 0:25:48 BG: Zero is a beautifully symmetric number. And you can imagine, as you were indicating, that if there’s some deep symmetry that says, “Aha! There’s a positive value contributing to this number and a negative value and there’s a symmetry that requires that they be equal in magnitude, but opposite in sign, therefore when they combine, you get zero.” That kind of an argument we could imagine happening, but if the number’s non-zero, then what do you do? You… 0:26:16 SC: Yeah. 0:26:16 BG: Is it a almost symmetry? A partial symmetry? Is there a way that, even if there is that kind of a structure, that it won’t be upset by further contributions that might be allowed by the quantum equations? And so, without zero as your anchor, you’re really floating off at sea, and that’s where we’ve been for a while. 0:26:38 SC: So we had… That is what we call the cosmological constant problem. Why is the real vacuum energy so much smaller than its natural value? Then once we found what we think is probably the cosmological constant in 1998, we were faced with a new problem in the coincidence problem, right? 0:26:52 BG: Yeah, right. Because the value is not only non-zero, it’s on par with the amount of mass energy that we observe in the universe from the molecules and atoms in stars, in galaxies, and even including the dark matter; it’s all roughly on par. So, why would it be the case… 0:27:11 SC: Yeah. 0:27:11 BG: That this non-zero amount of this cosmological constant, we often use the term, “dark energy” ’cause it’s energy that we don’t see, so it’s dark or invisible, why would it happen to have the value that’s so close with the density of energy from ordinary matter and energy, especially taking into account the fact that the amount of energy in ordinary matter, the density of that changes over time as the universe expands, that number gets smaller and smaller and smaller over time, which means that, in principle, there could be a mismatch in the far future between the amount of energy in this cosmological constant, which may be a number that doesn’t change… 0:27:51 SC: Yeah. 0:27:51 BG: As it relates to the amount of matter energy in the stuff of ordinary existence. So why, right now today in this epoch, are they close to each other? Again, it’s a problem that people come up with creative solutions for. But I think it’s, again, a mystery. 0:28:07 SC: Yeah. So just to put people in the mindset of where we were in 1997, before we found this. We had string theorists, who were compactifying the extra dimensions and finding different ways to make particles and so forth, and apart from the string theory, we still had these general arguments from quantum mechanics and quantum field theory that there should be a large cosmological constant, but it is small for some reason. So is it safe to say that most string theorists took as their task to find a way to hide the extra dimensions that left us with zero cosmological constant at the end of the day? 0:28:41 BG: Yeah. I’d say, 99% or more of us had that as the goal. The goal was to, not only compactify, that is make the extra dimensions small but makes them small in just the right way that it would agree with the particle properties of the world, and also at the same time, rid us of this cosmological constant problem by somehow ensuring that the amount of energy-suffusing space associated with this theory would be zero, because that was what everybody thought the answer would be. 0:29:14 SC: And there’s an even more subtle thing that I think is it harder to get across, but if you would put a string theorist up against the wall in 1997 and said, “Okay, the cosmological constant is not zero. Is it positive or negative?” They would have been much happier with a negative number than a positive number. 0:29:30 BG: That’s right. That’s right. There is a clear distinction in the mathematics between a positive cosmological constant, a positive amount of this energy, and a negative value for this energy, and again, a negative value for energy might lead some to wonder what in the world could that mean. And in the theory of gravity, energy really can be positive or negative. It sort of affects the way that space time curves. So that isn’t really a puzzle for us; the positive versus negative side. But certainly, the math of string theory was much happier with a negative or zero value… 0:30:05 SC: Or zero. 0:30:05 BG: Than it was with a positive value. So, there may have even been people in 1997, I would have to check historically, who might have said, “If we observe a positive value for the cosmological constant, then this theory can be discarded.” There may have been people who said that, “I’m not sure.” I certainly wouldn’t have said it at the time… 0:30:22 SC: Yeah. 0:30:22 BG: But there may have been people who felt that way. 0:30:24 SC: I do think that there were people who were at least saying that, “We have no idea how to get a positive… “ 0:30:29 BG: Right, right. 0:30:30 SC: “Cosmological constant in string theory.” And then, the universe intervened, as it so often does. Actually doesn’t do it enough, but it does it in… It’s very pleasant when the universe intervenes in a surprising way, right? 0:30:39 BG: Well, I’m not even sure how to judge the development in the following sense. Is it that string theorists are very clever mathematicians such that given a constraint that does come from the universe, namely the observation of a positive value of the cosmological constant, they were able to manipulate the theory in order to get that answer. Or is it that string theory is a very tight, logical structure, and it agrees or is able to agree with the observations because it’s a true description of reality? 