THINKING ABOUT THE UNIVERSE ON THE LARGER SCALES
[RAPHAEL BOUSSO:] We can ask ourselves questions at different levels of generality, or profundity, if you will, and I guess as a scientist it's important to strike a balance. We tend to not make much progress if we decide to work on the deepest, most far-reaching questions straight out. It's good to have those as a compass, but it's important to break things up in some way, and the way that I would break things up is to say, "the far-reaching questions are things like how do we unify all the laws of nature, how do you do quantum gravity, how do you understand how gravitation and quantum mechanics fit together, how does that fit in with all the other matter and forces that we know?" That's a really far-reaching and important question.
Another far-reaching question is "what does the world look like on the largest scales?" What does the universe look like on the largest scales? How special is the part of the universe that we see? Are there other possibilities? Those questions are connected with each other, but in order to try to answer them, we have to try to come up with specific models, with specific ways to think about these questions, with ways to break them down into pieces, and of course, most importantly, with ways to relate them to observation and experiment.
One important hint that came along on the theoretical side a long time ago was string theory, which wasn't invented for this sort of deep-sounding questions. It was invented to understand something about the strong force, but then it took on its own life and became this amazing structure that could be explored and which started spitting out these answers to questions that you hadn't even thought of asking yet, such as quantum gravity. It started doing quantum gravity for you.
This is a very controversial issue. There are other approaches to this problem of quantum gravity. I personally find the string theory by far the most well-developed and the most promising, and so I find myself looking for hints about the answers to these kinds of questions that are outlined by using string theory, by exploring the properties of this theory, by asking it what it tells us about these questions.
Another hint that helps us break things up and lower the questions down to accessible levels is, of course, observational: what do we see when we look out the window? The one thing that's really remarkable that we see, and it's remarkable in the way that the question of why the sky is not bright at night is remarkable, is (it sounds stupid, but when you really think about it, it's a profound question, and it needs an explanation: "Why isn't there a star everywhere you look?") A similar kind of question is: "Why is the universe so large?" It's actually extremely remarkable that the universe is so large, from the viewpoint of fundamental physics. A lot of amazing things have to happen for the universe to not be incredibly small, and I can go into that.
One of the things that has to happen is that the energy of empty space has to be very, very small for the universe to be large, and in fact, just by looking out the window and seeing that you can see a few miles out, it's an experiment that already tells you that the energy of empty space is a ridiculously small number, 0.000 and then dozens of zeros and then a 1. Just by looking out the window you learn that.
The funny thing is that when you calculate what the energy of empty space should be using theories you have available, really well-tested stuff that's been tested in accelerators, like particle theory, the standard model, things that we know work, you use that to estimate the energy of empty space, and you can't calculate it exactly on the dot. But you can calculate what the size of different contributions is, and they're absolutely huge. They should be much larger than what you already know it can possibly be, again, not just by factor of 10 or 100, but by a factor of billions, of billions of billions of billions.
This requires an explanation. It's only one of the things that has to go right for the universe to become as large as we see it, but it is one of the most mysterious properties that turned out to be right for the universe to become large, but it needs an explanation.
Funnily enough, because we knew that that number had to be so small, that is the energy of empty space, the weight of empty space, had to be so small, it became the lore within at least a large part of the physics community that it was probably zero for some unknown reason. And one day we'd wake up and discover why it's exactly zero. But instead, one day in '98 we woke up and discovered that it's non-zero. One day we woke up in '98 and we discovered that cosmologists had done some experiments that looked at how fast the universe has been accelerating at different stages of its life, and they discovered that the universe had started to accelerate its expansion, when we used to think that what it would do is explode at the Big Bang, and then kind of get slower and slower in the way that galaxies expand away from each other. Instead, it's like you went off the brakes and stepped on the gas pedal a few billion years ago; the universe is accelerating. That's exactly what a universe does if the energy of empty space is non-zero and positive, and you could look at how fast its acceleration is happening, and deduce the actual value of this number. In the last 13 years a lot of independent observations have come together to corroborate this conclusion.
It's still true that the main thing that we needed to explain is why the cosmological constant, or the energy of empty space, isn't huge. But now we also know that the explanation was definitely not going to be that for some symmetry reason that number is exactly zero. And so we needed an explanation that would tell us why that number is not huge, but also not exactly zero.
The amazing thing is that string theory, which wasn't invented for this purpose, managed to provide such an explanation, and in my mind this is the first serious contact between observation, experiment on the one side, and string theory on the other. It was always interesting to have a consistent theory of quantum gravity, it's very hard to write that down in the first place, but it turned out that string theory has exactly the kind of ingredients that make it possible to explain why the energy of empty space has this bizarre, very small, but non-zero value.
