Science or Sociology?
Joseph Polchinski, 5/20/07
This is a continuation of the on-line discussion between Lee Smolin and myself, which began with my review of his book and has now continued with his response. A copy of this exchange (without the associated comment threads) is here.
Dear Lee,
Thank you for your recent response to my review. It will certainly be helpful in clarifying the issues. Let me start with your wish that I do more to address the broader issues in your book. When I accepted the offer to review these two books, I made two resolutions. The first was to stick to the physics, because this is our ultimate goal, and because it is an area where I can contribute expertise. Also, keeping my first resolution would help me to keep the second, which was to stay positive. I am happy that my review has been well-received. Your response raises some issues of physics, and these are the most interesting things to discuss, but I will also address some of the broader issues you raise, including the process of physics, ethics, and the question in the title. Let me emphasize that I have no desire to criticize you personally, but in order to present my point of view I must take serious issue both with your facts and with the way that they are presented.
Regarding your points:
The fictitious prediction of a non-positive cosmological constant. This is a key point in your book, and the explanation that you now give makes no logical sense. In your book you say (A) “… it [a non-positive cosmological constant] was widely understood to be a consequence of string theory.” You now justify this by the argument that a non-positive cosmological constant is a consequence of unbroken supersymmetry (true), so A would follow from (B) Unbroken supersymmetry was widely understood to be a consequence of string theory. But even if this were true, it would not support your story about the observation of the dark energy leading to a “genuine crisis, … a clear disagreement between observation and a prediction of string theory.” There would already have been a crisis, since supersymmetry must obviously be broken in nature; seeing the dark energy would not add to this. But in fact the true situation, as you can find in my book or in many review articles, was closer to the opposite of B than to B: (B’) Supersymmetry is broken in almost all Calabi-Yau vacua of heterotic string theory. We have no controlled examples because at least one modulus rolls off, usually to a regime where we cannot calculate. The solution to this problem may have to wait until we have a non-perturbative formulation of gravity, or even a solution to the cosmological constant problem.
In your response you largely raise issues surrounding B’, including the Witten quote, but I want to return to what you have actually written in your book. It is a compelling story, which leads into your discussion of “a group of experts doing what they can to save a cherished theory in the face of data that seem to contradict it.” It surely made a big impression on every reader; it was mentioned in several blogs, and in Peter Shor’s Amazon review. And it never happened. It is an example of something that that happens all too often in your book: you have a story that you believe, or want to believe, and you ignore the facts.
You go on to challenge the ethics of string theorists in regard to how they presented the issue of moduli stabilization in their talks and papers. I am quite sure that in every colloquium that I gave I said something that could be summarized as “We do not understand the vacuum in string theory. The cosmological constant problem is telling us that there is something that we do not understand about our own vacuum. And, we do not know the underlying principle of string theory. These various problems may be related.” The cosmological constant and the nature of string theory seemed much more critical than the moduli stabilization problem, and these are certainly what I and most other string theorists emphasized.
This scientific judgment has largely been borne out in time. In 1995-98 these incredible new nonperturbative tools were developed, and over the next few years many string theorists worked on the problem of applying them to less and less supersymmetric situations, culminating in the construction of stabilized vacua. Obviously many questions remain, and these are widely and openly debated. It seems like a successful scientific process: people knew what the important problems were, worked in various directions (a fair number did work on moduli stabilization over the years), and when the right tools became available the problem was solved. As you point out, the stabilization problem is nearly one hundred years old, and now string theorists (primarily the younger generation, I might add) have solved it. You are portraying a crisis where there is actually a major success, and you are creating an ethical issue where there is none.
AdS/CFT duality. You raise the issue of the existence of the gauge theory. There are two points here. First, Wilson’s construction of quantum field theory has been used successfully for 40 years. It is used in a controlled way by condensed matter physicists, lattice gauge theorists, constructive quantum field theorists, and many others. To argue that a technique that is so well understood does not apply to the case at hand, the scientific ethic requires that you do more than just say Not proven! Sociology! as you have done. You need to give an argument, ideally pointing to a calculation that one could do, or at least discuss, in which one would get the wrong answer.
I have given a specific argument why we are well within the domain of applicability of Wilson: there are 1+1 and 2+1 dimensional versions of AdS/CFT, which are also constructions of quantum gravity, and for which the gauge theory is super-renormalizable (and there are no chiral fermions): the counterterms needed to reach the supersymmetric continuum limit can be calculated in closed form – thus there is an algorithmic definition of the gauge theory side of the duality. You could perhaps argue that there will be a breaking of supersymmetry that will survive in the continuum limit, and we could sit down and do the calculation. But I know what this answer is, because I have done this kind of calculation many times (it is basically just dimensional analysis). Similar calculations, for rotational invariance and chiral symmetry, are routine in lattice gauge theory.
As a further ethical point, in your book you state that it is astounding that Gary Horowitz and I ignore the question of the existence of the gauge theory, and you then use this to make a point about groupthink (this is in your chapter on sociology). While you were writing your book, you and I discussed the above points in detail, so you knew that we had not ignored the issue but had thought about it deeply. You do not even acknowledge the existence of a scientific counterargument to your statement, and in saying that Gary and I ignore the issue you are omitting facts that are known to you in order to turn an issue of science into one of sociology. Again you impose your own beliefs on the facts; thus I am reluctant to accept as accurate the various statements that you attribute elsewhere to anonymous string theorists and others.