0:31:15 SC: Yeah. 0:31:16 BG: And that’s the key question, right? Is it the case that string theorists are just so clever, that no matter what you give them, even if it turns out to be made up, they’re gonna find some way of explaining the data, or supposed data that you provide, or is it that it’s a great theory of the world, and therefore, if the world gives us this quality, it’s not surprising that the theory is able to explain it? 0:31:42 SC: Since I’m not a professional string theorist, I can also add that it’s possible that string theory is correct and the string theorists are very clever at the same time. [chuckle] 0:31:48 BG: Well, thank you. I will accept that. On behalf of the field I will accept that. 0:31:53 SC: So there we are in 1998, and the universe rudely tells us that it seems as if the vacuum energy is positive. We’re not even sure about that. There’s something pushing the universe apart. The simplest explanation is the cosmological constant, but it could be something more elaborate. So, string theorists leapt into action and said, “Alright, we’re gonna try harder to find ways of hiding the extra dimensions that have the property that the vacuum energy is positive.” 0:32:17 BG: Yes. 0:32:17 SC: So how did they do? 0:32:19 BG: Well, it’s interesting. One paper in particular, I think, changed most people’s mind. It’s a paper called usually, KKLT, after the authors who were responsible for this paper. And what they found is that by throwing everything together that string theory had in its toolbox. 0:32:42 SC: The kitchen sink. 0:32:42 BG: The kitchen sink, the proverbial kitchen sink, they were able to combine those ingredients in just the right way to give at least a strong argument that string theory allowed for a positive amount of this cosmological constant, this positive vacuum energy. And with that paper, thousands of others were then written, riffing on this idea, developing this idea, trying to see how this idea might be made compatible with other observations. That’s sort of an endless industry that was spawned by this paper, and at the same time, it gave us confidence that the theory could actually agree with observations. Without that, you’re in a curious quandary. Because, if the theory can’t accommodate this observation, then either the theory is wrong, or perhaps the observation itself needs further refinement, and maybe that version of it, the theory would be able to accommodate, but once the possibility of string theory agreeing with those observations was on the table, the floodgates were open and everyone cheered and went forward. 0:33:54 SC: Except not everyone cheered. 0:33:56 BG: Yes. 0:33:56 SC: Because there was the downside, that once you can find a way of compactifying the extra dimensions that gives you a positive vacuum energy, you can find many. 0:34:05 BG: Yeah. 0:34:05 SC: A butt-load would be the technical term, right? 0:34:06 BG: I’m not sure if I… I have never encountered that technical term, [chuckle] but I will add it to my vocabulary. Yes, that did have another effect, which is one that you’re referring to, where people recognized that there were just so many ways in which the extra dimensions could be curled up, in principle in a manner that would be compatible with this positive amount of the vacuum energy, that the old dream, which certainly motivated me when I was a graduate student, and I think motivated many other in the field, the old dream was, “Here is a theory that is going to give us a unique description of reality. Everything that you wanna know about the world will emerge from an industrious, careful analysis of the mathematical equations, and Einstein’s dream is therefore at hand.” That was the view in the 1980s. The view radically changed post-1998, and these papers that were able to show that the positive amount of dark energy could be explained within string theory, because now the view was, “There are a huge number of distinct ways of curling up the extra dimensions that will be compatible to the positive vacuum energy, and the best that we can hope to do is some statistical analysis on this vast collection, this vast landscape of possibilities, and perhaps the way that we’ll describe our world is by saying, “Hey, there are many, many, many shapes for the extra dimensions compatible with all we observe.” 0:35:38 BG: “Ours is somehow more likely. There are more of them that agree with our observations, than had the observations been different. And in that way we explain our universe, not by a unique description of reality, but rather by a statistical averaging that suggests that we’re, run of the mill, and therefore ordinary, and therefore the likely outcome of this unfolding, guided by the equations of string theory.” It’s a very different way of looking at reality. 0:36:05 SC: Yeah. And then, even your tone of voice indicates it’s not quite as satisfying as the original one. 0:36:10 BG: Well, yes. How beautiful would it be… 0:36:11 SC: Right. 0:36:12 BG: To have a unique description of the world, and out of the mathematics everything that we know emerges. 0:36:18 SC: And you have to go with a combination of the theory and the observations, right? You don’t get to choose. 0:36:20 BG: That’s right. And what happens is your aesthetic sense of what’s beautiful changes over time. I think it’s partly guided by the way these theories evolve. And there’s certainly some who have suggested that this landscape of possibilities is even more beautiful, because it then eliminates certain class of questions you can always ask of a theory, why did it turn out exactly that way, right? Why didn’t it turn out somewhat different? And in string theory, the answer would be, “Well, actually, it did turn out different. It turned out different in many different universes, and we are simply one of the vast collection of universes. So that question doesn’t hold the same bite as it did when there was one unique answer and you questioned why it turned out that way. There are many possibilities. We’re one of many. We’re actually a run of the mill, ordinary, expected answer that comes out of this vast collection and that’s all there is to it.” 0:37:13 SC: It’s like an arranged marriage. You get married first, love develops later with this view of the world. 0:37:17 BG: That’s right. You could look at it that way. 0:37:19 SC: But okay. When you start using words like “likely” and “evolve” and so forth, now, rather than the strict string theory problem, we bring in a cosmological problem, right? 