I thought I was going to become a mathematician, and then decided to study physics instead, at the last minute, because I realized that I actually cared about understanding Nature, and not just some abstract, perhaps beautiful, but abstract construct. I went to Cambridge, the one in England, for my PhD. I worked with Stephen Hawking on questions of quantum properties of black holes, and how they might interplay with early universe cosmology. I went on to Stanford for a post-doc.
At Stanford I talked a lot to Andrei Linde and to Lenny Susskind, and we all felt that it was time for string theory to have some sort of say about cosmology, that string theory had not really taught us enough about cosmology, and we started thinking in various, different ways about how string theory might do that.
One idea that was floating around was called the holographic principle. This is an idea that deals with the question of how much information you need to describe a regional of space-time at the most fundamental level, and surprisingly the answer is not infinity. Even more surprisingly, the answer doesn't grow with the volume of the region. As T'Hooft and Susskind had first intuited the answer is related to the area surrounding the region. But the idea didn't really fully work, especially in cosmology. So one of the topics that I worked on was trying to understand whether this idea of the holographic principle is really correct, whether it can be formulated in such a way that it makes sense in all imaginable space-time regions, in cosmology, inside black holes, and not just in some harmless place where gravity is not important. That turned out to be true, and so that was very exciting.
Another topic that I started thinking about was trying to understand the small but non-zero value of the cosmological constant, energy of empty space, or as people like to call it, dark energy. I worked on that subject with Joe Polchinski, at KITP, in Santa Barbara, and we realized that string theory offers a way of understanding this, and I would argue that that is the leading explanation currently of this mysterious problem. From Stanford I went on to a post-doc at Santa Barbara, and then after a number of small stops here and there, including one year at Harvard. In 2004 I joined the faculty at Berkeley, where I am now a professor in the Physics Department.
I don't do experiments in the sense that I would walk into a lab and start connecting wires to something. But it matters tremendously to me that the theory that I work on is supposed to actually explain something about Nature. The problem is that the more highly developed physics becomes, we start asking questions which, for technological reasons, are not in the realm of day-to-day experimental feedback. We can't ask about quantum gravity and expect at the same time to be getting some analog of the spectroscopic data that in the late 19th century fed the quest for quantum mechanics. And I think it is a perfectly reasonable reaction to say, "Well, in that case I think that the subject is too risky to work on." But I think it's also a reasonable reaction to say, "Well, but the question, it's obviously a sensible one." It's clearly important to understand how to reconcile quantum mechanics and general relativity. They're both great theories, but they totally contradict each other, and there are many reasons to believe that by understanding each other we will learn very profound things about how Nature works. Now, it could be that we are not smart enough to do this, in particular without constant feedback from experiments, but we could have been pessimistic at so many junctures in the past and we found a way around.
I don't think that we're going to understand a lot about quantum gravity by building more particle accelerators. We'll understand a lot of other things, even a few things about quantum gravity, but ratherindirectly. But we'll look elsewhere, we'll look at cosmological experiments, we'll use the universe to tell us about very high energies. We'll come up with ideas that we can't even dream about right now. I'm always in awe of the inventiveness of my experimental colleagues, and I don't doubt that they will deliver for us eventually.
It has been said that it's been a golden age for cosmology in the last 15 years or so, and it's true. I was very lucky with timing. When I was a graduate student, the COBE satellite was launched, and started flying and returning data, and that really marked the beginning of an era where cosmology was no longer the sort of subject where there were maybe one or two numbers to measure and people had uncertainties on say how fast the universe expands. They couldn't even agree on how fast galaxies are moving away from each other. And from this, we move to a data-rich age where you have unbelievably detailed information about how matter is distributed in the universe, how fast the universe is, not just expanding right now, but the expansion history, how fast it was expanding at earlier times, and so on. Things were measured that seemed out of reach just a few years earlier, and so indeed it's no longer possible to look down on cosmology as this sort of hand-waving subject where you can say almost anything and never be in conflict with the data. In fact, a lot of theories have gone down the road of being eliminated by data in the past 15 years or so, and several more are probably going to go down that road pretty soon.
An example of a theory that has been ruled out is one of the ideas for how structure originally formed in the universe. Why isn't the universe just some sort of homogenous soup? Why are there clumps of galaxies here, empty spaces there, another galaxy here? How did that come about, and how did the particular way in which these objects are distributed come about? Why are they the size they are, why aren't they larger or smaller, why isn't there maybe just one galaxy which is really huge, and the rest, all we can see, is empty? This clearly needs an explanation.
