DOES THE UNIVERSE LOOK THE WAY IT DOES?
[SEAN CARROLL:] Why does the universe looks the way it does?
This seems on the one hand a very obvious question. On the other hand, it is an interestingly strange question, because we have no basis for comparison. The universe is not something that belongs to a set of many universes. We haven't seen different kinds of universes so we can say, oh, this is an unusual universe, or this is a very typical universe. Nevertheless, we do have ideas about what we think the universe should look like if it were "natural", as we say in physics. Over and over again it doesn't look natural. We think this is a clue to something going on that we don't understand.
One very classic example that people care a lot about these days is the acceleration of the universe and dark energy. In 1998 astronomers looked out at supernovae that were very distant objects in the universe and they were trying to figure out how much stuff there was in the universe, because if you have more and more stuff — if you have more matter and energy — the universe would be expanding, but ever more slowly as the stuff pulled together. What they found by looking at these distant bright objects of type 1A supernovae was that, not only is the universe expanding, but it's accelerating. It's moving apart faster and faster. Our best explanation for this is something called dark energy, the idea that in every cubic centimeter of space, every little region of space, if you empty it out so there are no atoms, no dark matter, no radiation, no visible matter, there is still energy there. There is energy inherent in empty spaces. We can measure how much energy you need in empty space to fit this data, this fact that the universe is accelerating. This vacuum energy pushes on the universe. It provides an impulse. It keeps the universe accelerating. We get an answer and the answer is 10-8 ergs per cubic centimeter, if that is very meaningful.
But then we can also estimate how big it should be. We can say, what should the vacuum energy have been? We can do a back-of-the-envelope calculation, just using what we know about quantum field theory, the fact that there are virtual partials popping in and out of existence. We can say, there should be a certain amount of vacuum energy. The answer is, there should be 10112 ergs per cubic centimeter. In other words, 10120 times as much is the theoretical prediction compared to the observational reality. That is an example where we say the universe isn't natural. There is a parameter of the universe, there is a fact about the universe in which we live — how much energy there is in empty space — which doesn't match what you would expect, what you would naively guess.
This is something a lot of attention has been paid to in the last 10 years or even before that, trying to understand the apparently finely tuned nature of the laws of physics. People talk about the anthropic principle and whether or not you could explain this by saying that if the vacuum energy were bigger, we wouldn't be here to talk about it. Maybe there is a selection effect that says you can only live in a universe with finely tuned parameters like this. But there is another kind of fine tuning, another kind of unnaturalness, which is the state of the universe, the particular configuration we find the universe in — both now and at earlier times. That is where we get into entropy and the arrow of time.
This is actually the question that I am most
interested in right now. It's a fact about the universe in which we observe that there are all sorts of configurations in which the particles in the universe could be. We have a pretty quantitative understanding of ways you could rearrange the ingredients of the universe to make it look different. According to what we were taught in the 19th century about statistical mechanics by Boltzmann and Maxwell and Gibbs and giants like that, what you would expect in a natural configuration is for something to be high entropy, for something to be very, very disordered. Entropy is telling us the number of ways you could rearrange the constituents of something so that it looks the same. In air filling the room, there are a lot of ways you could rearrange the air so that you wouldn't notice. If all the air in the room were squeezed into one tiny corner, there are only a few ways you could rearrange it. If air is squeezed into a corner, it's low entropy. If it fills the room, it's high entropy. It's very natural that physical systems go from low entropy, if they are low entropy, to being high entropy. There are just a lot more ways to be high entropy.
If you didn't know any better, if you asked what the universe should be like, what configuration it should be in, you would say it should be in a high entropy configuration. There are a lot more ways to be high entropy — there are a lot more ways to be disorderly and chaotic than there are to be orderly and uniform and well arranged. However, the real world is quite orderly. The entropy is much, much lower than it could be. The reason for this is that the early universe, near the Big Bang, 14 billion years ago, had incredibly low entropy compared to what is could have been. This is an absolute mystery in cosmology. This is something that modern cosmologists do not know the answer to, why our observable universe started out in a state of such pristine regularity and order — such low entropy. We know that if it does, it makes sense. We can tell a story that starts in the low entropy early universe, trace it through the present day and into the future. It's not going to go back to being low entropy. It's going to be compliant entropy. It's going to stay there forever. Our best model of the universe right now is one that began 14 billion years ago in a state of low entropy but will go on forever into the future in a state of high entropy.