0:37:29 BG: Yes, that’s right. 0:37:30 SC: It’s one statement that in the world of possibilities, there’s 10 to the 500 or whatever different ways that string theory could be compactified. That’s the landscape of possibilities. But let’s ask about, so, which one becomes real? Or which many become real? And that’s when the string theorists realized they need to think about inflationary cosmology, right? 0:37:48 BG: That’s right. Because if you have this collection of universes allowed by the mathematics, you have to say to yourself, “Is there a mechanism by which one or many or all of them might actually be brought into existence?” And that’s where a union with inflationary cosmology gives you a natural way forward, because even before string theorists were talking this language about many possible universes, the inflationary folks realized that inflationary cosmology naturally gave rise to more than one Big Bang, if you frame it that way. There’s this inflationary fuel that gives rise to repulsive gravity that drives everything apart, but it’s virtually impossible to use up that fuel completely. 0:38:29 SC: Right. 0:38:29 BG: So some of the fuel, in some sense, drives our Big Bang, but some is left over, and in fact, some is created by that very process, and that additional fuel gives off different Big Bangs at various and far flung locations in a much bigger cosmos, a much bigger cosmology. Combine that idea with string theory, and you say, “Aha! Maybe inflation doesn’t just fuel other universes in the conventional sense of three dimensions of space. Maybe it gives rise to other universes that have these extra dimensions too, and moreover, maybe the different universes produced by inflation have different shapes for the extra dimensions. So now in principle, you’ve got a mechanism that leverages the insights of inflationary cosmology, the insights of string theory, to suggest an incredibly rich cosmos, in which there are many universes each with a different shape for the extra dimensions and therefore each with different fundamental physics. And we live in one universe with a particular shape for the extra dimensions and not another, because it’s the universe in which that shape gives rise to the properties of the electron and the quarks and the chemistry and the biology that allows us to exist. 0:39:34 BG: So we are here because the shape allows us to exist here. We’re not somewhere else because of the shapes. They aren’t incompatible with the chemistry and biology that allows our form of life to exist. 0:39:44 SC: And inflation, in some sense, went through that same aesthetic shift that string theory went through, in the sense that I believe the original goal of inflation was to say, “We see features of the universe. It looks more or less the same on very large scales. So, I’m gonna come up with a dynamical mechanism that says why it had to be exactly that way.” And it was only by examining the theory more carefully, you realized, “Well, like it or not, somewhere else in the universe, inflation is still going on and things could look very different from place to place.” 0:40:14 BG: That’s right. And to be fair, some or one of the pioneers of the inflationary theory, if he were sitting at this table, would say, “You guys are nuts.” 0:40:26 SC: Yeah. 0:40:26 BG: He would say, “I now disavow this approach to cosmology because it gives rise to this possibility of other universes. That’s a possibility that I don’t consider still to be within the realm of scientific investigation.” 0:40:40 SC: We can say that it’s Paul Steinhardt. I wanna get him as a future podcast guest… 0:40:42 BG: Good. Good. 0:40:43 SC: ‘Cause I wanna get that perspective. 0:40:44 BG: Yes, and Paul and I, as of course, Paul has had these conversations with many people, but I’ve had a running conversation, an email debate if you will, with him over the course of many, many years, where the emails became so densely threaded with the back and forth so we had to color code it to know who said what when. And I see his perspective. I don’t agree with his perspective, as fully as he proposes it. I think that we have to be very careful about theories that propose other universes. We have to recognize that we need a larger mathematical architecture that can really allow us to make predictions within that kind of larger cosmological framework, and I don’t think that we have that on the table yet… 0:41:29 SC: Right. 0:41:29 BG: The thing that needs to be further developed. I feel that it can be developed. Paul thinks that it is so far beyond where we currently stand that that may be wishful thinking, and until it’s developed, we should not propose this as a bonafide cosmology. I think that’s really where the difference is. 0:41:46 SC: Yeah. I think that’s fair. And I think that there’s sort of different levels of ambition here, right? One is, I think what we would all… The highest level is we would like to make predictions. We would like to say, “Well, this is what you should expect under this ensemble.” But there’s a weaker level which I think a lot of string theorists are happy with right now, which is to say if nothing else, this picture of inflation and the string theory landscape makes it possible that somewhere there will be conditions where we could live. 0:42:14 BG: Right. 0:42:15 SC: So, the fact that we live in one of them shouldn’t be that surprising, and that like it or not, that’s the anthropic principle, right? 0:42:20 BG: Yeah, and in fact, a version of that underlies the gold standard of physics, which is the standard model of particle physics. We always put forward the standard model of particle physics as a grand achievement of the 20th century in which we could describe the interactions of electrons and quarks and all particles of that sort, and they explain data from the Large Hadron Collider. But of course, the standard model of particle physics itself is one of an infinite collection of theories that differ by slight variations in numbers, constants, that are within the equations. And how do we figure out those numbers? 