There were a number of different theories on the market. One of them was inflation. One of the nice things about it was that it was not originally invented for the purpose of explaining this, but it turned out to have something to say about this question. Then there are other theories that were also reasonably well motivated, such as cosmic strings, not the same thing as the string theory strings, but objects that we call topological defects. Basically, these are objects which are string-like, and energy sort of locked into them in a way that it can't get out because of the way that the universe cooled down as it was expanding very early on. And cosmic strings would lead to some sort of structure if you have the right kind of cosmic strings around, but it makes very different detailed predictions about what that structure looks like, what kind of imprints it leaves in the cosmic microwave background that satellites like COBE have nowmeasured so well, and that Planck is currently measuring with incredible precision.
We already know enough about the cosmic microwave background that we can completely rule out the possibility that cosmic strings are responsible for structure formation. It's, of course, possible that there are cosmic strings out there, but they would have to be of a type that has not had any impact on structure formation.
Inflation looks really good. It's not like we have a smoking gun confirmation of it, but it has passed so many tests, it could have been ruled out quite a few times by now, that it I would say is looking really interesting right now.
Inflation comes in many detailed varieties, but it does make a number of rather generic predictions, and unless you work very hard to avoid them, they come with pretty much every inflation model you grab off the shelf. One of those predictions is that the spatial geometry of the universe would be flat. It should be the kind of geometry that you learn about in high school as opposed to the weird kind of geometry that mathematicians study in university, and that has turned out to be the case. To within a percent precision, we now know that the universe is spatially flat. Inflation predicts a particular pattern of perturbations in the sky, and again, to the extent that we have the data, and we have very precise data by now, there was plenty of opportunity to rule out that prediction, but inflation still stands. So there are a number of general predictions that inflation makes which have held up very well, but we're not yet at a point where we can say, it's this particular make and model of inflation that is the right one, and not this other one. We're zooming in. Some types of inflation have been ruled out, large classes of models have been ruled out, but we haven't zoomed in on the one right answer, and that might still take a while, I would expect.
I was saying that string theory has in a way surprised us by being able to solve a problem that other theories, including some that were invented for that purpose alone, had not been able to address, i.e. the problem of why empty space weighs so little, why is there so little dark energy. The way that string theory does this is very similar to the way that we can explain the enormous variety of that we see when we look at the chair, the table, and the sofa in this room. What are these things?
They're basically a few basic ingredients, electrons, quarks, and photons. You've got five different particles, and you put them together, and now you've got lots and lots of these particle. There are very few fundamental ingredients, but you have many copies of them. You have many quarks, you have many electrons, and when you put them together you have a huge number of possibilities of what you can make. It's just like with a big box of Legos, there are lots of different things you can build out of that. With a big box of quarks and electrons you can build a table if you want, or you can build a chair if you want. It's your choice. And strictly speaking, if I take one atom and I move it over here to a slightly different place on this chair, I've built a different object. These objects in technical lingo will be called solutions of a certain theory called the standard model. If I have a block of iron, I move an atom over there, it's a different solution of the standard model.
The fact that there are innumerably many different solutions of the standard model does not of course mean that the standard model of particle physics (this triumph of human thinking) is somehow unbelievably complicated, or that it's a theory of anything, or that it has no predictive power, it just means that it is rich enough to accommodate the rich phenomenology we actually see in nature, while at the same time starting from a very simple setup. There are only certain quarks. There is only one kind of electron. There are only certain ways you can put them together, and you cannot make arbitrary materials with them. There are statistical laws that govern how very large numbers of atoms behave, so even though things look like they get incredibly complicated, actually they start simplifying again when you get to really large numbers.
In string theory we're doing a different kind of building of iron blocks. String theory is a theory that wants to live in ten dimensions, nine spatial dimensions and one time. We live in three spatial dimensions and one time, or at least so it seems to us. And this used to be viewed as a little bit of an embarrassment for string theory, not fatal, because it's actually fairly easy to imagine how some of those spatial dimensions could be curled up into circles so small that they wouldn't be visible even under our best microscopes. But it might have seemed nicer if the theory had just matched up directly with observation.
It matches up with observation very nicely when you start realizing that there are many different ways to curl up the six unwanted dimensions. How do you curl them up? Well, it's not like they just bend themselves into some random shape. They get shaped into a small bunch of circles, whatever shape they want to take, depending on what matter there is around.
