Scientific American [SA]: String theory tells us that particles are these tiny loops or squiggles all tangled together. What has string theory done that we should believe any of that?
Raphael Bousso [RB]: String theory offers a framework in which all forces are naturally, completely unified, including gravity. We really don't have anything else that achieves the same kind of unification. If you ask what string theory has done, for example, it describes in principle how the particles that make up gravity interact with each other. And it has explained in certain very special cases the entropy of black holes, which is a big problem in quantum gravity.
SA: In the past few years string theorists have started thinking about cosmology, in particular this dark energy that seems to be making galaxies spread apart faster over time. What's the fascination?RB: We don't really know what this stuff is. There are a lot of different possibilities for types of matter that will act the way that this dark energy seems to be acting on our universe. From a theorist's standpoint they are very different things. An example of that distinction is whether that dark energy is really what we call a cosmological constant, in which case its density is fixed and will never change. Or if it is something that acts for a while like a cosmological constant, accelerating the universe, but eventually gets diluted. That's something that we currently can't distinguish very well with the experimental evidence, but it has an enormous effect on the large-scale structure of the universe and what the world will look like in the far future. It would be very nice to understand what kinds of dark energy are favored from a theoretical perspective. The biggest question is, why is it there at all? And we really have a hard time understanding that because it's so incredibly small yet it isn't zero. That poses a huge challenge for theory to explain.
SA: So far string theorists haven't had much luck tackling dark energy, correct?
RB: There is a tension there. What most people would agree on is that it's very likely that the explanation of the origin of the cosmological constant will come from a quantum theory of gravity. That wouldn't have to be string theory. But string theory is the best, most accurate and most powerful candidate theory that we have. Now the tension comes from the fact that it's been very difficult to find cosmological solutions, in particular solutions with positive dark energy, in string theory. [In general relativity, the cosmological constant could be positive and repulsive or negative and attractive.] While string theory's our best candidate for quantum gravity, we're a little disappointed by the fact that so far we've not managed to model universes with dark energy in string theory.
SA: What makes the problem difficult?RB: There is a problem in universes with a positive cosmological constant. Now this problem doesn't occur for all types of dark energy, but for a certain class of universes that exhibit dark energy you cannot measure the [end] state [of particle interactions], because particles get causally separated. There's no one who can see them all. In that sense you cannot measure the result of any scattering [of particles]. Experiments in high-energy physics are best described by the formalism called the S-matrix, which gives you the probability, for all the different things that you put in, of all the different things that could come out. That formalism comes from the days when we thought that all of the world of physics is particle accelerators, where we're playing "God" [more literally, an observer at the edge of spacetime] sitting on the outside sending some particles in -- say an electron and a positron or something -- crashing them together with great force and looking at what comes out.
This thing that describes the relation between what you shoot in from far away and what comes back out from that interaction region, when the particles are again well separated and detected in your detector, that thing is the S-matrix. Because we were doing physics at a very small scale, that language was a useful language to describe the world. String theory, which historically is rooted in particle physics, likes to predict an S-matrix and not much else. But clearly that language can't be right to describe an experiment in cosmology, where we don't have any control over what "God" sent in. We're just looking through our telescope and seeing some stuff that hits us. So the difference between cosmology and the S-matrix is that in the S-matrix you're outside looking in and in cosmology we're inside looking out.
SA: Is this a problem only for universes with dark energy?
RB: You might have already been very suspicious, dark energy or not, of the idea that an S-matrix could describe experiments in cosmology. What people have sharpened lately is the statement that you simply cannot even define an S-matrix in many cosmological space times, in particular some in which there is dark energy. The reason for that is that to define an S-matrix, you have to be able to look at what comes out of an experiment at arbitrarily large distance scales. You have to let particles get far, far away from each other so that they stop interacting and you can really say, this is what came out and not something else. If the universe accelerates too fast, it's not possible for a single observer to see all the particles that come out. Some of them disappear behind what's called an event horizon. I can't look at them and then bring the information back to me, the spacetime in between me and the particles is accelerating too fast. So that poses a challenge in the sense that we simply don't know what replaces the S-matrix as the correct "observable." We don't know what the right question is that we want our theory to answer in such cosmologies. If it turns out that we can describe dark energy in string theory in some model, then we would expect that string theory is going to tell us, what are the observables, what are the questions we can ask in that model?
SA: Could string theory ever be up to this challenge?
RB: What we should focus on is the question of whether or not string theory is currently developed enough to understand cosmology and dark energy, or whether there are some important bits that we're still missing. If you look at history, what we call string theory today is a vastly richer structure than what we called string theory 10 years ago [when physicists couldn't use it to calculate the entropy of a black hole]. It seems to me there's a real possibility that trying to use string theory as we see it today to explain the cosmological constant problem is like trying to use the 10-years-ago string theory to explain black hole entropy. Maybe we're not quite there yet, maybe we need to make some conceptual progress in the theory before we can do that. So my own interest is in trying to get some hints of what kind of things we might be missing, in which directions do we need to explore.
SA: What kind of hints have you and others seen?
RB: The hints that we are getting are similar to the kind of hints we've been getting from semi-classical [not fully quantum mechanical] physics about black holes. Semi-classical analyses told us that black holes have an entropy, though it didn't tell us where that entropy comes from microscopically. [The entropy of a glass of water comes from the many possible equivalent arrangements of the molecules within.]
In the case of universes with a positive cosmological constant, semi-classical physics, and in particular an idea called the holographic principle [which holds that the maximum entropy of a region of spacetime is proportional to its area, as opposed to its volume], is telling us that those universes have a finite entropy. In other words, you simply cannot put a black hole, which is the densest, most entropic object you can imagine, beyond a certain size into a universe with positive cosmological constant. No experiment that you make in such a universe will ever see more entropy than about the inverse [of the value of the] cosmological constant. As the dark energy goes to zero, that statement goes away.
What we're finding is this pattern where the presence of dark energy -- it has to be a fixed cosmological constant to really make this statement -- seems to correspond to theories with a finite entropy. These [finite-entropy theories] are things that haven't really popped up yet in string theory or, for that matter, anywhere else. And that's the kind of statement that might be a very useful hint as to which direction we should be looking in.
April 7, 2003
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JR Minkel,
Scientific American
© JR Minkel,
Scientific American