0:42:56 SC: Like the mass of the electron and so forth. 0:42:58 BG: Yeah, the mass of the electron, the strength of the electromagnetic force, the strength of the nuclear forces, and we have no idea what is the explanation for those numbers. We take it from experimental observation. So we look out at the world, we make measurements, we tune our theory in order that it can explain those measurements, and then we go further to make new predictions about things that we haven’t yet measured. And from that perspective, maybe string theory should be viewed as one of a large collection of descriptions of worlds. And what we do is, we figure out what the right version of that theory is through observation and experiment and in that way, winnow it down to a single description, or a handful of descriptions, compatible with observation. And therefore having a great many possible universes coming out of the mathematics, maybe is not all that unfamiliar, because that’s exactly what happens with the standard model of particle physics. 0:43:52 SC: Yeah. But okay. I should mention that even before we discovered the cosmological constant and the string theory landscape, different uses of the word ‘discover’ in that sentence, but we were talking about the cosmological constant problem, and Steven Weinberg talked about this possibility of a multiverse; Steven Weinberg, one of the leading physicists of the 20th century. And so he tried to make an argument that if there were multiverse with different values of the vacuum energy from place to place, we should expect to see a small but non-zero value in our universe. Did you buy that at the time? Do you buy it now? 0:44:30 BG: Well, I buy it as an interesting piece of data where, under a certain set of assumptions, you’re naturally led to imagine that the universe would have a non-zero cosmological constant, whose value actually turns out to be on par with observation. I think that’s an interesting sentence to be able to utter that. At the same time, many have… 0:44:52 SC: And he did it before we saw it. 0:44:54 BG: And he did it before we saw it. So he’s an incredible, insightful physicist, the grand master of physics, still with us, and utterly an amazing job in figuring this way of thinking about the world. Now, at the same time, many have criticized that as the assumptions that were made that certain other qualities of the world would be fixed and unchanging, and only allowing the cosmological constant to be the sole parameter that you dial. That turns out to be a very limited framework, and if you relax it, then the prediction of the value of the cosmological constant is also relaxed and need not be on par with the value that’s been observed. So it’s all just to say, putting the details aside, that, yes, under a certain limited set of assumptions, you can make statements, as Weinberg did before the observations were made, that are on par with what ultimately was found. Post facto, the belief that you have that that truly is an argument supporting the prediction, is perhaps somewhat weaker… 0:45:58 SC: Right. 0:45:58 BG: Than Weinberg himself might have articulated at the time. 0:46:01 SC: And so I think that this is getting us in the right direction in the sense that, if you believe that there could very plausibly be this multiverse with different parts of the landscape being realized in the ensemble, then certainly from that assumption, so you can say, “Okay, somewhere there’ll be a world in which we can live.” But making predictions involves other issues, like, how much volume of space are occupied by these different possibilities? How many stars form in all of them? How many observers form in all of them? Do we know what an observer is? Do we know what life is? Have we made progress on these questions? 0:46:39 BG: Yes, I’d say there’s been a very small amount of progress relative to the towering difficulty of the problems that you articulated. So it’s not like we’re stuck, but I would say that we’re nowhere near being able to say, “Oh, just a few more details and we’ll have finished this off and really be able to make these kinds of probabilistic, statistical statements about physics in a universe that, or a vast cosmology, that has all these universes within it.” So, yes. Progress, no. Nowhere near the answer. 0:47:13 SC: And that’s the heart of the worry of someone like Steinhardt, which is he thinks that there isn’t an answer. There’s an infinite number of everything. You can’t say there’s more of one thing than another. You can’t make any predictions whatsoever. Is that right? 0:47:23 BG: Yeah. That is at the heart of it. And my own feeling, and of course, I think many in the field, and I’m interested to hear your view, is that it doesn’t seem as insuperable to me. 0:47:35 SC: Yeah. 0:47:35 BG: It seems to me difficult. It seems to me vitally important to make these theories scientifically sound. But I don’t see that there is some insurmountable hurdle that’s facing us. We’re pretty clever. We’re pretty smart as a community. And I think that we will be able to make headway on this. 0:47:54 SC: Yeah, no, I think that’s more or less exactly my view. Certainly, I don’t think that we should now give up on the possibility of coming up with some principle or some understanding. Let’s accept the problem is a good one, absolutely, and therefore, try to solve it, not just declare defeat from that surely. 0:48:10 BG: Right, right, right. 0:48:11 SC: But okay, other people worry, and I think I know the answer to this myself, but let’s hear it in your voice. Other people worry that this is just putting human beings back at the center of the universe in some sense, to say that rather than being scientists, making predictions and saying what things should be, using these anthropic or environmental selection arguments, makes things a little bit too anti-Copernican; too human-centered. Is that something we should worry about? Is it kind of a cop-out? 0:48:40 BG: No, I don’t see it that way at all. It’s an observational fact that we’re here, and therefore any successful theory should be compatible with that observation. It’s one of many observations of the world that a theory needs to be compatible with, and you use those observations that are most potent at winnowing down the spectrum of possibility. So the fact that we are going to impose on this collection of universes that the conditions need to allow us to be here to make statements. That is just pure logic. 