Why do we find ourselves so close to the aftermath of this very strange event, this Big Bang, that has such low entropy? The answer is, we just don't know. The anthropic principle is just not enough to explain this. We really need to think deeply about what could have happened both at the Big Bang and even before the Big Bang. My favorite guess at the answer is that the reason why the universe started out at such a low entropy is the same reason that an egg starts out at low entropy. The classic example of entropy is that you can take an egg and make an omelette. You cannot take an omlette and turn it into an egg. That is because the entropy increases when you mix up the egg to make it into an omelette. Why did the egg start with such a low entropy in the first place? The answer is that it is not alone in the universe. The universe consists of more than just an egg. The egg came from a chicken. It was created by something that had a very low entropy that was part of a bigger system. The point is that our universe is part of a bigger system. Then you can start to try to understand why it had such a low entropy to begin with. I actually think that the fact that we can observe the early universe having such a low entropy is the best evidence we currently have that we live in a multiverse, that the universe we observe is not all that there is, that we are actually embedded in some much larger structure.
We are in a very unusual situation in the history of science where physics has become slightly a victim of its own success. We have theories that fit the data, which is a terrible thing to have when you are a theoretical physicist. You want to be the one who invents those theories, but you don't want to live in a world where those theories have already been invented because then it becomes harder to improve upon them when t
hey just fit the data. What you want are anomalies given to us by the data that we don't know how to explain.
Right now, we have two incredibly successful models — in fact three if you want to count gravity.We have for gravity Einstein's Theory of General Relativity, which we have had since 1915. It provides a wonderful explanation of how gravity works from the solar system to the very, very early universe — one second after the Big Bang. In particle physics, we have the standard model of particle physics based on quantum field theory, and it predicts a certain set of particles. It was assembled over the course of the '60s and '70s, and then through the '80s and the '90s all we did was confirm that it was right. We got more and more evidence that it fit all of the data. The standard model is absolutely consistent with the observations that we had. Finally, in cosmology we have the standard Big Bang model — the idea that we start in a hot dense state near the Big Bang. We expand and cool over the course of 14 billion years. We have a theory for the initial conditions, where there were slight deviations in density from place to place and these slight deviations grow into galaxy and stars and clusters of galaxies.
The three ingredients — the standard model of particle physics, general relatively for gravity, and the standard model of Big Bang cosmology — together fit essentially all the data we have. It makes it very difficult to move beyond that, but it's crucial that we move beyond that because these ideas are mutually inconsistent with each other. We know they can't be the final answer. We have these large outstanding questions. How do you reconcile quantum field theory and quantum mechanics more generally, which is the basis of the standard model, with general relativity, which is the way that we describe gravity? These two theories are just speaking completely different languages and that makes it very difficult to know how to marry them together. In cosmology, we have the Big Bang, which is a source of complete mystery. How did the universe begin? Why were the initial conditions like they were? That is something that we need to figure out. We also have hints of things that don't quite fit into the model. We have dark matter, which cannot be accommodated in the standard model of particle physics, and we have dark energy making the universe accelerate, which is not something that we can do. We can basically put a fudge factor into the equations that fit the data, but again we don't have an understanding of why it is like that, where that comes from.
What we want to do is move beyond these models that fit the data and are phenomenological and basically about fitting the data and move to a deeper understanding. What are the fundamental ingredients out of which gravity and particle physics arise? What are the things that could have happened at the Big Bang? There are a bunch of ideas out there on the market.
