Sunday, July 24, 2005

Strings as Microsoft

This is my (first) reply to the discussion over at under Sean's article called "Two cheers for string theory", especially the article itself.

There are many points in the text that I agree with and the author seems to have a remarkably sane idea what string theory is all about even though he is not a practitioner. There are other, more technical points, where corrections are necessary. Sean has not really considered the implications of the last 10 or 20 years in string theory but most of the non-professional readers of their blog misunderstand these implications as well, so it does not seem to matter and the readers are satisfied.

No doubt, it would be more encouraging if more than string theory as of 1985 presented by a non-string-theorist was needed for a full satisfaction. But one should not forget that there are many people, often outside the blogosphere, who care about the difference between string theory as of 1985 and 2005.

Let me start with some comparisons mentioned in the discussion.

String theory is Microsoft of quantum gravity. Unlike Robert, I have no serious problems with this comparison. Microsoft is more about success and competition while string theory is about the lasting intellectual value. But the degree to which string theory dominates the research in quantum gravity is analogous to the extent to which Microsoft dominates the world of operating systems. On the other hand, our loop quantum gravity colleagues should definitely feel flattered if someone compared them to the Apple or Linux of quantum gravity.

The reason is that the Apple computers more or less work, and sometimes the same thing holds even for the Linux computers.

Microsoft is gonna release a new operating system in 2006; a successor of Windows XP. It used to be called Longhorn, but on Friday they announced that it will be called Microsoft Windows Vista. I am looking forward to see this system, and I hope that string theory will offer something comparably striking by 2006. Meanwhile, many of us will continue to admire Microsoft and Bill Gates whose acts have been critical for the PC industry. When I learned that the BASIC for Commodore 64 - a home computer we played with as kids - was made by Bill Gates, my admiration doubled. And it did not disappear even when Bill Gates praised the brand new type of capitalism in China (formerly known as communism) and helped the Chinese bastards to ban MSN blogs containing the word "democracy".

Don't get me wrong: Linus Torvalds and Steve Jobs are also amazing guys! It would be harder to say the same thing about all the activists whose goal is to eliminate commercial software and force everyone to use their favorite semi-functional open source software.

String theory vs. QFT and Standard Model

Another comparison Sean offered was between string theory and quantum field theory. His goal was to suggest that string theory was not a particular model - such as the Standard Model - but a whole framework - such as quantum field theory. Definitely, string theory provides us with a new set of mathematical tools and concepts to study spacetime physics that goes beyond quantum field theory.

But in a specific technical sense, string theory is more analogous to the Standard Model, indeed. It's because string theory is one theory. While different quantum field theories are physically disconnected - although they can be mathematically similar - different backgrounds in string theory are solutions of the same underlying equations. We should imagine the Hilbert spaces of backgrounds in string theory to be unified into one Hilbert space. Moreover, the conditions of one background can usually be locally reconstructed in another background.

The haystack (or landscape) of these classical solutions of string theory is much more complex than in the case of the Standard Model, but the analogy holds. In fact, string theory is an even more specific model than the Standard Model; the Standard Model (with neutrino masses) has about 30 free parameters. String theory, on the other hand, is a completely unique theory and it has no free, continuous, adjustable, dimensionless parameters.

In some sense, string theory may look as a framework and a loose network of new ideas. But in a very technical sense, string theory is a completely rigid and unique conglomerate of these new ideas.

Sean's argument that string theory is a framework, not a specific model, is being used to justify the opinion that string theory does not have to predict particular numbers that can't be extracted from the Standard Model and GR. From a general intellectual or mathematical viewpoint, I agree with this thesis. String theory is continuously generating a lot of new mathematical ideas and new physical intuition that helps us to solve mathematical problems and compute things in new ways. It is also an amazingly consistent mathematical structure that is deeply rooted in physical reasoning. This itself justifies the research.

The value of a unification of GR and QM

From a physics point of view, I disagree with Sean's comment that string theory is justified as a physical theory even if it makes no new predictions. He emphasizes that string theory should be sold as the leading candidate to unify GR and QM. That's fine. But the only physical reason why we need to unify GR and QM is the fact that our world apparently respects both the postulates of QM much like it contains phenomena of GR. In other words, we need to unify them because we need to make predictions for our real world where electroweak, strong, and gravitational forces operate together and happily.