0:49:16 SC: Right. 0:49:16 BG: It has nothing to do with putting us back in the center of things. And again, it’s not the only condition that we put on things. It’s one of a grand collection and it may be a potent one in order to make a first step in slicing down the range of possibilities. So I don’t find that a concern at all. 0:49:34 SC: I’d like to say that we’re not surprised that life grew up on the biosphere or the atmosphere of the earth, even though there’s a lot more space in between the planets. There’s clearly a selection effect here, and that’s okay. 0:49:44 BG: Yeah, the fact that we’re here and not on Pluto. 0:49:47 SC: Yeah. 0:49:48 BG: That’s understandable by virtue of the conditions here versus those on Pluto. 0:49:53 SC: It’s not even a planet, you know. 0:49:54 BG: I’ve heard that. 0:49:55 SC: Yes. I did it on a whole other podcast. 0:49:56 BG: That will be another good idea. 0:49:58 SC: Already was. Mike Brown was a previous guest. 0:50:00 BG: Oh okay, gotcha. 0:50:00 SC: Okay, but on the other hand, on the slightly more pessimistic side, this idea of eternally inflating cosmos, going on forever, a large, maybe infinite number of local conditions in different parts of it, does lead us to some bizarre things, right? 0:50:17 BG: Yeah. 0:50:17 SC: My favorite bizarre thing is the Boltzmann brain problem. 0:50:20 BG: Yeah right. 0:50:21 SC: Can you explain that problem to us and give us your feelings about it? 0:50:24 BG: Yeah. If you ask yourself, in the far future, if there’re just particles drifting around in the void, could a random fluctuation of the positions of those particles somehow come together to randomly yield structure? And there’s a non-zero chance that that could happen, in enough time, in enough space, these kinds of very unlikely coming togethers of particles are bound to happen, and indeed, the structures could be things that are familiar to us. In fact it could be a human brain, just randomly forming out in the void from particles that are floating around in the darkness. And that human brain could have within it memories, impressed by virtue of the particle configurations. Right now, as I look out in the world, I remember a past when I was a kid growing up and learning quantum mechanics and quantum… 0:51:20 SC: You think you remember a past. 0:51:20 BG: I think I remember, exactly. That’s exactly the point, because right now, all those memories are just configurations of particles, right here, right now. So, if we were to create that configuration of particles, it would have the same memories and sensations and therefore think that it had a history that never existed. So, it’s possible that brains could form out there in the void spontaneously. The problem with that, and the reason why people like to ensure that the theory gets rid of this as a prediction, is that the reason we believe in the equations is because we believe that we encounter data supporting the predictions of those equations. But if we can’t trust any of our memories, we can’t trust our memories of seeing data that supported the very theories that lead us to the possibility that there’s a brain floating in the void. So, we come into a kind of skeptical nightmare where we undercut the very rationality of thought. 0:52:11 BG: So the goal of many theories is to find some way of not only explaining everything that we see in the world around us, explaining that the conditions allow for human life to exist, but also somehow avoiding the possibility that in the distant future, these brains will form in the void. 0:52:28 SC: Right. 0:52:29 BG: And if you can do that, we feel that the theory has a better chance of being correct, because it doesn’t suffer from this logical, skeptical nightmare that can emerge in theories that allow these Boltzmann brains to form. 0:52:43 SC: So, should we be worried about the multi-verse? Is it generically true that in these stories of eternal inflation and the landscape, there are more Boltzmann brains in some sense than ordinary observers? Or do we not know? 0:52:55 BG: Well, it depends again, in some sense, at the level of explanation that you’re shooting for. So, if you’re happy to say that yes, these brains may be out there in other realms, but we’re going to limit our explanation of our observations to the small part of the multiverse, and within that, we can tell a self-consistent story and maybe in our universe within the multiverse, perhaps the universe ends before there’s time for these Boltzmann brains to form. Then, much like the standard model that is one of many theories that explains observations, this would be one of many universes that explains our observations without running into the skeptical nightmare of Boltzmann brains. However, if you’re looking for the full explanation of reality, then that isn’t good enough. 0:53:41 SC: Yeah. 0:53:41 BG: And in the full explanation of reality you do face a quandary, which is, if I say to you, “Where did your brain come from?” The natural answer, if you believe in this Boltzmann brain scenario is, “Well, it just formed right now in the void and all these memories that I have are nonsense, or things that never took place.” And that’s an uncomfortable state of affairs. And you definitely wanna have some way of retorting that criticism of your theory. And people have come up with various ideas trying to make it that the regions in which these Boltzmann brains form somehow have a very extraordinarily low probability. So yes, it’s possible, but compared to the reality that we’re familiar with, it’s just so unlikely, that somehow we can push it to the side. But in a universe that, or multiverse that lasts forever and perhaps goes on forever, it’s sorta hard to make those cuts. 0:54:31 SC: Right. 