You raise again the issue of a weak form of Maldacena duality. As you know, it is very difficult to find a sensible weak form that is consistent with all the evidence and yet not the strong form. In my review I have gone through your book and papers and identified three proposals, and explained why each is wrong. Again, you have not acknowledged the existence of scientific counterarguments, but have just reasserted your original point. If your arguments had been made in a serious way, I would expect that you would have given some deep thought to them and be ready to defend them.
There are some interesting points, one of which I will turn to next.
The role of rigor and calculation. Here we disagree. Let me give some arguments in support of my point of view. A nice example is provided by your paper `The Maldacena conjecture and Rehren duality’ with Arnsdorf, hep-th/0106073.
You argue that strong forms of the Maldacena duality are ruled out because Rehren duality implies that the bulk causal structure is always the fixed causal structure of AdS_5, and so there cannot be gravitational bending of light. But this would in turn imply that there cannot be refraction in the CFT, because the causal structure in the bulk projects to the boundary: null geodesics that travel from boundary to boundary, through the AdS_5 bulk, connect points that lie on null boundary geodesics. Now, the gauge theory certainly does have refraction: there are interactions, so in any state of finite density the speed of propagation will be less than 1. (Since Rehren duality does not refer to the value of the coupling, this argument would hold even at weak coupling, where the refraction can be calculated explicitly.)
You have emphasized that Rehren duality is rigorous, so apparently the problem is that you have assumed that it implies more than it does. Generally, rigorous results have very specific assumptions and very precise consequences. In physics, which is a process of discovery, this can make them worse than useless, since one tends to assume that their assumptions, and their implications, are broader than they actually are. Further, as this example shows, a chain of reasoning is only as strong as its weakest step. Rigor generally makes the strongest steps stronger still – to prove something it is necessary to understand the physics very well first – and so it is often not the critical point where the most effort should be applied. Your paper illustrates another problem with rigor: it is hard to get it right. If one makes one error the whole thing breaks, whereas a good physical argument is more robust. Thus, your paper gives the appearance of rigor, yet reaches a conclusion that is physically nonsensical.
This question of calculation deserves further discussion, and your paper with Arnsdorf makes for an interesting case study, in comparison with mine with Susskind and Toumbas, hep-th/9903228. (I apologize for picking so much on this one paper, but it really does address many of the points at issue, and it is central to the discussion of AdS/CFT in your various reviews.) You argue that there are two difficulties with AdS/CFT: that strong forms of it are inconsistent with the bending of light by gravitational fields, and that the evidence supports a weaker relation that you call conformal induction. We also present two apparent paradoxes: that the duality seems to require acausal behavior, and negative energy densities, in the CFT. The papers differ in that yours contains a handful of very short equations, while ours contains several detailed calculations. What we do is to translate our argument from the imprecise language of words to the precise language of equations.
We then find that the amount of negative energy that must be `borrowed’ is exactly consistent with earlier bounds of Ford and Roman, gr-qc/9901074, and that a simple quantum mechanical model shows that an apparent acausality in the classical variables is in fact fully causal when one looks at the full quantum state. Along the way we learn something interesting about how AdS/CFT works.
This process of translation of an idea from words to calculation will be familiar to any theoretical physicist. It is often the hardest part of a problem, and the point where the greatest creativity enters. Many word-ideas die quickly at this point, or are transmuted or sharpened. Had you applied it to your word-ideas, you would probably have quickly recognized their falsehood. Further, over-reliance on the imprecise language of words is surely correlated with the tendency to confuse scientific arguments with sociological ones.
Finally, I have recently attended a number of talks by leading workers in LQG, at a KITP workshop and the April APS meeting. I am quite certain that the standard of rigor was not higher than in string theory or other areas of physics. In fact, there were quite a number of uncontrolled approximations. This is not necessarily bad – I will also use such approximations when this is all that is available – but it is not rigor. So your insistence on rigor does not actually describe how science is done even in your own field.
Background independence. I think people are a bit tired of the who-is-more-background-independent argument, since it seems to come down to definitions. Let me put things in physical terms. As you say, suppose that the strong form of Maldacena duality is true. This would mean that we can consider a box as large as we want – a light-year, 106 light-years, with an arbitrarily small negative cosmological constant, and AdS/CFT provides a complete construction of quantum gravity within that space. This would include: the formation and decay of (nonsupersymmetric) black holes; graviton scattering at hyper-Planckian energies; physically continuous transitions from one topology, through a quantum state with no geometric interpretation, to a different topology; states where a submanifold of spacetime has a noncommutative geometry; states with a variety of apparent geometric singularities, where the physics is nonsingular. All of these, and many others with a variety of geometries and topologies (you can put a lot in an AdS box), and arbitrary quantum superpositions of them, can be identified in the gauge theory, and so are described algorithmically by the duality. It may not include spaces with interesting cosmologies, or with an effective positive cosmological constant. You call this a very weak and limited form of background independence.
Even here you are blowing things out of proportion: your reply refers five times to the “global symmetry algebra,” but almost immediately after the original work of Maldacena, the duality was extended to systems with reduced symmetry, or none. Your own PI colleagues, Alex Buchel and Rob Myers, have made important contributions to this subject, and I note also the series of papers by Hertog and Horowitz on strongly time-dependent boundary conditions.