For fundamental physics, we have string theory as the dominant paradigm. We don't know that string theory is right. It could be wrong, but for many years now people have been working on string theory, suggesting that we replace the idea of tiny little particles making p the universe by tiny little loops of string. That single idea taken to its logical conclusion predicts a whole bunch of wonderful things, which unfortunately we can't observe. This is just a problem with our ability to do experiments compared to the regime in which string theory might become important. We can't make a string by itself. We can't observe the stringiness of ordinary particles because the energies are just too high. In string theory, you predict that there should be extra dimensions of space. There should not only be the three dimensions of space that we know and love — up, down, forward, backward — but there should be extra dimensions, and those dimensions are somehow invisible. They could all be curled up in really tiny balls and we just can't see them. In fact, we will never see them plausibly, depending on how small they are. Or some of them could be big, and we are stuck on some subset. We can't get to the extra dimensions, and this is the idea that we live on a brane. One of the questions that string theory puts front and center is, if the theory itself — string theory — likes to predict that there are extra dimensions, then where are they? Not only where are they, but why are they not visible? What happened in the universe to make these dimensions invisible? There are a bunch of ideas.
I recently wrote a paper with Lisa Randall and Matt Johnson about how we could have started in a universe that had more dimensions, and then undergone a transition to a big space where some of the dimensions were curled up. This is a provocative idea that also feeds into cosmology. The point is that you can't just sit down and try to reconcile gravity — the laws of general relativity — with quantum mechanics, without also talking about cosmology and why the universe started in the state that it was in. The way we have to go is to look at what happened before the Big Bang. Right now, the best model that we have for what happened at what we now call the Big Bang, which is the favorite one among cosmologists, is inflation. The idea is that there was a temporary period of super fast acceleration that took a tiny little patch of the universe and smoothed it out, filled it with energy, and then that energy heated up into ordinary particles and dark matter, and that is what we see as the Big Bang today.
But inflation has a lot of questions that it doesn't answer. The most obvious question is, why did inflation ever start? You say, well, there is a tiny little patch. It was dominated by some form of energy. How unlikely can that be? Roger Penrose and other people have emphasized that it is really, really unlikely that can be. Inflation does not provide a natural explanation for why the early universe looks like it does unless you can give me an answer for why inflation ever started in the first place. That is not a question we know the answer to right now. That is why we need to go back before inflation into before the Big Bang, into a different part of the universe to understand why inflation happened versus something else. There you get into branes and the cyclic universe.
I really don't like any of the models that are on the market right now. We really need to think harder about what the universe should look like. If we didn't have some prejudice for what the universe did actually look like from doing experiments, we should try to understand what we would expect just from first principles as to what should the universe look like, and then see how that comes close or comes far away from looking like the actual universe. It's only when we take seriously what our theories would like the universe to look like and then try to match them with the universe that we see that we can take advantage of these clues that the experiments are giving us to try to reconcile the ideas of quantum mechanics, gravity, string theory and cosmology.
One of the interesting things about the string theory situation, where we are victims of our own success, where we have models that fit the data very well but we are trying to move beyond them, is that the criteria for success has changed a little bit. It's not that one theory or another makes a prediction that you can go out and test tomorrow. We all want to test our ideas eventually, but it becomes a more long-term goal when it's hard to find data that doesn't already agree with the existing theories. We know that the existing theories aren't right and we need to move beyond them.
Quantum mechanics and general relativity are incompatible, but nature is not incompatible with itself. Nature figures out some way to reconcile these ideas. String theory is the obvious case of somewhere where it has been heavily investigated, starting in the '60s and '70s and taking off to become very popular in the '80s. Here we are in almost 2010 and it's still going strong without having made any connection to experiments. You might want to say at some point, "show me the money". What have you actually learned from doing this? String theorists have learned a tremendous amount about string theory, and the question remains, have we learned anything about nature? That is still an open question.
One of the reasons why string theory is so popular among people who have thought about it very carefully is that it really does lead to new things. It really is fruitful. It's not that you have make some guess like, oh, maybe space time is discrete or maybe the universe is made of little molecules or something like that, and then you say, okay, what do you get from that? By making this guess that instead of particles there are little strings, you are led to thinking if I put that into the framework of quantum mechanics I get 10 dimensions. Then, oh, it also needs to be supersymmetric. There are different kinds of particles that we actually observe in nature and if we try to compactify those extra dimensions and hide them, we begin to get things that look like the standard model. We are learning things that make us think that we are on the right track.