0:54:32 BG: So this is… It is an issue that needs to be addressed. 0:54:35 SC: Yeah. But isn’t it also possible that, just at the technical level of mathematics, that we’re being a little bit too glib about these 10 to the 500 different compactifications of string theory? Is it possible that maybe they’re just temporary? If they all dissolve away can we hope to maybe recover some more unique prediction for what the universe should look like? 0:54:53 BG: Yeah. In fact, people have written along those lines. I had one paper a couple of years ago which tried to argue that there is an instability in a landscape, that most of these other universes would pretty quickly disintegrate. And if that were the case, then you wouldn’t have to deal with them on an equal footing, because they might be here for a brief moment, but then they’re gone. 0:55:13 SC: Yeah. 0:55:13 BG: There’s some criticism of that paper and it goes on… 0:55:17 SC: No. [laughter] 0:55:17 SC: We’re usually so polite to each other. 0:55:20 BG: That’s right, that’s right, yeah. But it’s just to say that, yes, we may be too quickly accepting the possibility of all these other realms and maybe deeper analysis, which people are now starting to undertake in earnest, might find that, yes, they are allowed by the most superficial analysis of the equations, but a deeper analysis allows us to get around them in some way, either that they’re not really there or they’re unstable, or somehow our realm rises up with such a fantastically large probability that the others can somehow be ignored. So all of these are on the table in order to avoid this problem of a theory that undercuts its own rationality. 0:56:06 SC: Does it seem strange to you that in all of these stories of eternal inflation the past of the universe seems so dramatically different than the future? 0:56:14 BG: It does. And it’s a question I know that has troubled you. And we’ve had conversations about this about this over the years. When you’re dealing within a theory, whose equations seem to make no distinction between what you call forward in time or what you call backward time, and yet you look at a reality that has such a radical difference between what we humans call forward in time and what we humans call backward in time, that mismatch makes you scratch your head. And we have been scratching it and there are solutions on the table. I know that you’ve put forward a number of ideas along those lines. I have too, now and then. Not as many or as effective as yours perhaps. But it is an issue that at the moment we pretty much solve by fiat. 0:56:58 SC: Right. 0:56:58 BG: We say, “At the Big Bang conditions were highly ordered.” We don’t know why. We don’t know how it came to be. But if we posit that, then there’s a natural asymmetry that emerges, not from the equations, but from the conditions, and the conditions of low entropy, high order naturally unfold to a future that has lower order, higher entropy, and that yields us a distinction between forward and backward, but we really put it in by hand. It’s not something that emerges from some fundamental principle. 0:57:26 SC: They’re very recently has been some people, you alluded to this earlier, but now I guess it’s time to dig into it. There’s been a recent set of claims that say, “You know, back in 1998 when we talked about this kitchen sink construction that gave us a positive vacuum energy, maybe we were too hasty.” 0:57:45 BG: Yeah. 0:57:45 SC: “Maybe we were a little bit too glib there.” And we could poke holes in that. And maybe, may be the reason why none of these constructions are perfectly convincing is because, in fact, string theory just doesn’t let you have a positive cosmological constant. Can you tell us about this idea? 0:58:01 BG: Yeah. So when we do analysis in string theory, we generally do it within an approximation scheme. We don’t often have the capacity to analyze the equations with a full precision. So we ignore certain parts of the equations and try to argue that what we ignore doesn’t change our conclusions in any deeper or important way. It may qualitatively affect them somewhat, but we think the general conclusion would still hold. And that was certainly the approach that was taken in KKLT; this famous paper that introduced a way of getting the positive vacuum energy. People now have revisited those approximation schemes and called them into question. Now, as far as I know, the authors of the paper fully stand by their paper. 0:58:49 SC: They have not backed down. 0:58:50 BG: They have not backed down. 0:58:51 SC: Yeah, that is my impression. Yes. 0:58:52 BG: Yeah. Whereas there are others in the community at least calling attention to the possibility that we may have all bought in a little too quickly to the approximation scheme that gave rise to those solutions, and were that to be the case, it would be fantastically interesting. Obviously, it would call into question over a decade, maybe close to two decades, of research, which again, that’s how it goes. 0:59:17 SC: Yeah. 0:59:18 BG: That’s why science is beautiful. It’s self-correcting. There’s no error that will stand the test of time, because people always go back and always think through and always take a sledgehammer to the try to smash results of the past. This is a result that people thought would be impervious to that kind of a sledgehammer attack. And who knows? Maybe it is. But it’s good. It’s healthy, that it’s back on the table and people are examining it as a possible thing that we’ve bought into too quickly. 0:59:44 SC: But what do we say, if on the one hand you say, string theory does not have any solutions, plausibly, with a positive vacuum energy, but the astronomers have observed a positive vacuum energy? 