A second physics point concerns the constraints. It is not that I am ignorant of the conventional wisdom here, I am challenging it. You believe that the large Hilbert space in which the constraints act is necessary in order to describe all possible backgrounds of quantum gravity. No, only the much smaller set of states that satisfy the constraints is needed. The larger space may play a useful auxiliary role, but it is not physical: the universe cannot be in such a state, and observables must keep the system within the physical subspace. So what are these larger spaces for? One thing we have learned, from emergent gauge theory, is that they are not necessary: one can start from a system with no constraints, only physical variables, and the constraints are needed only to describe the classical limit efficiently. We have learned a similar lesson from dualities such as AdS/CFT: these larger spaces are very different in different classical limits, they are not intrinsic to the quantum theory. Thus, all this focus on constraints is putting effort into something that is unphysical and actually intrinsic to a certain classical limit.
Cosmology. I have agreed that we may be far from sharp prediction. However, string theory has played a valuable role in suggesting new ideas. Moreover, the variety of kinds of models being explored phenomenologically is large; it is clear that some of these arise easily in the landscape (e.g. a pure cosmological constant), while others may be rigorously excluded (the constraints of Arkani-Hamed et al, and others).
Regarding the atomic analogy, the long period that I was referring to was the hundred years between the first scientific argument for atoms (Dalton) and the confirmation (Brownian motion). I agree, however, that one should not get too caught up in analogies. No analogy is perfect: in the 19th century there was a wealth of unexplained phenomena from the natural world, while our current era is historically exceptional in that phenomena beyond the Standard Model are so few.
RHIC. You say that quantum gravity is not being used here. But the QCD plasma entropy is being related to the Bekenstein-Hawking entropy, which depends on hbar, and the ideal viscosity (a concept discovered through AdS/CFT, which is now a standard idea in heavy ion physics) is quantum mechanical.
Moreover, I am puzzled by your repeated statement that the evidence supports AdS/CFT describing only classical supergravity. The gauge theory is fully quantum mechanical, so if it contains classical gravity why is this not exactly what we are all looking for: a theory that unites Einstein’s theory and quantum mechanics? This should be of great interest to anyone working on quantum gravity – how does the gauge theory manage to do this? So we look closer, and we find that it’s… string theory! It is clear why you have trouble with this: according to your book, gravity is a theory of principle, which must be understood by seers, while gauge theory is a constructive theory, which can be built by craftsmen. AdS/CFT would then imply that craftsmen are dual to seers.
But seriously, duality does erase distinctions that we make with our classical experiences and vocabularies, because one quantum theory has many classical limits. Thus, quantum mechanics first erased the distinction between particles and waves. QFT dualities erased the distinction between quanta and solitons, which once seemed absolute. Maldacena duality erases at least much of the distinction between gauge theory and gravity. Unexpected perhaps, but those who ignore this lesson are likely to end up as backward-seers rather than forward-seers.
Other physics. Sean has suggested that I comment on the understanding of string theory in time-dependent backgrounds. Here I will give my own way of thinking about this, which is rather particle-physicsy; other string theorists might emphasize different things. If you have the flat spacetime S-matrix, you actually know a lot about curved spacetime, since you can form a very complicated geometry by throwing together a lot of gravitons in a coherent state. From a particle physics perspective, where the goal is to measure the underlying Lagrangian, this is enough: the S-matrix encodes all local physics in curved spacetime. Further, with this effective Lagrangian one can study processes in a fully curved spacetime, as long as the curvature stays below the string scale. One can then list things that are not covered by this: first, cosmological questions like initial conditions and spacetime singularities, and these are indeed open questions and the subject of active research; second, the possibility of an intrinsic non-locality in physics, so that local measurements do not capture everything. The second possibility has been widely discussed: the black hole information paradox gives a strong indication that such nonlocality exists; the black hole complementarity principle, and the holographic principle, are general statements of the nature of the nonlocality; and, the BFSS matrix theory and AdS/CFT duality are very concrete realizations of locality emerging from a nonlocal starting point. Certainly deep questions about the nature of time remain, and I expect that the solutions will build on our current understanding of the holographic principle.
On the UV finiteness of string perturbation theory, the one-line physics proof is that the regions of world-sheet moduli space that would correspond to UV divergences in field theory actually turn out to describe IR physics. The decomposition of moduli space that Zwiebach uses to formulate closed-string field theory is probably the best for seeing this. The IR divergences are described by low energy effective field theory, so the finiteness problem is reduced to the already-solved problem of IR divergences in quantum field theory. This may seem awfully simple, but I have done enough calculational checks of different parts of it to take it seriously.
Ethics and sociology. Coming back to ethics, the principal scientific ethic is that scientists take responsibility for what they say: When a statement is made, to what extent has it been thought through, and appropriate checks and counterarguments considered (and, yes, the appropriate calculations done)? To what extent are known difficulties acknowledged? When a new counterargument is given, is it addressed, and the original assertion modified if necessary? Are facts presented in a clear and direct manner? This is howscientists judge one another. It is clear why this is necessary: science works by the parallel activity of many minds, and it is necessary that information be exchanged in as accurate a way as possible. Given the above discussion, I find your claim to the ethical high ground to be ironic.
Regarding group-think: you interpret the reaction of string theorists to your book as more evidence for your point of view. Rather, I think that much of this is a natural reaction to what many see as a distorted presentation of the facts. Regarding the personal insults, I think that you set the tone here with characterizations such as that quoted in the New Yorker, so it seems like posturing for you to claim the high road when a few string theorists respond in kind. However, I hope that those contributing to this discussion will try to keep to the same reasoned attitude that I have tried for.