A consistent reconciliation of QM and GR in d=4 or higher turns out to be an interestingly constrained and difficult mathematical task whose solution is most likely unique up to dualities and equivalences. The solution is called string/M-theory. But we would never know that such a reconciliation is an interesting problem if we did not see both GR and QM in the world around us. And the only useful and physically valuable result of such a reconciliation are new predictions - qualitative or quantitative. For the reconciliation to be meaningful, we must be able to say something that the previous theories were silent and ignorant about. In particular, this includes the "overlap" regions where both GR and QM are necessary, such as the black hole singularity and the Big Bang.

There seems to be no argument about the fact that string theory has provided us with new sensational insights into many corners of mathematics and mathematical physics: into geometry of Calabi-Yau spaces (including mirror symmetry), equivalences between objects and phenomena that a priori look completely different (dualities), holography and the AdS/CFT correspondence, the role and fate of fields such as tachyons, geometrical realization of many mathematical systems that looked non-geometrical before, and so on.

It has also given us many new ideas how new interesting physics "behind the corner" may possibly look like and in 2005, most stringy as well as non-stringy phenomenologists admit that the majority of new good ideas for model building in the last 10 years came from string theory. We don't need to argue about these things; everyone who wants to be "in" tries to extract some valuable insights from the reasoning discovered by string theorists.

Value for physics as opposed to mathematics

But all these things are victories in physically inspired mathematics and the search for better mathematical tools to study physics. They're not victories in physics itself. I consider string theory to be more than just a miraculous generator of new mathematical insights about objects inspired by physics. I believe string theory is a new, deeper theory to accurately describe actual physical phenomena; probably a theory of everything. By a "new" theory, I mean that it is not physically equivalent to the previous theories such as the Standard Model (an example of a QFT), but it contains all of their wisdom and something more.

I don't see what the unification of GR and QM would be good for if it did not allow us to calculate new numbers about a world containing both GR and QM, at least in principle. Notice that this is the same comment that is emphasized whenever I explain why the attempts of loop quantum gravity to unify pure GR with QM are not only failing but also misguided from the very beginning. It is not exactly just some abstract QM that we want to unify with pure GR and we have no experimental evidence that pure GR should be compatible with pure QM without other forces: we want to unify the well-known quantum phenomena - namely gauge theories with fermions - with gravity.

Loop quantum gravity can't do it because these sectors remain independent, even in the most optimistic case in which the Standard Model is successfully added to LQG with the right low-energy limit. String theory does achieve this goal because gauge theories, fermions, and gravity are all parts of its low-energy limit. But in order to achieve the goal fully, it should also be used to derive the right spectrum of particles with the right parameters either from no input or from a smaller set of assumptions than required by the previous theories.

Concerning loop quantum gravity, I also disagree with another point of Sean: that all of us should offer our support to loop quantum gravity and other problematic directions in order to create an environment of competition. In my opinion, scientists should provide hints where to go according to their best knowledge. My best knowledge about loop quantum gravity implies that it is a misguided approach to physics. There undoubtedly exist people with a different opinion but it is impossible to lend your support to a particular human activity just because some other people like it. These people may only like it because a third group of people likes it - and the source of the love may remain obscure. That's wrong. Scientists' responsibility is to offer their independent opinion. Mine is that loop quantum gravity is a wasted time and money. And social-engineering of competition is plain wrong.

Ann Nelson and Occam

Occam's razor dictates me to agree with Ann Nelson in one point: if the prediction of the parameters or other numbers absent in the Standard Model is impossible, then the Standard Model should be favored as a physical description of reality because it is simpler and requires the same (or smaller) number of input parameters as the stringy landscape picture, for instance. My feeling is that some colleagues of ours truly love mathematical derivations and translation of one kind of physics into another kind of physics; even if the amount of predictions agrees, they will prefer a starting point that is as different from the final outcome as possible and that is as complex as you can get.

My opinion - and I suspect that the opinion of Ann Nelson and most phenomenologists as well - differs. A more convoluted starting point and a longer chain of reasoning from this starting point to the final result is only justified when either the explanatory power is extended, or the amount of parameters or independent assumptions and concepts is reduced.