0:59:53 BG: Good. That is a natural question. And it could well be that this positive vacuum energy might not be constant. So, we’ve observed it over a relatively short period of time. So we know that the accelerated expansion began, I don’t know, seven, eight billion years ago… 1:00:09 SC: Yeah. 1:00:10 BG: And perhaps it’s still going on. 1:00:11 SC: By a short period of time, we don’t mean 20 years. We mean a couple of billion years. 1:00:14 BG: A couple of billion years. 1:00:15 SC: Yeah. 1:00:15 BG: But the future will have many more billions of years than the billions that we have so far had access to. In principle, the universe could go on for trillions, and maybe even infinitely long; we don’t know. And in that scenario, in the very far future, perhaps it’s the case that the vacuum energy slowly decays. Maybe it gets smaller and smaller. Maybe in the very far future it will be gone. And those kinds of solutions, with a steadily decaying vacuum energy, are somewhat easier to accommodate within our theories. So it could be the case that what we’re learning is that the particular version of positive vacuum energy that we thought was compatible with observations and with the mathematics of string theory, maybe that’s, naïve version is not the one that the universe makes use of nor which the equations of string theory can accommodate. Maybe it’s is more subtle version, where the energy kind of decays or changes over time. Maybe that’s both compatible with our observations and with a more refined mathematical analysis on string theory. 1:01:20 SC: And are you saying that this is an experimentally testable prediction of string theory? [chuckle] 1:01:23 BG: Yeah. It’s sort of interesting how the critics of string theory say, completely divorced from observation or experimenting, yet here we’ve had a bulk of our conversation driven by an observation that took place in 1998, an observation that won the Nobel Prize; a significant observation. So it kind of tells the lie of string theorists ignoring or having nothing to do with observation or experiment. But I would say it’s too quick to say that this is a prediction of string theory. We need to understand the mathematics better, and we need to go back to the papers of the late 1990s and determine whether or not we agree with that analysis, whether that analysis needs to be changed, and if it does need to be changed, yes, it could be the case that we come out with a prediction that the dark energy, the energy of empty space, should change over time. 1:02:13 SC: Right. 1:02:13 BG: That could be an interesting prediction, if indeed this is the way the analysis unfolds. 1:02:18 SC: And it is a major program of observational cosmology… 1:02:22 BG: Absolutely. 1:02:22 SC: To test whether this is the case. 1:02:22 BG: Absolutely. 1:02:24 SC: We’re spending millions of dollars. 1:02:25 BG: We’re spending a lot of money to do this. And the other thing to bear mind is it could be that those results are inconclusive. 1:02:33 SC: Right. 1:02:33 BG: It could appear that the dark energy is constant at the level of accuracy that we’re able to muster with the technology that we have at our disposal. It could still be changing. 1:02:43 SC: Yeah. 1:02:43 BG: And that’s, again, the way science progresses. So it could be that it requires a 100 or 500 years into the future before we’re able to actually come up with a definitive observational statement about how the dark energy changes in time, but maybe we’ll get lucky. 1:02:58 SC: Yeah. 1:02:58 BG: Maybe the change is sufficiently large that we’ll be able to detect it and that, again, will be one of these inflection points in our analysis of string theory. 1:03:06 SC: Okay. To wrap things up, a couple of more big picture questions here. We’ve turned on the Large Hadron Collider a while ago. We found the Higgs boson. Nobel Prizes were handed out. Everyone’s very happy. 1:03:18 BG: And tears were shed. 1:03:19 SC: Which was a beautiful thing. 1:03:20 BG: Yes, exactly. And tears of joy. Right? 1:03:22 SC: And of relief. 1:03:24 BG: Although tears could also have been shed by the folks who didn’t get the Nobel Prize but were associated, but let’s leave that for another discussion. 1:03:30 SC: Tears all over. 1:03:31 BG: All over. 1:03:31 SC: But also tears because we haven’t found anything else. 1:03:34 BG: Yeah, yeah. 1:03:35 SC: Right? And there certainly is, at least, an association of string theory with this idea of supersymmetry. 1:03:41 BG: Yeah. 1:03:41 SC: Of a hypothetical theory, symmetry of nature that could have been discovered at the LHC. In fact, maybe next year it will be, but it hasn’t been yet. What is your feeling of what we’ve learned from that lack of discovery? 1:03:56 BG: Well, I certainly, frequently when I would speak about these ideas in public settings would point to supersymmetry, as the most likely way that we would have experimental insight into whether string theory was right or wrong. And I think many of us hoped that the Large Hadron Collider would turn up the collection of particles that supersymmetry requires that have never been observed. In fact, when I do a survey of my own papers, just as sort of one data point, since I was a graduate student back in the ’80s, a significant fraction of them rely on the idea of supersymmetry. So, finding it would have been very, very exciting for a lot of people, whose worked for decades, assumed that it was true. Now, the fact that we’ve not seen it is not in any way proof that string theory is wrong, and I don’t say that joyfully. 1:04:47 SC: Right. 1:04:48 BG: If it was proof, going back to how we began, if it was proof the string theory was wrong, I would be thrilled, ’cause then it would be time to let the theory go and to move on to other things. 1:04:58 SC: We want to know the answer. 1:05:00 BG: We want to know the answer. 1:05:00 SC: Whatever it is. 1:05:00 BG: Exactly. And that’s not facetious, that’s really, straight on, how we look at physics as an approach to understanding reality. But the fact that it has not yet been discovered, and the fact that it may not be discovered in the coming year or so at the Large Hadron Collider, could all amount to the statement that we need a more powerful machine to reveal it. That certainly is compatible with our understanding of the mathematics. 