Overwhelmingly the concentration on string theory is a scientific judgement, made by a very diverse group of theorists. Look at any of the several dozen most well-known string theorists: my own scientific experiences and tastes, both inside and outside string theory, are very different from any of theirs, just as they are from each other. I think of myself as a theoretical physicist first, and cross over the boundaries between string theory and several other fields depending on what looks important and interesting, as do many others. String theorists can be rather focussed, but they are not as closed to new ideas as you portray. For example, such ideas as holography and eternal inflation were developed outside of string theory, and might have become `alternative ideas.’ Instead they were recognized as likely parts of the big picture.
There is a reasonable concern that younger string theorists, educated in string theory rather than in other fields, might find it harder to cross these lines. Indeed, during the first and second string revolutions, there was inevitably more concentration, as these new ideas opened up a whole range of new concepts and methods. It is a very positive development that new connections between string theory and other areas have developed – heavy ion physics, low energy hadronic physics, LHC physics, cosmology, mathematics, general relativity, and many areas of quantum field theory – and that many young people are taking advantage of the opportunity to cross these lines, and in both directions. This broadening of perspective should be, and I think is, strongly encouraged.
Coming back to the question in the title, I have agreed that sociological effects exist; they must, since science is a human activity. However, when I read your book, knowing the facts, the case actually seems quite weak. To make the case for a strong sociological effect, at each turn you are forced to stretch the facts beyond recognition. On the other hand, when you discuss the science, your overemphasis on the usefulness and applicability of rigor ignores the kind of physical reasoning that physicists actually use in practice with great success, so your are leaving out at least 95% of what makes physics really work.
Sean – Please to know you have such an open healthy attitude in 72.
Eric – Is it clear (perhaps except to you) that you are desperately holding on to well-tried approaches. I too first heard of the vacuum selection principle some 20 years ago. The fact that none is found is one reason behind the big trouble with ST. For a long time I believed in much of ST. Today, I don’t believe there is such thing as 1-d string, period. The universe is not 10/11-d, although I am still open to 4+1d (and some form of brane concept but not the current one). Therefore, there is no need for any vacuum selection principle. As D Gross said there is something very fundamental missing in our picture. To me, the biggest contribution of ST to physics is showing convincingly that its basic assumptions, postulates, conjectures, and finding are all wrong as a physical theory. (But certainly a lot of the nuts-and-bolts could be useful down the road.)
A few little points:
1. A claim that Peter is making along the discussion which is of interest is that current string theoretic models being more and more complicated is an indication that the theory is heading in the wrong direction or that it failed. I think it is an interesting issue how such a claim can at all be discussed and examined (and even if it can be examined at all.) It can well be argued that more and more complicated models are quite expected also in a successful development of a scientific area. Anyway it is an interesting issue.
2. ML (the owner of ‘the reference frame’) raised an interesting point that the overall assessment of string theory is too ambitious project to be scientifically fruitful. (Mentioning ML’s full name will cause the comment to be blocked.) I think there is some truth in this claim as indeed the overall assessment of ST is well beyond the horizon. (Sean’s remark #72 expresses a similar idea.) Sometimes, miraculously, studying mundane matters changes dramatically the horizons of knowledge but discussing matters well beyond the horizon while of interest is often not so scientifically fruitful.
3. The issue of rigor and the points that Joe raised regarding it (as the strong counter points by Hendrik) are certainly interesting and important. I realized what was the thing that disturbed me about Joe’s comments concerning rigor. It is actually the rhetoric more than the substance. In the scale between useful and useless (which has a lot of grey colors) there is no such thing as “worse than useless”. Similarly, in the scale between right and wrong (also with a lot of greys) there is not really a place for “not even wrong”.
The physicists endeavor of quantum gravity as the mathematicians journey for mathematical rigor of the foundations of physics cannot really be tagged as “useful” in the ordinary usage of the word ‘useful’. (Compared, e.g. to the usefulness of garlic.) Some mutual empathy can be useful. (And potentially each of these two endeavors can occasionally offer useful insights to the other.)
4. If I can recommend to you a useful and beautiful academic area which has connections with and applications to all of the exact sciences as well as practically all areas of social science and some areas of humanities, which also has important connections to many real life problems (and not the least, baseball) and to engineering, which is related to a lot of mathematics, both deep and simple both rigorous and heuristic, and to profound calculations; an area with subtle and controversial foundations, glorious history, with a few uphill struggles for recognition; an area offering difficult ethical and moral dilemmas, and if I may say so, an area with a brilliant future: This is the area of statistics .
Invcit #39:
When cosmologists started studying inflation in the 80’s, they found that in many models the universe would inflate to much greater than what we can see – there would be many `universes’ – and that different parts would have different laws of physics. Andrei Linde in particular argued that this is the way things are. If the landscape is right, then in string theory this is true in a big way. So we have to understand the `many worlds’ of this picture as we have understood the `many worlds’ of QM. The most exciting outcome would be if these were related. A selection of recent papers can be found at http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+ti+eternal+inflation&FORMAT=www&SEQUENCE=
Hendrik #35 and Gina #32:
I agree that I am going a little too far on this rigor thing. This is partly a response to Lee’s going way too far in the other direction, but also partly a reaction to my own misspent youth. I used to focus too much on rigor and formalism, and have become a much more creative and productive scientist since learning, very slowly, to see through these to the physics. Hendrik – if you can tell me, in a non-technical way, what Dimock, Wiesbrock, and/or Rehren have shown, it would be interesting and I will respond if have anything useful to say. I agree that there are some elegant and enlightening proofs, especially in statistical mechanics, but there are also examples like the continuum limit of Yang-Mills in 4 dimensions, which is a standard calculation in a quantum field theory course (asymptotic freedom), but took Tadeusz Balaban over 300 pages in Comm. Math. Phys. to make mathematically rigorous. So this is why I say that what we can understand physically much more than we can prove.