String theory as we know it today may be used to calculate the Planckian scattering in some backgrounds. (Incidentally, for Peter Woit, the gravitational potential of an electron is "-M_e.G/r".) That's a stimulating progress, but the real victory in physics only occurs once we become able to calculate the Planckian scattering - the transition between low energies and the black hole creation - in the real world. The importance of this next step - to describe the effects in the real world - has become particularly pressing at the moment when we decided that the number of backgrounds in string theory is probably large, and therefore the collective predictions for all backgrounds are potentially highly ambiguous and essentially arbitrary until we find a selection principle. A larger number of critical points in the landscape does not mean that we should give up the goal to extract predictions beyond the Standard Model from string theory; it just means that the vacuum selection mechanisms will be a more important part of the full story than we had thought previously.

If the string theorists ever give up the task to calculate the numbers that can't be predicted by the previous theories, the string theory research should be moved to mathematics departments. Physics is about understanding the actual material physical world we live in. Mathematical beauty is a great thing, but for a physicist it should be just a hint that she is on the right track. It cannot be the ultimate justification of a proposed theory. Progress in physics always means that a larger number of phenomena can be calculated and predicted more accurately using a theory with less independent assumptions, defining concepts, and parameters.

String theory has the capacity to achieve this goal maximally, and if we transform ourselves into pessimists and fool ourselves by pseudo-arguments that the progress is impossible and that we should be even happy with such a postmodern and I would say scary expectation, we're gonna be in a big trouble.

Strings are just a piece

Also, another problem with Sean's text is that he paints string theory as we knew it 20 years ago or so. (It's not such a big problem at their blog whose typical readers who are not professionals - and some of those who are - are more interested about the YES/NO wars about string theory rather than the difference between string theory in 1985 and string theory in 2005.)

Today, string theory is not just a theory of strings. The perturbative approach to string theory based on one-dimensional elementary objects was a very fruitful point to start with, but we know today that it is far from being the whole story. The strings may be viewed as fundamental objects in the weakly coupled regime only; in other limits, other objects may "look" fundamental even though they were interpreted as solitons in the weakly coupled limit. In a recent article about the depth of ideas, I also explained that the very idea to replace point-like particles by strings is not deep. It only becomes a powerful idea once the special properties of two-dimensional conformal field theory are revealed.

In other words, when a person who does not understand conformal field theory in 2 dimensions at the technical level says that the idea to replace point-like particles by strings does not look deep to her but rather shallow and convoluted, I completely understand where she's coming from. But I would also like to tell her that if she learns how the relevant mathematics works, she will understand why strings are so special. But it requires a lot of calculations and the power of strings can't be obvious to a layman after 1 minute.

This point is rarely emphasized, so let me say it again. The laymen who consider strings as the elementary building blocks to be a shallow idea are correct at the beginning; but there is a lot of mathematical facts that can't be obvious from the very beginning that eventually make strings much more remarkable than one might have thought. This implies a recommendation for the laymen: slow down your far-reaching conclusions about string theory until you learn how its machinery works at the technical level.

Today, "string theory" is a kind of misnomer. The theory is based on many other concepts, too - but it does not make it less reliable. On the contrary. Clifford Johnson is very right when he disagrees with Sean and mentions that M-theory in 11 dimensions which has no strings is an equally valuable and qualitatively understood limit of the whole theory as the five superstring theories in 10 dimensions.

Point-like terminology

Sean mentions that he does not understand why the regular quantum field theories are said to be based on "point-like particles". It's because the quantum fields assign an operator to every point in spacetime. In string theory, it is different, indeed. For example, if you formulate string theory using the language of string field theory, you must assign an operator to every one-dimensional contour (string) embedded into spacetime. The number of degrees of freedom you see perturbatively is just much larger than in quantum field theory. (But at the very end, paradoxically, you end up with a holographic theory whose number of degrees of freedom is smaller than in any local point-like quantum field theory.) The fact that the operator at a given point can't be quite identified with the actual physical particle is an irrelevant technical complication that does not reduce the large technical difference between point-like field theories and string theory.

Wrong attempts to separate str-ing theory

Several participants in the discussion try to follow Peter Woit and divide string theory to the "good" stuff - new approaches of QCD including the AdS/CFT correspondence, insights about mirror symmetry - and the bad stuff - which includes the 10-dimensional and 11-dimensional vacua as the unifying starting point to include all of physics.