In the 1990s there was a second superstring revolution that really convinced a lot of the skeptics that we were on the right track. There are still plenty of other skeptics who remain unconvinced. One of the things we learned is that different versions of string theory all come from the same underlying theory. Instead of there being many, many different versions of string theory, there is probably only one correct underlying theory that shows up in different ways. What you might have thought of as different versions of the universe, different versions of the laws of physics, are really more like different phases of matter. For water, we have liquid water, we have ice, we have water vapor. Depending on the conditions that the water is in, it will manifest itself in different ways and it will have different densities, different speed of sound, things like that. String theory says that is what space time can be like. Spacetime can find itself in different phases, like liquid water or frozen ice. In those different phases the local laws of physics — the behavior around you — can look completely different. It can look dramatically different.
The most famous example was discovered by Juan Maldacena, a young string theorist, who showed that you could have a theory in one version of which spacetime looked like gravity in five dimensions, and in another version of which it looked like a four dimensional theory without any gravity. There are different numbers of dimensions of space. In one version of the theory there is gravity and in another there is no gravity, but they are really the same theory under it all. To say that string theory of gravity is already not quite the whole story. It's a theory of, some versions look like gravity, some versions you don't have any gravity.
The reason why that is so crucial is that there are a lot of philosophical problems that arise when you try to quantize gravity that don't arise when you try to talk about ordinary theories of particle physics without gravity. For example, the nature of time. Does the universe have a beginning? Do space and time emerge, or are they there from the start? There are very good questions to which a priori we don't know the answer, but string theory has now given us a concrete explicit playground, a toy example, where in principle all the answers are derivable. In practice, it might require a lot of effort to get there, but you can translate any question you have into a question ordinary field theory without gravity. There is no beginning to time. Time and space are there, just as they are in ordinary particle physics.
We have learned a lot from string theory about what quantum gravity can be like. Whether or not it actually is, quantum gravity shows up in the real world, is still a little bit up for grabs. One of the problems is it's easy to say you have different phases and that is interesting. The problem is that there are far too many phases. It's not like you have 10 or 12 different possibilities and you need to match the right one onto the universe. It's like we have 101,000 different possibilities, or even maybe an infinite number of possibilities. Then you say, well, anything goes. You run into problems with falsifiability. How do you show that a theory is not right if you can get anything from it? My answer to that is we just don't know yet. But that does not imply that we will never know.
The other thing is that we predict in string theory that there is a multiverse, that not only can you have different conditions in different places in the universe, but you will. If you combine ideas from string theory with ideas from inflation, you imagine that this universe that we observe ourselves to be in is only a tiny little part of a much, much larger structure where things are very different. People say, can you even talk about that and still call yourself a scientist? You talk about all this stuff we can never observe. The thing to keep in mind is that the multiverse is not a theory. The multiverse is a prediction of a theory. This theory that involves both string theory and inflation predicts that there should be regions outside what we can observe where conditions are very different. That is a crucially important difference because we can imagine testing the theory in other ways even if we can't directly test the idea of the multiverse. The idea of the multiverse might change our expectations for why a certain thing that we observe within our universe is a problem or not. It might say this issue about the small vacuum energy that we have isn't a problem because we are just in one region of the universe that is not representative for one reason or another.
Basically, the short version of this long story is that we are on a long term project here. We have very good ideas within string theory for reconciling quantum mechanics and gravity. We don't know if it's the right idea, but we are making progress. The fact that we don't yet know the answer, we can yet make a firm falsifiable prediction for the Large Hadron Collider or for gravitational wave observatories or for cosmology, is not in any way evidence that string theory is not on the right track. We have to both push forward with the experiments, get our hands dirty, learn more about cosmology, dark matter and dark energy, and also push forward with the theories. Develop them to a point where we really can match them up to some experiment that we haven't yet done.
We need some great ideas to be pushing forward from the condition that we are in right now into the future, and my personal expertise is on the theoretical side of things. It is very often the case that the actual progress comes from the experimental side of things — and not just the experimental side of things, but from experiments you hadn't anticipated were going to surprise you. There are these wonderful experiments people are doing, not only the big experiments with LIGO, detecting gravitational waves, and the LHC looking for new particles, but also smaller, table-top experiments, looking for small deviations from Newton's Law of Gravity, looking for new forces of nature that are very weak or new particles that are very hard to detect. I need to say that it would be very likely that one of these experiments in some unanticipated way jolts us out of our dogmatic slumber and give us some new ideas.
