A couple of weeks ago I used the phrase “The Landscape” in the title of a post but I was really referring to my garden, and I went on to mention there that I had deliberately chosen a misleading title for fun. Several people would not have known why this was misleading. I’d like to explain what I had in mind. This is also a continuation of the story I began in another earlier post concerning approaches to cosmology in string theory, the subject of the workshop I’m attending at the Aspen Center for Physics.
(Cautionary note: I won’t be able to include lots of details. This is meant to be a light sketch of some of the activity going on in the field, and some of the questions that have arisen, aimed at non-experts. Of course, I invite useful discussion of all levels in the comments.)
I’m going to assume that you’ll recall the discussion from the earlier post, and the sketch to the right. The curve is a very simplified illustration of a very important point. It is the potential energy curve (I’ll often just say “potential”) for one of the scalar fields in the underlying theory, and it is hoped that almost all the scalar fields produced by string theory (showing up as one of the modes of the string, like all particles do in this approach to string theory) have a potential that is a bit like that. (I’ll give you a geometrical picture of what a scalar field is, in a while, if you’re not sure what that is.) There are two key features. 1) It has a nice well in the middle. This is where the scalar will like to settle, if anywhere near the well. 2) The value of the potential at the well (where the particle will settle) is positive.
This positivity is important. Such positive contributions to the total energy of the system will break the underlying “supersymmetry” of the string theory, and give a postitive value for the cosmological constant. (This potential energy of the system is referred to as the “vacuum energy”, being the “ground state” energy associated to universe thus constructed – this is the same as what a cosmological constant is, classically anyway.) We care about both of these because we know that the world is not supersymmetric (see the earlier post for what supersymmetry is) and because it is currently believed (and this may well turn out to be wrong (!) see Mark’s recent post) that our world does have a positive cosmological constant.
I should emphasize at this point that until recently, string theory studies have been mostly focused on models which were supersymmetric, in which case they have vanishing or negative vacuum energy (cosmological constant). A huge amount of knowledge and computational technques have been developed to study such cases. The possibility (and it is still just a possibility) that our universe might have a positive cosmological constant started a big discussion within the field about whether such vacua (solutions of the theory) could be reliably constructed within string theory, because it is very hard to do. I’ve already mentioned in the previous post that various scenarios (such as those of KKLT) were eventually presented for how such vacua could be constructed. The key ingredients are well-known. They are the “branes” (extended objects) of various sorts, and I also talked about those in that post.
Let’s move on a bit. What people are doing in the field now is exploring these constructions using the string theory technology we have available. The problem is that the computational technology is right at the edge of what we can do, and it is not easy to control these vacua. This means that people are still confused as to the reliability of the solutions that have been found, but – as far as is known – the basic scenarios which generate these sorts of solutions are very plausible indeed. Allied to that fact is the realization (pointed out first in this paper and explored and developed further in this paper) that there are very many vacua spanning rather closely spaced values of the cosmological constant. So there’s a lot of choices, basically, and they look a lot like each other. So you might ask “why choose one over the other?”. We’ll come back to that in a bit.
Within the limitations of the techniques that we have for exploring the contruction of these vacua it is now understood that there are vast numbers of these vacua, and a huge amount of them may have characteristics (such as the value of the cosmological constant) comparable to our world.
So I promised in my most recent post that this would have something to do with mountains. Let’s have a closer look at the picture I took up near the Maroon Lake earlier today:
Lets’s think of height as representing potential energy, just like on our earlier sketch. Let’s think of the valley (the surface of the lake, say) as being at zero energy. Then all higher elevations are positive energy, and you see that there are several interesting features. Staying in the valley for a moment, notice that there are several positions which have the same vanishing energy and are neighbours of each other. In other words, you can move around on the surface of the lake and stay at the same height. These are the supersymmetric vacua that we understand best. The degrees of freedom to move around on the surface of the lake and visit different supersymmetric vacua without changing height (no cost in energy) are those pesky massless scalar fields (“moduli”) that I mentioned in the earlier post. Horizontal position is the value of the field – a number. We need need to break supersymmetry and fix the scalars to specific values since we know that must be so from observation of our world.
So we are somewhere at higher elevation. In fact, we want to find a solution that is like a well in our original sketch: it’s the bottom of an isolated valley somewhere up in the mountains. If you squint at the photo, you can see some of them up there in the craggy shoulders of the Maroon Bells mountains. And there are lots of hidden ones. They all have interesting properties, and some of those properties match those of our world. The new results in the field – exploring the Landscape of possibilities (Ah! Now you see where the name comes from!) suggest that there are vast numbers of these which are all very close in characteristics to our world.