1:05:25 SC: Yeah. 1:05:25 BG: So, what I would say is, it is an interesting data point suggesting that the most straightforward version of the theory is perhaps not in agreement with observations, but it doesn’t, in any way, give us full insight into whether the theory is right or wrong. The theory is fully compatible with anything that will emerge from the Large Hadron Collider over the next year or two. 1:05:48 SC: But it is worrisome, even putting aside specific questions about string theory and supersymmetry, that we haven’t seen anything else. This is shocking from a very general particle physics perspective, right? 1:06:00 BG: Yes, absolutely. There is general arguments that our understanding from the equations of the standard model needed something else to emerge at roughly the scale at which the Large Hadron Collider is able to probe the world. Now, that really came, in some sense, from an aesthetic mathematical sensibility. We like our theories to not be highly tuned. We like our theories to be robust against small changes in parameters, and that’s really what led us to this generic notion that there needed to be something else. But the standard model all by itself, without anything else, could indeed explain the observations. I think many of us would find that hard to stomach from a mathematical standpoint, but the universe is not in the business of pleasing our mathematical tastes. So it could be that that just is how the world works, and that there isn’t anything else to be found until much, much, much higher scales, where ideas of quantum gravity will make an appearance. So, I think we need to be very careful in imposing human mathematical sensibility, and human aesthetic sensibility on how the world works. 1:07:15 SC: Yeah. And, as far as we know, there’s no kind of multiverse solution to that problem in the same way that there is for the vacuum energy, right? 1:07:21 BG: That’s correct. Yes. 1:07:22 SC: Yes. Okay. And okay, good. Then the final question is sort of a State of the Union address kind of question. String theory has been around a long time, the modern version of the string theory more or less coincides with your career as a physicist, right? I don’t know what the causality is there, but roughly speaking, the timing works out. 1:07:40 BG: Yeah. 1:07:41 SC: And it’s changed. There have been revolutions in the string theory, and I think the impression I get from talking to string theorists, and I think from the podcast with Clifford, there’s been an enormous amount of recent effort in applying ideas from string theory to this and that completely different physics problems, in nuclear physics, or atomic physics, or fluid dynamics or whatever. What is your feeling about the prospects for string theory’s original hope of being a theory of everything, being a quantum theory of gravity? 1:08:09 BG: Well, I’m still quite optimistic about its utility in answering those specific questions. The unified theory of gravity, quantum mechanics, perhaps explaining the particle properties and so forth. What I think is completely unclear is the timescale over which we’re going to learn whether it is that theory, and if it is that theory, the timescale over which we’ll be able to extract those qualities by virtue of having a sufficiently robust mathematical understanding of a very complex structure. So, my own sense is that there’s a possibility, that in the not too distant future, string theory might migrate out of physics departments into mathematics departments, where it will be pursued as an interesting piece of mathematical architecture that cries out for a deeper understanding and deeper analysis, but there may be a phase during which its connection to physics is relatively modest or non-existent, because it’s hard for a theory of physics to flourish without contact with observation and experiment. Now we saw, again, just to go back to our conversation, there can be unexpected links between observation and theory. The observation of the motion of galaxies wouldn’t at first sight be the place you’d look for some evidence or observations relevant to a theory that’s talking about the smallest things in the world, right? 1:09:37 SC: Right. 1:09:37 BG: That seems to be the biggest gulf imaginable. And yet, through our conversation we’ve gone through the history of how there is a link between the two, which is exciting. So we would need to have our eyes open and not think that string theory is now sequestered into a more mathematical part of the academic world, but that may be where its development sits for some period of time. 1:10:01 SC: Aren’t you cross-appointed in physics and math here at Colombia? 1:10:04 BG: Yes, I hedged my bets on that. 1:10:06 SC: You’re safe. 1:10:06 BG: I’m safe. 1:10:08 SC: But in some sense was it too much to ask back in the ’80s that we were gonna use string theory to get the Theory of Everything, and calculate the mass of electron and things like that? 1:10:19 BG: Well, “too much to ask” is an interesting sociological question, and I was there at the time, and I can tell you that the notion that we were on the verge of explaining it all didn’t come from some PR strategy. It was coming from a genuine excitement about… 1:10:37 SC: People believed in it. 1:10:38 BG: About where we might be. 1:10:38 SC: Yeah. 1:10:39 BG: So I don’t think you can criticize people for being excited about things, even though probably it was somewhat over-exuberant, but it came from a good place. It came from a genuine desire to understand the world, and I think that is something that we should celebrate and respect and recognize that it’s tapping into a human enthusiasm, and the human urge for understanding, and from that perspective it was pure. 1:11:07 SC: Here at the Mindscape Podcast we do not criticize people for being excited about good ideas. 1:11:10 BG: There you go. Good. Glad to hear it. 1:11:11 SC: So, Brian Greene, thanks so much for appearing on the podcast. 1:11:14 BG: My pleasure. [music]