Mike #67 Cecil #68:
“Do the string vacua with positive CC today look simple and natural or if they rather look artificial and far fetched? What new assumptions had to be applied to ST in achieve a positive CC?”
There is a general principle in physics, that we expect the equations to be simple (and beautiful, if that means anything), but that the solutions can be very complicated. This is after all the way science works, that we explain diverse phenomena in terms of simple equations. The world we see is certainly very complicated, with varied structures on many scales, and even microscopically most of the symmetry of the equations is broken. So by this measure the string vacua that we are discussing are not especially complex.
You might ask another question: we might expect that the universe had a simple initial condition – could these complicated solutions have actually been realized? Looking for example at the most-discussed model of initial conditions, the Hartle-Hawking `no-boundary’ proposal, this gives rise to complicated vacua as easily as simple ones, there is no penalty for complexity.
The history, as one might expect, has been to understand the simple solutions first and then work towards more complicated ones. When solutions of the necessary complexity (broken supersymmetry) were reached, e.g. Silverstein 2001 and KKLT 2003, positive and negative cc’s were both there. It seems like a successful scientific process, Smolin’s claims of crises, ethical failings, and wrong predictions notwithstanding.
Lee:
Three points:
First, regarding the false prediction: As Sean points out at length, there is a world of difference between `X has not been shown’ and `Not-X is predicted.’ Now you change the subject to the former, but in your book you have told a detailed, specific, and compelling story of the latter. Amos and many others have found this to be “the most persuasive thing in the book,” and yet it is sheer fiction. To repeat: my review pointed out that your story was manifestly inconsistent with the history of string theory; you came back in your response with an explanation that made no logical sense; now you blame differing memories,
change the subject, and express annoyance at having your facts challenged.
Second, regarding your assertion, that the evidence supports a weak form of the Maldacena conjecture: arguably this is one of the most important points of science in the book, since it relates to string theory’s claim to be a non-perturbative construction of quantum gravity. Therefore it is reasonable to assume that your words “a weak form of the Maldacena conjecture” actually have some definite meaning. I know that your book does not cite your paper with Arnsdorf, you have not cited any scientific papers at all here. So I have gone to your various scientific papers in which you compare the status of different theories of quantum gravity, and the paper with Arnsdorf is the primary reference on this point. If this is withdrawn, not much if anything is left. I have found another “weak form” definition in your book, as I have noted, but this is tantamount to a full theory of quantum gravity, so it is not very weak at all. Now you say that you
“do suspect that there is a weaker conjecture that is consistent with all evidence, let me come back to that sometime when I have time to think it over carefully.” One would have expected that you would have thought it over when you made the original statement.
By the way, I think that you are wrong about where your paper with Arnsdorf went astray (unless in more than one point) – I believe that it was in inconsistent interpretations of the expression “fixed causal structure.” But if you are correct, that the problem is a limitation of the applicability of Rehren duality, then it must fail in any interacting QFT (because the interaction always produces refraction, which your argument forbids): this would imply that Rehren duality can hold only in free field theory. This would confirm my overall point of view, that it is easy to prove trivial things, and much harder to prove things that are physically interesting.
Third, regarding sociology: You say
Apologies, I hit `submit’ before fixing my formatting at the end:
This is exactly what you have done, and I have already pointed out where…
Yes, I know this, and it is why I am so perturbed to find my discussion of the existence of the CFT placed in this part, and characterized as a sociological argument, and a prime example of groupthink. The construction of quantum field theories is a deeply scientific subject to me, and one that I have given great thought. You may disagree with me (though I am rather certain that I have the science right here), but to dismiss this scientific issue as sociology and groupthink is outrageous. I find it particularly outrageous because many members of the public, and even some scientists in other areas, have accepted your claims throughout the book with remarkable credulity. Hence the effort I am making here.
To summarize, I am not picking nits here, but focussing on some of the most important points: your central historical story, one of the central pieces of physics, and a major sociological argument (and one that refers to me directly); however, this kind of exaggeration and manipulation of the facts runs throughout the book.
Smolin’s chapter 16 discuss a lot of interesting physics before proceeding to the (less interesting, in my opinion) sociology. So it can be regarded as prestigious to be mentioned also in this chapter along with Maldacena, Mandelstam, Witten and others. Lee’s specific point is not convincing. Horowitz and Polchinski compared AdS/CFT to the Riemann hypothesis as being in the category “true but unproven”. This is a nice analogy which can be flattering to everybody. Lee’s specific point is that the Riemann hypothesis is a conjectured relation between two structures that exist mathematically. Somehow I do not think Lee’s distinction makes a lot of difference and I would not be surprised if there are important conjectures in the area of mathematics about relations between two structures which are not known to exist mathematically, and their mere existence is part of the conjecture. Anyway, my impression is that AdS/CFT for string theory is like the smile for the famous cat, which is present even when the cat itself cannot be seen. And maybe it holds a key for rigor as well.