Similarly to how the shape of your Lego car depends on how you put the pieces together, the shape of this chair depends on how you put the atoms in it together, the shape of the extra dimensions depends on how you put certain fundamental string theory objects together. Now, string theory actually is even more rigorous about what kind of fundamental ingredients it allows you to play with than the Lego Company or the standard model. It allows you to play with fluxes, D-branes, and strings, and these are objects that we didn't put into the theory, the theory gives them to us and says, "This is what you get to play with." But depending on how it warps strings and other objects called D-branes and fluxes in the extra six dimensions, these six dimensions take on a different shape. In effect, this means that there are many different ways of making a three-dimensional world, just as there are many ways of building a block of iron, or a Lego car, there are many different ways of making a three-plus-one dimensional-seeming world.
Of course, none of these worlds are truly three-plus-one dimensional. If you could build a strong enough accelerator, you could see all these extra dimensions. If you could build an even better accelerator, you might be able to even manipulate them and make a different three-plus-one dimensional world in your lab. But naturally you would expect that this happens at energy scales that are currently and probably for a long time inaccessible to us. But you have to take into account the fact that string theory has this enormous richness in how many different three-plus-one dimensional worlds it can make.
Joe Polchinski and I did an estimate, and we figured that there should be not millions or billions of different ways of making a three-plus-one dimensional world, but ten to the hundreds, maybe ten to the five hundred different ways of doing this. This is interesting for a number of reasons, but the reason that seemed the most important to us is that it implies that string theory can help us understand why the energy of the vacuum is so small. Because, after all, what we call "the vacuum" is simply a particular three-plus-one dimensional world, what that one looks like when it's empty. And what that one looks like when it's empty is basically, it still has all the effects from all this stuff that you have in the extra dimensions, all these choices you have there about what to put.
For every three-plus-one dimensional world, you expect that in particular the energy of the vacuum is going to be different, the amount of dark energy, or cosmological constant is going to be different. And so if you have ten to the five hundred ways of making a three-plus-one dimensional world, and some of them just by accident, the energy of the vacuum is going to be incredibly close to zero.
The other thing that is going to happen is that in about half of these three-plus-one dimensional worlds, the vacuum is going to have positive energy. So even if you don't start out the universe in the right one, where by "right one" I mean the one that later develops beings like us to observe it, you could start it out in a pretty much random state, another way of making a three-dimensional world. What would happen is it would grow very fast, because positive vacuum energy needs acceleration, as we observed today in the sky, it will grow very fast, and then by quantum mechanical processes it would decay, and you would see changes in the way that matter is put into these extra dimensions, and locally you would have different three-plus-one dimensional worlds appearing.
This is not something that I made up, this is actually an effect which predates string theory, which goes back to calculations by Sidney Coleman and others in the ‘70s and ‘80s, and which doesn't rely on any fancy gravity stuff. This is actually fairly pedestrian physics, which is hard to really argue with. What happens is the universe gets very, very large, all these different vacua, three-dimensional worlds that have positive weight, grow unboundedly, and decay locally, and new vacuole appear that try to eat them up, but they don't eat them up fast enough. So the parents grow faster than the children can eat them up, and so you make everything. You fill the universe with these different vacua, these different kinds of regions in which empty space have all sorts of different weights. Then you can ask, "Well, in such a theory, where are the observers going to be?" To just give the most primitive answer to this question, it's actually very useful to remember the story about the holographic principle that I told you a little bit earlier.
If you have a lot of vacuum energy, then even though the universe globally grows and grows and grows, if you sit somewhere and look around, there is a horizon around you. The region that's causally connected, where particles can interact and form structure is inversely related to the amount of vacuumed energy you have. This is why I said earlier that just by looking out the window and seeing that the universe is large, we know that there has to be very little vacuum energy. If there's a lot of vacuum energy, the universe is a tiny little box from the viewpoint of anybody sitting in it. The holographic principle tells you that the amount of information in the tiny little box is proportional to the area of its surface. If the vacuum energy has this sort of typical value that it has in most of the vacua, that surface allows for only a few bits of information. So whatever you think observers look like, they probably are a little bit more complicated than a few bits.
And so you can immediately understand that you don't expect observers to exist in the typical regions. They will exist in places where the vacuum energy happens to be unusually small due to accidental cancellations between different ingredients in these extra dimensions, and where, therefore, there is room for a lot of complexity. And so you have a way of understanding both the existence of regions in the universe somewhere with very small vacuum energy, and also of understanding why we live in those particular rather atypical regions.
What's interesting about this is the idea that maybe the universe is a very large multi-verse with different kinds of vacua in it was actually thrown around independently of string theory for some time, in the context of trying to solve this famous cosmological constant problem. But it's not actually that easy to get it all right. If you just imagine that the vacuum energy got smaller and smaller and smaller as the universe went on, that the vacua are nicely lined up with each one that you decay into having slightly smaller vacuum energy than the previous one, you cannot solve this problem. You can make the vacuum energy small, but you also empty out the universe. You won't have any matter in it.