Only a person who is completely ignorant about the way how string theory works - and Peter Woit and Ohwilleke are not the only ones - can say something so absurd. There is no way to eliminate the critical dimension and all other basic insights about string theory from the other, "good" applications of string theory. For example, the best understood example of the AdS/CFT correspondence involves the N=4 super Yang-Mills theory. The dual bulk description is the AdS5 x S5 background of type IIB string theory. Note that the total dimension is 5+5=10, as always required in type IIB string theory. All the detailed features, including the excited type IIB strings and branes of all kinds, can be derived not only from the bulk description but also from the gauge theory defined on the boundary!

String theory, at least in the highly supersymmetric vacua with 8 or more supercharges, is a fantastically rigid theoretical structure that holds together perfectly. If someone says that one can preserve the successes (as enumerated above) of string theory without preserving everything we know about its critical dimension and the basic knowledge of stringy dynamics in 10 and 11 dimensions and the compactifications, then she or he only shows that she or he is uninformed about the very basic facts of the field. String theory simply can't be separated in this way. It would be similar to the attempt to remove photons from QED.

Strong leadership of supersymmetry

Possibly, there are many intellectual directions - bosonic string theory, non-critical string theory, topological string theory, the landscape approaches - that will eventually be considered to exist outside the realm of "the" string theory (or will be considered inconsistent because of some non-perturbative subtleties). By "the" string theory, I mean the theory that has the beauties and that is relevant for the real world. But the different phenomena and relations between physical insights about the supersymmetric vacua of string theory can't be undone, and they will always be essential for our understanding of many things, including holography etc.

The less we rely on spacetime supersymmetry, the less reliable the different dualities and relations are. For example, the holographic dual of pure QCD in 4 dimensions probably has a different bulk dimension than 10 or 11 and it may be called a non-critical string theory (it is an ambiguous task to define the number of tiny dimensions in a background of string theory; only the large and nearly flat dimensions can be counted without doubts). But it is also the case where the existence of a quantitatively predictive dual (bulk) theory is uncertain and where string theory has not told us too much - at least not too many quantitative results.

The maximally supersymmetric backgrounds - such as the N=4 gauge theory - are best understood, and one can show that the dual is not just some generic five-dimensional gravitational theory, but the ten-dimensional type IIB string theory on a very specific background. All details work. It is not possible to eliminate some known aspects of ten-dimensional string theory from this picture! While various other approaches to quantum gravity are incoherent and dividable conglomerates of ideas, string theory is united.

United we stand, divided we fall.

1 comment:

  1. Lubos:

    Super string theory is based on the basic two hypothesis that fundamental spacetime dimentions are 10 and that fundamental particles are string like instead of point like. So to claim anything as a success or as a result of string theory, you have to show me that they came out of the two hypothesis: 10-D and string.

    I am against super string theorists for claiming any thing that remotely seem good as a "result" of super string theory. Those includes the anthropic principle, the holographic principle, Calabi-Yau, or even the so called AdS/CFT correspondence. Clearly all these stuff have nothing to do with the dimentionality or whether the particles are strings or points.

    Unless you can show that in a 10-D and stringy world all those results, like anthropic principle, holds, and in the otherwise case, if the world is not 10-D, but 4-D, those results no longer holds. You really can not claim those results as results of super string theory. You can probably claim some of them as results of the research works of some string theoretists, but they are still not the exclusive patents derived from the principles of string theories.

    I think AdS/CFT merely reveals a mathematics insight that we knew since elementary school: If you have a set of 10 equations, and you put one confinement condition in, it reduces to 9 equations. And if you started with 9 you would end in 8 with an confinement condition added. It surely looks like a useful mathematics tool to SST researchers, but it is wrong to claim it as a derived result from the string theory principles, because it is not.

    So, can you name just one thing, that can be derived if and only if the two hypothesis of SST is true? The only thing I can think of, is the claim that a self-consistent theory can only be possible if the domentionality is 10. Well, merely self-consistent is really a low end of requirement on the part of a theory. If a theory is not self consistent that means a logical error was made some where in the theory derivations, and it can already be thredded into recycle papers.

    If the nature is 4-D, and you can't figure out why it's 4, not 10 as you thought. Then it is not the nature that is wrong, it is you that are wrong, regard;ess how self-consistent you think your theory is.

    I have recently found some strong, indisputable reasoning and evidence to conclude that the fundamental dimentionality at microscopic scales is ZERO, not 4 and not 10. As a starter, consider why the parity conservation is broken. Why CP is broken. And why CPT broken has not been found yet. I will discuss this in further detail when I find time. But before I end, one more hint is any microscopic dimentional structure will break the Hawking and Bekenstein Bound.