Wednesday, August 29, 2007

Defending ideas we don't believe: string theory is a waste of time

Sean Carroll started an interesting game, collecting
the best arguments for things he doesn't believe.
While I also frequently find arguments supporting wrong ideas even weaker than they should be, I wouldn't be good in playing Sean's game. For example, if you ask me what good arguments I could give you to support the opinion that the society should "fight against climate change", I would have no idea.

If I knew such arguments, you would have already heard them from me. I am not trying to hide any good arguments that I am aware of. The proponents of the "dangerous global warming" theory often use really silly arguments but I think that the main problem is not that all of these people are silly; the main problem is that no good, defendable, rational arguments supporting their position exist.

Nevertheless, Sean wrote a collection of arguments for the first statement he doesn't believe, namely that
string theory is a waste of time.
The punch line is: the best argument that string theory is a waste of time is that the theory is simply too hard and right now we don't have any good reasons to think that all remaining big questions will be solved soon.

I couldn't agree more. It is indeed the best, and probably the only good argument supporting the statement above. String theory is hard and the recent progress doesn't suggest that it will be completely solved by the end of this summer. But the challenging character of the open questions and string theory itself is also the reason why it is attracting and why it has been attracting some of the smartest people on the planet.

As Sean correctly suggests, all other arguments that are being routinely offered to support the thesis are pure garbage - garbage that is good enough to influence many uninformed people. I will explain that the remaining arguments that Sean has fabricated are untrue or nonsensical, too.

Best science usually results from a close collaboration of theory and experiment, right?

Well, first, I don't really think that this assertion is true from a historian's viewpoint. I think that some of the best experiments in the history of physics were made by pure experimenters who didn't care about the theory much. And most of the best theories in physics were found by theorists who didn't think about doable experiments every day when they woke up. The latter group includes most of the theoretical giants of the 20th century, including Einstein, Planck, Dirac, Pauli, and dozens of others.

Of course that both kinds of research must eventually be linked as long as they refer to the real world. But the idea that this exchange must occur on a regular basis as well as the idea that there should be a fixed and prescribed percentage of experimenters and theorists that study every individual question in science is a childish silliness. It is an example of quotas and political correctness run amok. The analogy with the quotas for men and women couldn't be more obvious. Many key experimental discoveries in science remained purely experimental for quite some time and many key theoretical discoveries were found by purely theoretical means. Any attempt to systematically alter the composition of the naturally evolved research is bound to be counterproductive.

As Sean correctly says, the reason why people study quantum gravity i.e. string theory despite a very low probability that it can be directly tested by experiments is that they have a lot of sharp theoretical tools that largely compensate (or even overcompensate) the shortage of experimental tools.

I have already learned that this basic concept behind theoretical physics is next to impossible to grasp for virtually all laymen - a category that manifestly includes chairs of the mathematics departments at U.S. schools - because most people just don't understand how complex calculations or thinking may ever be relevant for the real world. They have never done a complex calculation leading to the right result and they think that no one else can do it either.

I assure you that it is not only possible to figure out things about the Universe by very complex theoretical thoughts and calculations that don't need to do experiments in the middle - but it has been the dominant strategy of theoretical physics for approximately 350 years and it is getting ever more powerful.

Ancient Greeks, alchemists, and the present

A Cosmicvariance commenter named Solipsist argues that the ancient philosophers used to think all the time and all their theories were ruled out in the age of empiricism. Well, not all of them (atoms were not) but more importantly, these ancient people were not thinking about the deeper origin of theories that have already been empirically verified. String theorists do. That's a huge difference.

Otherwise, one could offer analogous hostile comments about experimenters, too. Alchemists were doing experiments for centuries and they have never found the elixir of life. The modern theory even explains why they couldn't achieve their goals using their methods. ;-) Only very stupid people might want to generalize these episodes and think that "all experiments are rubbish" or "all theory is rubbish".

There are too many vacua i.e. solutions, right?

It seems that there exist very many maximally symmetric solutions of string theory - different kinds of vacua or Universes where someone could potentially live. Does it mean that string theory is less likely to be true?

I think that it should be completely manifest that such a conclusion is entirely irrational. We can't experimentally measure or count the number of Universes where the particle spectrum and fundamental constants differ from ours. Because we don't know the right answer, we must be equally open-minded about all possible answers. If experimental data about this question are absent while theoretical arguments imply that 10^{500} is the most likely estimate for the number of quasirealistic vacua, then it is the most likely estimate for the number of quasirealistic vacua. Period.

The theory is, more directly or less directly, based on observational data. Claiming that we don't like its answers to a question that can't be experimentally decided and we prefer to rely on our prejudices is a textbook example of an unscientific approach. Even if someone doesn't realize that string theory is almost guaranteed to be correct, it is the only scientific framework we have that has the capacity to answer similar questions. If someone prefers preconceived dogmas or metaphysical traditions over precious calculations, he's just not a scientifically minded person.

Another question is how to find the right spot in the landscape and whether we should be looking for it at all. No solid arguments exist here. But the very counting is a matter of doing science right.