Joe wrote about his attitude towards rigor that it is ” also partly a reaction to my own misspent youth. I used to focus too much on rigor and formalism, and have become a much more creative and productive scientist since learning, very slowly, to see through these to the physics.”
It is always interesting and moving to see people reflecting on their youth. Let me suggest that the years spent on rigor and formalism were not wasted, not only because rigor and formalism are important scientific values, but also because “learning very slowly to see through these to physics” correctly , may well depended on those years of struggle with them. It will be interesting to see Joe’s further reflection on this, say, in 2027.
Sean,
“One way or another, we are going to have to live with whatever is true. The universe doesn’t care whether we can predict the mass of the muon or not.”
The problem with the landscape is not that it doesn’t allow us to predict the muon mass but that it doesn’t allow us to predict anything at all. There is zero evidence for the kind of “correlations” you mention: no reason for them to be there, and people who have done calculations looking for them haven’t found anything useful. Similarly for a “cosmological selection principle”.
Yes, we have to live with whatever truth the scientific method turns up. But what is going on here is not the scientific method. Instead we’re being sold a “theory” that can’t predict anything because a lot of people refuse to admit it has failed. This is not normal science.
Dear Eric,
I spent many years working on formulating a completely non-perturbative formulation of string/M theory, I have a strategy, which has led to some results (certainly non-rigorous). Here are some of the papers where these results were presented. hep-th/0003285, hep-th/0006137.hep-th/0002009, hep-th/0104050 (which I am most proud of), hep-th/0503140. Since you think this problem is the key to the landscape crisis I would hope you are working on it, I would be curious if you want to share your strategy and results.
On polarization, I don’t think there needs to be a polarization and it would be much healthier for science if there was none, which would mean that all approaches to quantum gravity would be considered the same general field, with people typically working on different approaches and being in research groups with people in other approaches, going to the same conferences etc. This is how we work in the quantum gravity world and we have often reached out to the string theorists to include them in our conferences and to support hiring them to balance our departments, institutes and research groups. I am not the only person in this world who has worked also on string theory and there are also instances, some very recent, in which people in LQG advocated or supported hiring string theorists. The polarization comes from people who want to promote one approach to a field of its own that works in isolation from the others, who do not reciprocate this openess and inclusiveness to approaches not their own.
To Joe and others,
I will try to reply in more detail later, but I am traveling for most of the next two weeks. So I will address only the “false prediction” issue. First, note that the wording on 153-5 is careful and shows some nuance. I emphasize “I don’t know of any particular string theorist who predicted that the cc could not be a positive number, but…” “Indeed there were theorems …AT LEAST AS LONG AS QUANTUM EFFECTS WERE NEGLECTED…” which is a fair characterization of Witten’s comments, from which I next quote. and then I stress, “In this case the optimists were correct.” I don’t think your comments do justice to the care and nuance here.
But I am also happy to say that were I revising the book I would stress that there were different views between 98 and 03 about whether the problem of making a string theory with a positive but tiny cc was a crisis or not. I have learned some things from this discussion which would certainly lead to a still more nuanced telling of this part of the story. However, I do not agree that there was no sense that this was an issue, because I have vivid memories of discussions with people who shared a sense of crisis over this issue.
Thanks,
Lee
Dear Professor Polchinski,
your answer about string vacua made sense to me. In my words:
The equations are simple, solutions may be complicated, this is, how good physics has always been so far. After all, the complexity of the world, we see around us, has to go somewhere. As you said, the better question to ask is probably, can those string vacua with positive CC occur naturally given the best cosmologic theories we have today. And I understand, the answer is yes, equally well as some simple string vacua.
May I bother you with another question?
What worries me, is, what Sean says:
“The universe doesn’t care whether we can predict the mass of the muon or not.”
To me it does not seem to be an indication of great optimism for string theory, that Sean mentions, what we might not be able to calculate without mentioning, what we are hoping to calculate, be it tomorrow or one day in the future. May I ask you, what you hope to calculate from string theory? As far as I understand, the theory has a huge space of adjustable parameters, so don’t we need a lot of predicitions (or maybe postdictions) to balance that? Is there hope to arrive at a string vacuum reproducing the particle spectrum we know about plus predicting some new particles, we will then see with our newest collider?
Mike,
String vacua are not trying to reproduce the complexity of the world, just the complexity of the SM Lagrangian, which is not very complicated. Actually, as far as I can tell, the equations that determine string vacua aren’t any simpler than those of the SM Lagrangian. What is going on here is not normal physics.
Good luck getting Sean or anyone else to tell you what predictions they expect to get out of the landscape. There are currently no landscape predictions about what the LHC will see, nor any reasonable hopes for getting any.
The Standard Model is pretty complicated. It’s based on the gauge group SU(3) X SU(2) X U(1), with three different gauge coupling constants, and with left-handed Weyl fields in 3 copies of tthe representation (3,2,+1/6)+(3bar,1,+1/3)+(3bar,1,-2/3)+(1,2,-1/2)+(1,1,+1), and a complex scalar field in the representation (1,2,-1/2). All Yukawa couplings allowed by the gauge symmetry must be included; this allows for three different 3×3 complex matrices of Yukawa couplings (though many phases can be absorbed by field redefinitions, leaving 13 parameters to be specified: 9 eigenvalues and 4 mixing/phase angles). The eigenvalues range over 6 orders of magnitude. No one knows why.