I have an opinion which is slightly heterodox, about the standard ideas in cosmology. The inflationary universe scenario, that Alan Guth really pioneered, people like Andre Linde and Paul Steinhardt really pushed very hard. This is a wonderful idea, which I suspect is right. I suspect that some part of the history of the universe is correctly explained by the idea of inflation, the idea that we start in this little tiny region that expanded and accelerated at this super-fast rate. However, I think that the way most people, including the people who invented the idea, think about inflation is wrong. They are too sanguine about the idea that inflation gets rid of all the problems that the early universe might have had. There is this feeling that inflation is like confession — that is wipes away all prior sins. I don't think that is right. We haven't explained what needs to be explained until we take seriously the question of why inflation ever started in the first place. It's actually a mistake and something wrong on the part of many of the people who buy into inflation that inflation doesn't need to answer that question because once it starts it answers all the questions that you have.
When I was in graduate school happily reading all these different papers and learning different things, some of the papers I read were by Roger Penrose, who was a skeptic about the prevailing conventional wisdom concerning the inflationary universe scenario. Penrose kept saying over and over again in very clear terms that inflation doesn't answer the question we want answered because it doesn't explain why the early universe had a low entropy. It says why the universe evolved in the way it did by positing that the universe started in an even lower entropy state than was conventionally assumed. It's true that if you make that assumption, everything else follows, but there is no reason, Penrose said, to make that assumption. I read those papers and I knew that there was something smart being said there, but I thought that Penrose had missed the point and so I basically dismissed him.
Then I read papers by Huw Price, who is a philosopher in Australia and who made basically the same point. He said that cosmologists are completely fooling themselves about the entropy of the universe. They are letting their models assume that the early universe had a low entropy, the late universe has a very high entropy. But there is no such asymmetry built into the laws of physics. The laws of physics at a deep level treat the past and the future the same. But the universe doesn't treat the past and the future the same. One way of thinking about it is, if you were out in space floating around, there would be no preferred notion of up or down, left or right. There is no preferred direction in space. Here on earth, there is a preferred notion of up or down because there is the earth beneath us. There is this dramatic physical object that creates a directionality to space, up versus down. Likewise, if you were in a completely empty universe, there would be no notion of past and future. There would be no difference between one direction of time or the other.
The reason we find a direction in time here in this room or in the kitchen when you scramble an egg or mix milk into coffee is not because we live in the physical vicinity of some important object, but because we live in the aftermath of some influential event, and that event is the Big Bang. The Big Bang set all of the clocks in the world. When we go down to how we evolve, why we are born and then die, and never in the opposite order, why we remember what happened yesterday and we don't remember what is going to happen tomorrow, all of these manifestations of the difference between the past and the future are all coming from the same source. That source is the low entropy of the Big Bang.
This is something that was touched on way back in the 19th century when the giants of thermodynamics like Boltzmann and Maxwell were trying to figure out how entropy works and how thermodynamics works. Boltzmann came up with a great definition of entropy and he was able to show that if the entropy is low it will go up. That is good because that is the second law of thermodynamics. But he was stuck on this question of why was the entropy low to begin with. He came up with all these ideas which are very reminiscent of the same kinds of ideas that cosmologists are talking about today. Boltzmann invented the idea of a multiverse, the anthropic principle where things were different in some regions of the universe than in others and that we lived in an unrepresentative part of it. But he never really quite settled on what he thought was the right answer, which makes perfect sense because still today we don't know what the right answer is. We know very well how to explain that I remember yesterday and not tomorrow, but only if we assume that we start the universe in a low entropy state.
I like to say that observational cosmology is the cheapest possible science to go into. Every time you put milk into your coffee and watch it mix and realize that you can't unmix that milk from your coffee, you are learning something profound about the Big Bang, about conditions in the very, very early universe. This is just a giant clue that the real universe has given to us to how the fundamental laws of physics work. We don't yet know how to put that clue to work. We don't know the answer to the who done it, who is the guilty party, why the universe is like that. But taking this question seriously is a huge step forward in trying to understand how the universe that we see around us directly fits into a much bigger picture.