A large number of universes may mean that it will be harder to make progress. It can mean that the final results won't be as uniquely cool as many have hoped. But the large number cannot influence our ideas about the validity of the theory. When a 19th century theorist predicted that the number of atoms in a bottle of milk would have to be around 10^{26}, the number was larger than the numbers that most people knew. But this fact certainly didn't mean that the atomic theory became less likely. It was a legitimate prediction of the size of the atoms - even though these atoms couldn't have been seen for another century. Only unscientific people could have doubted that the prediction was legitimate. And it was the right prediction, of course.

String theory isn't a theory, right?

A lot of misconceptions about this question follow from confusing terminology. What do we mean by string theory and M-theory?

In the 1970s and 1980s, people discovered the Feynman diagrams for this theory, generalizing diagrams in perturbative quantum field theory: they have realized that the fundamental objects in perturbative string theory looked like strings. They thought that everything one could learn about the theory would always be formulated in terms of strings and their properties.

In the 1990s, it was realized that this old paradigm was too narrow-minded. Some of the previous general facts - the key role of strings - were downgraded to mere artifacts of an approximation. The full theory also contains black holes, branes of diverse dimensions, and all these entities are able to get transformed into each other. Moreover, it was realized that the strongly coupled limit of ten-dimensional type IIA string theory is an eleven-dimensional theory. Because one couldn't say anything specific about this eleven-dimensional theory - except for its low-energy limit (supergravity) - it was mysteriously named M-theory.

People thought that this eleven-dimensional M-theory was so mysterious and so special that once we understand the rules that control its eleven-dimensional dynamics, all mysteries of string theory would be solved, at least in principle.

This opinion turned out to be naive. Matrix theory became the first setup in which the eleven-dimensional dynamics can be exactly, non-perturbatively defined and studied. But Matrix theory is nevertheless unable to define dynamics of string theory in all possible contexts (even though type IIA and E8 x E8 string-theoretical vacua are among those that are completely captured by Matrix theory). Each vacuum requires us to define a new matrix model and the matrix description of most vacua is unknown.

With these insights, people realized that the eleven-dimensional vacuum described by M-theory is just another special limit of the full theory, much like ten-dimensional type I, IIA, IIB, HE, HO string theories. Each limit is useful to calculate results in its vicinity but less useful to calculate results in distant regions of the configuration space. The only difference between five string theories and M-theory is that M-theory has eleven dimensions instead of ten. But you should add it as the sixth supersymmetric background in a maximum spacetime dimension.

If you return a little bit, people thought that M-theory would explain everything about all string theories. That's why they were using the term "M-theory" in two ways that were non-equivalent even though many people thought that they were equivalent. One of the meanings of "M-theory", the narrow one, was the eleven-dimensional dynamics connected to type IIA string theory; the other, broader meaning was "the full theory unifying all wisdom of string theory".

Once people realized that these two concepts are not the same thing, they had to refine the meaning of "M-theory". Among the physicists in the field, the term "M-theory" is now exclusively used for descriptions of physical systems that are based on eleven-dimensional spacetime with supersymmetry. Nevertheless, the laymen still use the term "M-theory" to refer to the full theory that has "superseded" string theory, partially because they have not yet been told that the eleven-dimensional dynamics doesn't expose all secrets of string theory.

The laymen and journalists have been using the term "M-theory" in a wrong way for at least 10 years and I think that it is already time for them to learn that they misinterpret the meaning of "M-theory". In fact, you can see that Sean uses the term "M-theory" incorrectly, too. Physicists in the field only use "M-theory" for one of the limits of the full theory - the limit that has 11 dimensions - and for its compactifications where those 11 dimensions may still be seen. And they continue to use the term "string theory" (instead of "M-theory" or something else) for the full structure that connects all the limits (previously called "string theories") and that is studied by string theorists. It is a kind of misnomer because strings no longer play a qualitatively different role from other objects in this full theory. But nevertheless, it is terminology that stuck.

"String theory" now means the full theory studied by string theorists while, of course, terms like "type IIA string theory" are still used for the particular limiting descriptions.

So if you use the term "string theory" in the same way as physicists do, the assertion that "string theory is not a theory" is certainly incorrect. If you use the most refined definition of the word "theory" that theoretical physics can offer today, string theory is a perfect example of a "theory". It only has one kind of dynamics even though the set of phenomena that follow from it is very rich. If you imagined that it can be described by a local Lagrangian much like quantum field theories, the Lagrangian would be unique. It has many fields and degrees of freedom and a complicated configuration space. But its structure is uniquely determined.

We can't write the full Lagrangian that covers all aspects of string theory and we actually think that the theory is not defined by the old-fashioned spacetime Lagrangians. But if we ask any meaningful physical question about the dynamics, we may always derive an unambiguous answer just like we can do whenever we have the full Lagrangian in a quantum field theory.

The complete definition of the full string theory that would transform every question about the set of vacua and their dynamics to a fully rigorous mathematical problem isn't available at this moment. But a full definition is available for many subsets of the string-theoretical configuration space and moreover, all the right qualitative (and some quantitative) answers may be found in virtually all corners of string theory. This is a highly non-trivial fact that implies that string theory almost certainly exists as a unique, rigorously definable mathematical structure. If it didn't exist, it could have broken down in hundreds of corners and under hundreds of extreme circumstances. So far, it has never broken down.