And all this yields exactly massless neutrinos. Neutrino masses require more fields and more parameters.
It’s not going to be easy for some extremely elegant theory to reproduce this mess. In fact, I know of no example in physics where an elegant theory has a big mess as the UNIQUE solution. On the other hand, it’s often possible to get a landscape of MANY DIFFERENT complicated solutions to nice equations (e.g., molecular dynamics). To me, the big sociological mystery is why we ever thought it was going to be different this time.
Mark,
The SM choice of gauge groups (U(1), SU(2), SU(3)) a list of 3 of the simplest Lie groups, the representations of the fermions are all in the simplest defining rep. The only thing about this which is slightly complicated is the U(1) hypercharge assignments. What is more complicated is the Higgs sector, the part of the SM we’re not happy with anyway. Almost all of the SM parameters are the Higgs Yukawas.
But “complexity” is a relative notion, and you’re completely ignoring my claim that the equations one has to solve in order to find the “vacuum state” corresponding to our world are at least as complicated if not more so than the ones that define the String theorists are misleadingly claiming to have a simple set of equations whose solution reproduces the “complicated” standard model. This just is not true. If you disagree, please show us explicitly the set of equations, over which variables, whose solutions give a fully stabilized vacuum state of a string theory whose low-energy limit looks more or less like the SM.
in previous comment there’s a “SM” missing, in “if not more so than the ones that define the SM.”
Peter claims: ” the equations one has to solve in order to find the “vacuum state” corresponding to our world are at least as complicated if not more so than the ones that define the SM”
So what? Are these equations required to be simpler? Is such a simplification always the case when a large, deeper, and more comprehensive physics theory includes an earlier theory of much more limited scope?
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I don´t know about everybody else, but in my browser comments below some point appear cut on the left margin. If that is a problem on the cosmic variance site I’d wish it could be fixed, as i is too bad to be unable to follow this very interesting discussion.
I would consider the explanation via quantum mechanics of the periodic table of elements to be elegant and simple (even though the detail is complicated). The entire “landscape” of chemistry and biology follows (in principle) from the same explanation. Yet it is not a landscape in the string theory sense, because there is a uniqueness to the explanation, we just cannot compute it. There are not twenty versions of water. I do call it a landscape because our ability to make pro-active predictions is rather limited (given physics one cannot predict the DNA molecule), but given a (chemistry) phenomenon, we can provide an explanation in terms of the constituent parts (given physics one can construct a useful account of the DNA molecule.)
String theory does not shine in any of these types of explanations.
More complex mathematical models for the physical world are justified if there is a pay-back in terms of solid predictions which can validate the need for the additional complexity. The nemesis of physics is the endlessly complex theory which makes no falsifiable predictions and is proudly defended for being incomplete.
Ockham’s razor (entia non sunt multiplicanda praeter necessitatem): “Entities should not be multiplied beyond necessity”.
String theory multiplies entities without necessity. Where is the necessity for anything in string? If there is no falsifiable prediction, there is no necessity.
Don’t get me wrong: I’m all for complex theories when there is a pay-back for the additional complexity. In certain ways, Kepler’s elliptical orbits were more ‘complex’ than the circular orbits of both Ptolemy and Copernicus, oxidation is more complex than phlogiston, and caloric was replaced by two theories to explain heat: kinetic theory of gases, and radiation.
These increases in complexity didn’t violate Ockham’s razor because they were needed. Maxwell’s aether violated Ockham’s razor because it required moving matter to be contracted in the direction of motion (FitzGerald contraction) in order for the Michelson-Morley experiment to be explained. This was an ad hoc adjustment, and aether had to be abandoned becaus it did not make falsifiable predictions. Notice that Aether was the leading mathematical physics theory of its heyday, circa 1865 when Maxwell’s equations based on the theory were published.
String theory has not even led to anything predictive like Maxwell’s equations. String theorists should please just try to understand that, until they get a piece of solid evidence that the world is stringy, they should stop publishing totally speculative papers which saturate the journals with one form of speculative, uncheckable orthodoxy which makes it impossible for others to get checkable ideas published and on to arxiv. (Example: Sent: 02/01/03 17:47 Subject: Your_manuscript LZ8276 Cook {gravity unification proof} Physical Review Letters does not, in general, publish papers on alternatives to currently accepted theories…. Yours sincerely, Stanley G. Brown, Editor, Physical Review Letters.)
Publius, it happens for me (margins clipped) only with Internet Explorer. As some would say, find a real browser, like Firefox.
My problem with the margins disappeared when I upgraded from IE6 to IE7, which is freely available from M$.
Dear Prof. Polchinski, regarding the side issue of rigor:-
This is not my favourite piece of mathematical physics either;- I am not so convinced by the approach of lattice QFT. This illustrates a central problem for mathematical physics, in that the same piece of physics may have many different ways of being made rigorous. The physics produces a set of structures in an ill-defined framework, so there may be several rigorous frameworks in which the physics structures can be realized. Nevertheless, this work needs to be done in order to analyze the physics structure properly, and to find the most appropriate formal framework for the physics.
I agree that we lag very far behind in making established physics rigorous,- the burning example is of course the standard model (or even its component theories e.g. quantum gauge theory). As physics, the standard model functions pretty well without any rigour. But we do not fully understand it until it has been made rigorous (and hence cannot extrapolate it confidently into new areas). Establishing a rigorous standard model is still a work in progress, although already a great deal has been learned from analyzing some of its components.