This was disappointing to some poeple. This is because there was a hope that string theory might produce a single vacuum which corresponds to our world, with all properties of our world determined by this single solution. In the setup visualized in this hope, all we had to do was study hard and find this solution and thereby understand once and for all why our world is the way it is: The world would be string theoretic, as would follow from the fact that it had popped out as the unique solution to string theory. This was the old “Theory of Everything” story, which I’ve already pointed out on this blog as being frightfully naive, in my opinion (see beginning of next paragraph for why I think so). (It must be said that when Green and Schwarz pointed out the results of certain computational miracles in the early days of string theory showing that these theories -potentially containing both quantum gravity and particle physics ! – were consistent, the enthusiasm which ensued about the prospects of the theory is quite understandable. But we’re a bit more sober these days, and rightly so.)
Instead, a new movement began. The idea began to arise that maybe not everything about our universe is fundamentally computable in string theory. As I’ve said before on this blog, in view of the history of the way science has always worked (new theories take over and extend the range of applicabiltiy the old, again and again) this is not an entirely unreasonable characteristic of any physical theory. I would go as far as to say that it is perfectly fine for us to accept that this might true about string theory while still remaining extremely enthusiastic about it, given its remarkable properties.
But it did not stop there. Still hanging on to the idea that string theory is some sort of “final theory”, some people – most famously, Lenny Susskind at Stanford (who I’ve just noticed has a Wikipedia entry!) – began to combine that idea of lots of solutions (with apparently no dynamical way (physics reason) to choose just one) with the idea that our world would have to be explained by “Anthropic” reasoning (an idea which had been brought into particle physics discussions earlier by Steven Weinberg). Something along the lines of “we live in this particular solution of string theory because it has characteristics conducive to us living in this particular solution of string theory”. Many people just don’t like this approach, and say that it is no longer science. We can talk about that at length, but that’s not really the point of this post. All you need to know is that this is the origin of the Big Discussion that people will tell you is going on in string theory right now.
Sure, it’s a big discussion, but it is entirely overstated that this is the one thing occupying the minds of all string theorists, and that the fate of the entire field depends upon the outcome of this argument. (This is the impression given in publications such as the New York Times, who seldom tell you what’s going on in a field unless there’s a good controversy to present, and also on blogs such as this one.)
So why, you ask, are all these people to whom I alluded not worrying about the issue? Are they just: 1) Out of the loop? 2) Careless? 3) Begging to get their grants cut?
The answer is simple. The discussion is an interesting one to have, and it is good that there are people having it, but frankly it is far too premature to conclude much about anything about these issues. There are several things that we simply do not know about the theory, and several things over which we have little computational control. First, we do not really have a proper non-perturbative formulation of the theory. What I mean by this is that we already know that string theory is not a theory of strings. It is only describable in terms of strings when a certain parameter is rather small. This parameter (called the “string coupling” in this regime) measures how likely strings are to split into other strings or join together to make other strings, processes which can change the physics. We can compute relably when this parameter is small. In 1995 or so it was realised that when this parameter is large, we lose the nice description in terms of strings and other things happen. One of the things that can happen is that extended objects -the branes- become important, and we have not yet developed the techniques for handling all that these branes can do. And that may just be the begining of the story of the interesting physics that can happen. It is this interesting physics that has allowed us to construct these scenarios for constructing the very vacua that have begun this exciting discussion. We must not forget that we have not finished the job that we began – to understand the theory.
One key thing to note about the landscape picture is the lack of control we still have for studying the whole picture. As Steve Giddings pointed out in a seminar yesterday (here at the workshop) that he was giving on some new results in the subject, it is as though the mountains are partly shrouded in thick clouds, and so we cannot see the whole picture. (Greg Moore, in the audience, pointed out that we don’t know if we can understand how to move from one valley to another without going into the clouds either, which, to my mind, further illustrates our current limitations.) Worse than that, there is still the possibility that knowing the entire landscape using current approaches may be of limited use if there is an as yet undiscovered dynamical mechanism which favours one region of the landscape over another. What I’m saying is that by all means we should explore the Landscape and learn as much as we can, but we should remember the limitations of the techniques that we have, and so not use what we find to conclude things too hastily.
Lots of things can happen to make the Big Discussion/Argument all yesterday’s news, and most of them I’m sure I don’t know – nobody knows: that’s why it’s called “Research”. As I said, it is still possible that there is a dynamical vacuum selection mechanism out there which might reduce the huge number of apparent solutions down to a few, or even one. More conservatively, it might turn out that we learn new physics for exploring the solutions (better control of D-branes and other “R-R backgrounds”, as the terminology goes) and rule out several of them, reducing the number to something considerably less dramatic, which might help put the Anthropic philosophy to rest. This would need to be accompanied by a giving up of that need to elevate the theory to being a “Final theory”. If one just thinks of it as just a physical theory, then there is no pressure to make it explain everything.
I suspect that when we understand the theory better we will see that there are good reasons not to expect that the it need be the Final Theory. It is has anything to do with nature, it’s probably just the Next Theory, albeit a very elegant and powerful one which will change the way we think about spacetime and the entire universe. This will still be something to be extremely excited about, even though it won’t be the end of the story.