We don't have the exact equation that defines the shape of America but you can try to walk around the continent and convince yourself that the continent exists anyway, despite the absence of the U.S. equation that could be printed on your shirt. The people who say that America doesn't exist are simply wrong. String theory is in the same situation except that you must replace walking by calculations.

String theory has no universal predictions, right?

This is another common misconception. People like to say that "anything goes" in string theory. But that's complete rubbish. If you actually look at the physicists who haven't yet understood string theory and analyze what they think about many kinds of questions, you will find out that their answer to virtually every question is wrong.

Some believe that the information is lost in black holes. Others believe that there are no degrees of freedom besides the metric tensor. Pretty much the same people believe that geometrical quantities are well-behaved observables at the Planck scale and they usually have a discrete spectrum. Similar people believe that the Planck scale physics eliminates the need for anomaly cancellation. There exist hundreds of qualitative questions that are clearly and unambiguously answered by string theory even though most people who can't follow the correct arguments would end up with wrong answers.

From this viewpoint, the differences between the different solutions (or vacua) of string theory are negligible technicalities. The qualitative facts how physics works are completely unified and some of the quantitative facts are unified, too.

Sean correctly says that some facts about the spectral density and the asymptotic behavior of scattering amplitudes only hold at weak coupling and don't extend to the full string theory. That's of course correct. Some of them don't. But some of the features of string theory do. You could say the very same thing about QCD or any other theory in physics. For example, QCD predicts various power laws that only work at weak coupling i.e. high energies but they don't imply anything at the hadron scale.

It is not the main goal of a physical theory to produce easy slogans that are easily memorizable, verifiable, and that can be used to impress and mislead laymen in books and newspapers - even though this is exactly what people like Lee Smolin think. The actual goal of a theory such as QCD or string theory is to correctly predict the results of a whole class of phenomena. Most of these phenomena require one to understand what's going on at the technical level and will be either boring or impenetrable for laymen and journalists. But that's simply how Nature works. Get used to it.

And that's the memo.

1 comment:

  1. Dear Luboš

    I would extremely appreciate your opinion on definition of the total black
    hole partition function via the Feynmanian integral over moduli space M

    Z_BH = int_M DM Z_TOP (M)

    Define graded Hopf/Grothendieck-Teichmuller group manifold M

    M = qE_8 <-U-dual-> qE_9 <-U-dual-> qE_10 <-U-dual-> ... <-U-dual-> qE_n

    whose submoduli spaces of graded moduli space generate the modular union by
    the inclusion system

    qE_8 -> qE_9 -> qE_10 -> ... -> qE_n


    qE_8 = SO(qO + qO) + (qO x qO)^2

    Moduli space of graded hyperbolic quantum deformed group manifold M leads to
    exponential growth of rank of holographically dual group of cascading throat
    of generalized conifold and in the process whose Weyl group of root space
    makes rank of vacuum torsion variable. Total number of generators grows
    expo-exponentially with exponentially growing rank of M. Outgrowth is that
    the roots of M have uncountable degeneration. Ireducible representation of
    U-dual modular group M are K-theoretic knots of dilaton/tachyon which are
    just condensates of one unstable graded quantum deformed octonionic black
    hole throat. We identify T-dual modular group which makes the group rank
    variable, S-duality cascade of generalized conifold throat and U-duality
    chain which permutes NS-NS/R-R potentials and arbitrarily sets dilaton value
    on the one side, with affine Weyl group of quantum deformed root system of M
    on the other side.

    There exists isomorphism between U-dual modular group M and moduli space of
    U-dual instanton. The interchange of moduli of U-dual instanton is just
    Weyl transformation in M. Isomorphism between topological amplitudes of
    U-dual instanton and root lattice of M provides information about algebraic
    structure of nonperturbative contributions to vacuum potential. U-dual flux
    through U-dual cycle is

    Ng = int psi = V_vaccum = 0

    Monodromy of M makes volume of U-dual cycle and dimension of wrapping U-dual
    brane variable. (Group manifold M permutes charges of the U-dual black
    brane/U-dual vacuum torsion.)

    There exists module homomorphism between affine Weyl group of root space M
    and nonassociative deformed fractal attractor of condensation of Hagedornian
    tachyon/U-dual instanton inside deformed throat of generalized conifold
    (throat which fills group manifold M). Hagedornian tachyon orbits of affine
    Weyl group of U-dual root system is fundamental observation. U-dual black
    hole throat degenerations are determined by the U-dual automorphic forms
    (degenerations are generalized Fourier coefficients of modular forms of M).
    Outgrowth is that nilpotent orbits of M defines topological string
    amplitudes. Thus we're Feynmanian integrating over U-dual modular space M
    because of U-dual instanton tunneling amplitude we require observe. Notable
    consequence is

    uncountably degenerate U-dual root space = uncountably degenerate U-dual
    black hole throat = int_M DM Z_TOP (M) = 0

    Thank you very much for your opinion on this consequence!
    With great respect