What was remarkable was that string theory was the first theory that provided a way of solving this problem without leading to a prediction that the universe is empty, which is obviously fatal and immediately rules out that approach. That, to me, was really remarkable because the theory is actually so much more rigid, you don't get to play with the ingredients, and yet it was the one that found a way around this impasse and solved this problem.
I think that the things that haven't hit Oprah yet, and which are up and coming are questions like, well, if the universe is really accelerating its expansion, then we know that it's going to get infinitely large, and that things will happen over and over and over. And just simply because if you have infinitely many tries at something, then every possible outcome is going to happen infinitely many times, no matter how unlikely it is. This is actually something that predates this string theory multiverse that I was talking about. It's a very robust question in the sense that even if you believe string theory is a bunch of crap, you still have to worry about this problem because it's based on just observation. You see that the universe is currently expanding in an accelerated way, and unless there's some kind of conspiracy that's going to make this go away very quickly, it means that you have to address this problem of infinities. But the problem becomes even more important in the context of the string landscape because it's very difficult to make any predictions in the landscape if you don't tame those infinities.
Why? Because you want to say that seeing this thing in your experiment is more likely than that thing, so that if you see the unlikely thing, you can rule out your theory the way we always like to do physics. But if both things happen infinitely many times, then on what basis are you going to say that one is more likely than the other? You need to get rid of these infinities. This is called, at least among cosmologists, the measure problem. It's probably a really bad name for it, but it stuck.
That's where a lot of the action is right now. That's where a lot of the technical work is happening, that's where people are, I think, making progress. I think we're ready for Oprah, almost, and I think that's a question where we're going to come full circle, we're going to learn something about the really deep questions, about what is the universe like on the largest scales, how does quantum gravity work in cosmology? I don't think we can fully solve this measure problem without getting to those questions, but at the same time, the measure problem allows us a very specific way in. It's a very concrete problem. If you have a proposal, you can test it, you can rule it out, or you can keep testing it if it still works, and by looking at what works, by looking at what doesn't conflict with observation, by looking at what makes predictions that seem to be in agreement with what we see, we're actually learning something about the structure of quantum gravity. So I think that it's currently a very fruitful direction. It's a hard problem, because you don't have a lot to go by. It's not like it's an incremental, tiny little step. Conceptually it's a very new and difficult problem. But at the same time it's not that hard to state, and it's remarkably difficult to come up with simple guesses for how to solve it that you can't immediately rule out. And so we're at least in the lucky situation that there's a pretty fast filter. You don't have a lot of proposals out there that have even a chance of working.
The thing that's really amazing, at least to me, is in the beginning we all came from different directions at this problem, we all had our different prejudices. Andrei Linde had some ideas, Alan Guth had some ideas, Alex Vilenkin had some ideas. I thought I was coming in with this radically new idea that we shouldn't think of the universe as existing on this global scale that no one observer can actually see, that it's actually important to think about what can happen in the causally connected region to one observer. What can you do in any experiment that doesn't actually conflict with the laws of physics and require superluminal propagation. We have to ask questions in a way that conform to the laws of physics if we want to get sensible answers.
I thought, okay, I'm going to try this, this is completely different from what these other guys are doing, and it's motivated by the holographic principle that I talked about earlier. I was getting pretty excited because this proposal did not run into immediate catastrophic problems like a lot of other simple proposals did. When you go into the details it spit out answers that were really in much better agreement with the data than what we had had previously from other proposals. And I still thought that I was being original.
But then we discovered, and actually my student I-Shend Yang played a big role in this discovery, that there is a duality, an equivalence of sorts, and a very precise one between this global way of looking at the universe that most cosmologists had favored, and what we thought was our radical new local causal connected way of thinking about it. In a particular way of slicing up the universe in this global picture in a way that's again motivated by a different aspect of the holographic principle, we found that we kept getting answers that looked exactly identical to what we were getting from our causal patch proposal. For a while we thought, okay, this is some sort of approximate, accidental equivalence, and if we asked detailed enough questions we're going to see a difference, and instead what we discovered was a proof of equivalence, that these two things are exactly the same way of calculating probabilities, even though they're based on what mentally seemed like totally different ways of thinking about the universe.
That doesn't mean that we're on the right track. Both of these proposals could be wrong. Just because they're equivalent doesn't mean they're right. But a lot of things have now happened that didn't have to happen, a lot of things have happened that give us some confidence that we're on to something, and at the same time we're learning something about how to think about the universe on the larger scales.