A bit of a tall order, but since the original claim was that string theory can benefit from the rigorous approaches, I’ll write something in this general area. Formally, the (free open bosonic) string is defined as an infinite collection of quantum oscillators together with a set of gauge transformations (generated by constraints). This abstract structure can easily be encoded in terms of a C*-algebra with the action of the group of gauge transformations on it (cf. Commun. Math. Phys. 156, 473-525 (1993)). Now in the usual approach to strings the algebraic structure of strings is realized (quantized) as operators (a) on Fock space, and (b) with a normal ordering convention. This creates two problems: first, the constraints acquire a central term (anomaly) which makes them second class, hence they cannot be satisfied. Second, the Fock complex structure is not left invariant by the gauge transformations. These problems lead then to a range of further choices, e.g. a maximally commutative set of constraints is selected and imposed as `weak’ constraints. Since these still do not have a solution due to continuous spectrum problems, a Gupta-Bleuler method of imposition is taken, and this leads to the dimension 26 requirement for positivity of the final space. These problems can be circumvented by a different choice of representation of the original algebraic system. Such representations are available to you because this is an infinite dimensional canonical system. Even if one takes the reduced set of constraints, one can avoid Gupta-Bleuler (and indefinite metric) by selecting other representations in which the constraint condition makes sense (see the paper http://arxiv.org/abs/math-ph/9812022 for this). I suspect that the dimension 26 requirement is purely due to the incompatibility between the Fock representation and the gauge transformations. Even Mickelsson found this requirement early in Commun. Math. Phys. 112, 653-661 (1987) when he took the orbit of Fock structures generated by gauge transformations and considered Diff S^1-invariant sections of the bundle of Fock spaces. So, if one abandons the Fock representation, I think the dimension 26 restriction may be lifted.
(My apologies for the references to my own papers above;- it is just that I know their contents the best).
Dimock has a few papers on strings, in e.g. http://arxiv.org/abs/math-ph/0102027v1 he constructs a rigorous covariant free bosonic string as an operator theory (this is not new, it is already in Commun. Math. Phys. 156, 473-525 (1993)). The constraints cannot be satisfied due to continuous spectrum problems, so, to satisfy them he picks out certain components of an integral decomposition of his Hilbert space which implies a mass quantization for the string. As for Wiesbrock, he takes an idea of Witten in Nucl. Phys. B 268, 253 (1986) that for interacting strings the splitting and joinings define a groupoid structure. In Commun. Math. Phys. 136, 369-397 (1991) Wiesbrock constructs a C*-algebra which carries all the representations of this groupoid. A review of this paper is at Commun. Math. Phys. 156, 522-525 (1993). Rehren has a more descriptive paper of his work at http://arxiv.org/abs/hep-th/9910074v1.
“As physics, the standard model functions pretty well without any rigour. But we do not fully understand it until it has been made rigorous (and hence cannot extrapolate it confidently into new areas).”
I do not understand how you can make such a statement. The Standard Model breaks down at the scale at which the Higgs self interaction develops a Landau pole. No amount of mathematical rigour is going to help you “extrapolate it confidently” into the energies above that.
So, if one abandons the Fock representation, I think the dimension 26 restriction may be lifted.
Bad idea. It is an experimental fact that energy is bounded from below. Hence you need representations of lowest-energy type!
It is an important but not very widely known fact that conformal anomalies have been observed experimentally, at least in computer experiments. The free energy per unit length in a infinitely long strip of width L acquires a universal correction proportional to c/L, and this prediction has been confirmed. More generally, the central charge couples to length scales, e.g. the cosmological constant.
I suspect that the dimension 26 requirement is purely due to the incompatibility between the Fock representation and the gauge transformations.
Anomalies have a beautiful geometric interpretation. I don’t understand how some algebraic understanding of field theory could vitiate this understanding and magically cause anomalies to disappear.
96 invcit
If the initial assumptions of the SM are made clear, and it is rigorously constructed (hence without contradictions) then it cannot “break down” in a logical sense. So it can be applied wherever its assumptions hold, which is what I meant by “extrapolate it confidently”. It becomes then a purely experimental matter to determine its domain of physical applicability.
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97 Thomas Larsson on Jun 3rd, 2007 at 9:13 am
An “experimental” fact can only give you a requirement on your final physical system i.e. after constraining is done, not before. So the defining representation has a lot of freedom in it. In fact, in our treatment of Gupta-Bleuler in http://arxiv.org/abs/math-ph/9812022 we did obtain Fock representations on the final physical algebra, but the important fact is that these representations did NOT come from an initial Fock representation.
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98 Aaron Bergman on Jun 3rd, 2007 at 9:19 am
A bit hard to answer in this generality;- If you look at the Carey-Ruijsenaars paper, anomalies are there obtained by the twist of quasi-free second quantization. These anomalies definitely need not appear in other representations.
Sorry, nested blockquotes didn’t work;- here’s a better rendition of my response to Thomas Larsson above:
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97 Thomas Larsson on Jun 3rd, 2007 at 9:13 am
An “experimental” fact can only give you a requirement on your final physical system i.e. after constraining is done, not before. So the defining representation has a lot of freedom in it. In fact, in our treatment of Gupta-Bleuler in http://arxiv.org/abs/math-ph/9812022 we did obtain Fock representations on the final physical algebra, but the important fact is that these representations did NOT come from an initial Fock representation.