April 20, 2006

Inventors in the Landscape

Bert Schellekens has written a note The Landscape "avant la lettre" on the history of string theory landscape as he has experienced it. Whatever one's opinion of string theory and the landscape in particular, nightmare or brightware, it is pretty safe to say that most of us have had such periods as Schellekens, at some time, perhaps with less grandiose problems. In the golden 1960's, George Zweig must have been very frustrated.

After some leisurely thinking, I accept, for the moment, the landscape may be a logical possibility after all. It would imply a radically new (less attractive, fuzzy) paradigm for fundamental physics. It may even have some support from the arguments of no boundary initial condition theory, as discussed by S. Hawking and T. Hertog. Look also here and here.

I quote parts of Schellekens' paper, first from the introduction:

    "In 2003 L. Susskind published his paper entitled “The Anthropic Landscape of String Theory” [1], which I read with great pleasure. The reason was that, many years before, I had come to the conclusion that everything we knew about String Theory was pointing towards an “anthropic landscape” of vacua. I had advocated this idea consistently during many years, on the basis of far less evidence than we have today. It seemed obvious to me, but the response I got was frustrating."

    "I have considered many times writing a paper about my ideas, but I could not bring myself to write something that seemed so obvious. It would have been a paper with many words an no formulas, and it was not at all clear where to publish it. There were no blogs, no homepages, no “arxives”, and no obvious journal to send it to. And furthermore the hard evidence was not available yet. One valid objection was that we did not know enough about string theory yet to make any claim about the existence of a large number of non-supersymmetric, stable vacua. Today that is still an often-heard objection. My feeling about that was exactly what was written in [1], “if we find one such vacuum we are going to find a huge number of them”. To me that was clearly the message String Theory was sending us already in 1986, but most people preferred to ignore it, although of course everyone agreed that the number of supersymmetric vacua was huge."

    "It is difficult and dangerous to claim with the benefit of hindsight that one arrived at some conclusion at a particular time. After 1986 it took some time to understand that all four-dimensional string vacua that were proliferating quickly had moduli, and that this was an important problem. It took some time to appreciate that they were all related to each other, and could be thought of as ground states of one theory, the Heterotic string. And of course there were five string theories, not just one. The most common attitude was to ignore the others and assume that one day we might know what was wrong with them. This was also my point of view until 1994, but uniqueness of the underlying theory was anyhow not the most crucial part of the argument. Apart from that issue, I was already defending a point of view quite similar to the one expressed in the 1998 speech during my time at CERN, which in any case means before 1992. I had discussions about that with many people and encountered a lot of resistance, and I do not recall anyone wholeheartedly agreeing with me. It is therefore somewhat strange that after 2003 some people started telling me “this is what I have always been saying”."

    "Most people associate the Landscape with an anthropic solution to the cosmological constant problem. For me that was not the crucial issue. Even if we came to the conclusion that the cosmological constant was not anthropically tuned after all, I would still expect an anthropic landscape for the structure and parameters of the standard model. String Theory was the first and so far only theory that made the question about uniqueness of the standard model unavoidable. Most, if not all, other attempts to “derive” the structure of the Standard Model involve a new layer of gauge theories, for example composite models or GUTs. Then on inevitably runs once again into the same problem one tries to solve, namely an essential non-uniqueness. The most promising candidate, SO(10) Grand Unification, requires an unexplained triplication of families and has a large number of parameters, even if one takes this choice of gauge group for granted. The only hope for uniqueness is a theory that itself has a chance of being unique, namely a theory of gravity. Such a theory, String Theory, was explored during the past decades, and it gives a very clear answer: there is no unique ground state, but a landscape of vacua. It is in my opinion the only answer that makes sense, and the fact that this answer came out of String Theory is a sign that we are on the right track. I see this as a fundamental result that may even survive if String Theory turns out to be incorrect, or if String Theory is just the tip of an iceberg."

    "I expect that the String Theory Landscape will acquire an important place in science history. Of course its ultimate fate depends on the correctness of String Theory, and the unexpectedly huge size of the landscape is making it a lot harder to convince ourselves of that. But String Theory won’t be correct without the landscape being correct. And if that is true, it would be one the most fundamental discoveries one can make. It implies that we would know the answer to Einstein’s question if the creator of our Universe had any choice: indeed, we would know all the choices. This insight is probably the most important one we have obtained from string theory so far. It should be remembered that in 1984 this would have been completely unthinkable. Unlike the other main result we hope to get out of String Theory, consistent Quantum Gravity, the landscape emerged against everyone’s initial expectations and wishes. It is a revolution that is unfolding so slowly that few people even recognize it as such. But nevertheless, discovering that our standard model is just one entity in a huge landscape, and hence cannot be completely derived from first principles, is a paradigm shift for our field."

From the original talk, translated into English:

    "This line of thought fits in very well with a series of insights that pointed out our modest place in the cosmos. Our planet is not the center of the solar system, our sun is just one of many stars and not even a very special one, and the same is true for our galaxy. It seems natural to assume that also our universe, including the quarks, leptons and interactions we observe is just one of many possibilities."

    "This way of thinking has important consequences. If indeed our universe, including its laws of physics and the entire Standard Model is just one of many possibilities, this implies that there are limits to what we can compute. The properties of the quarks and leptons, their interactions and the parameters of the Standard Model (or at least part of them) were fixed at the birth of our universe, when a choice was made out of the many possibilities. We will never be able to compute that choice, because it could just as well have been different."

    "I have the impression that many of my colleagues believe or hope that this will ultimately not be the case. They hope to find a kind of mathematical formula that has only one solution. That single solution should then correspond to our four-dimensional world, including all quarks, leptons and the four basic forces. Also the values of the nineteen (or more) parameters, such as the masses of all particles, should then ultimately emerge as the outcome of a mathematical computation."

The final paragraph:

    "The foregoing was a sketch of a possible end of the story. It is the end that given the current state of affairs seems the most desirable to me, but in the end only hard results matter. Nature will probably not care much about my wishes. Despite the word “end” in the title it was not at all my intention to suggest that the end will be reached soon. On the contrary, it will take many decades of work to produce a complete map of String Theory. I am looking forward to an exciting continuation of this adventure."

[1] L. Susskind, “The anthropic landscape of string theory” arXiv:hep-th/0302219.

Finally, remember that some string and other theorists retire sooner, some later ;-)

April 04, 2006

Cosmological Constant and the String Landscape at Solvay 2005

This is a rapporteur's talk at the 23rd Solvay Conference by Joe Polchinski, the article is dated March 31, 2006. (I feel it is the best paper of the year until now.) The author divides theories of the cosmological constant (CC) into two groups: value fixed by theory and value adjustable like in string theory landscape. The central issue in the report is to discuss the extent to which physics is predictable. Polchinski sees three major questions in the CC: why it is not large, not zero, but comparable to the matter density now. He focuses mainly in the first question: "this is hard enough!"

The fixed value theories are discussed comparing the problem to Lamb shift (main topic in the 1947 Shelter Island conference). The author leads the reader through the Lamb shift in the presence of external gravitons discussion to short and long distance modifications to gravity. There is no solution visible in those directions.

In the adjustable scenario, several possibilities are mentioned: unimodular gravity, non-propagating four-form field strengths, scalar potentials with many minima, rolling scalar with nearly flat potential, spacetime wormholes, self-tuning, and explicit tuning (one or more free parameters). Among the mechanisms leading to the observed CC value the following are discussed: the Hartle-Hawking wavefunction favoring the smallest positive value of CC, the de Sitter entropy suggesting that the HH wavefunction has some statistical interpretation in terms of the system exploring all possible states, and the Coleman-de Lucchia amplitude for tunneling from positive to negative CC vanishing for some parameter range keeping the universe in the state of smallest positive energy density. Polchinski considers all these tantalizing in the same way as supersymmetry is as a solution for the CC problem. These mechanism would work in an empty universe. Next, I quote "In the course of trying to find selection mechanisms, one is struck by the fact that, while it is difficult to select for a single vacuum of small cosmological constant, it is extremely easy to identify mechanisms that will populate all possible vacua — either sequentially in time, as branches of the wavefunction of the universe, or as different patches in an enormous spatial volume. Indeed, this last mechanism is difficult to evade, if the many vacua are metastable: inflation and tunneling, two robust physical processes, will inevitably populate them all.

But this is all that is needed! Any observer in such a theory will see a cosmological constant that is unnaturally small; that is, it must be much smaller than the matter and energy densities over an extended period of the history of the universe. The existence of any complex structures requires that there be many ‘cycles’ and many ‘bits’: the lifetime of the universe must be large in units of the fundamental time scale, and there must be many degrees of freedom in interaction. A large negative cosmological constant forces the universe to collapse to too soon; a large positive cosmological constant causes all matter to disperse. This is of course the argument made precise by Weinberg, here in a rather minimal and prior-free form.

Thus we meet the anthropic principle. Of course, the anthropic principle is in some sense a tautology: we must live where we can live. There is no avoiding the fact that anthropic selection must operate. The real question is, is there any scientific reason to expect that some additional selection mechanism is operating?

If there is a selection mechanism, it must be rather special. It must evade the general difficulties outlined above, and it must select a value that is almost exactly the same as that selected by the anthropic principle, differing by one order of magnitude out of 120. Occam’s razor would suggest that two such mechanisms be replaced by one — the unavoidable, tautological, one. Thus, we should seriously consider the possibility that there is no other selection mechanism significantly constraining the cosmological constant. Equally, we should not stop searching for such a further principle, but I think one must admit that the strongest reason for expecting to find it is not a scientific argument but a psychological one: we wish fundamental theory to be as predictive as we have long assumed it would be."

That's correct, next comes a discussion of the string landscape. And a chapter "What is String Theory?" This is very interesting, of course. But the best I can do is to recommend everybody to read Polchinski's talk! Final quote from the end: "Let me close with a quotation from Dirac: One must be prepared to follow up the consequences of theory, and feel that one just has to accept the consequences no matter where they lead. And a paraphrase: One should take seriously all solutions of one’s equations. Of course, his issue was a factor of two, and ours is a factor of 10^500."