I am often surprised at the level of disdain and resentment with which string theory is viewed by non-string-theorists. I’m thinking not so much of people on the street, but of physicists, other scientists, and even other academics. As a physicist who is not personally identified as a string theorist, I get to hear all sorts of disparaging remarks about the field from experimental particle physicists, condensed matter physicists, astrophysicists, chemists, philosophers, and so on. I sometimes wonder whether most string theorists understand all the suspicion directed against them.
It shouldn’t be like this. String theory, with all of its difficulties, is by far the most promising route to one of the most long-lasting and ambitious goals of natural science: a complete understanding of the microscopic laws of nature. In particular, it is by far the most promising way to reconcile gravity and quantum mechanics, the most important unsolved problem in fundamental physics. At the moment, it’s a notably incomplete and frustrating theory, but not without genuinely astonishing successes to its credit.
The basic idea is incredibly simple: instead of imagining that elementary particles are really fundamentally pointlike, imagine that they are one-dimensional loops or line segments — strings. Now just take that idea and try to make it consistent with the rules of relativity and quantum mechanics. Once you set off down this road, you are are inevitably led to a remarkably rich structure: extra dimensions, gauge theories, supersymmetry, new extended objects, dualities, holography, and who knows what else. Most impressively of all, you are led to gravity: one of the modes of a vibrating string corresponds to a massless spin-two particle, whose properties turn out to be that of a graviton. It’s really this feature that separates string theory from any other route to quantum gravity. In other approaches, you generally start with some way of representing curved spacetime and try to quantize it, soon getting more or less stuck. In string theory, you just say the word “strings,” and gravity leaps out at you whether you like it or not.
So why wouldn’t anyone be happy about string theory? For one thing, we don’t understand the theory very well. It’s easy to say “replace particles with strings,” but quantum field theory isn’t really about “particles” — particles are just the observable momentum eigenstates in a perturbative regime, not the fundamental building blocks of the theory. At this point it’s a little unclear what the fundamental building blocks of string theory are; there are some reasonable proposals for complete non-perturbative definitions of the theory (matrix theory and AdS/CFT, for those in the know), but connecting these formulations to a more complete picture isn’t easy.
But most of the grumbles about string theory from other physicists aren’t about a complete non-perturbative definition of the theory — they are about the lack of connection to experiments. One often hears that string theory simply makes no predictions, but that’s clearly false. If you scatter two particles together, string theory unambiguously predicts that the cross-section should look stringy, not like that of fundamental point particles. [With caveats discussed in the comments.] The problem, of course, is that the difference between these two possibilities is only noticeable when the energy of the collision approaches the Planck scale (or really the string scale, likely to be similar) — fantastically far away from what we can actually reach in accelerators. So string theory makes predictions, it’s just that we are as yet unable to test them. In other words, string theory is either right or wrong, it’s our challenge to come up with clever ways to figure out which.
There is a matter of principle here that scientists, of all people, should understand. To wit, our current understanding of nature — based on classical general relativity and the quantum-mechanical Standard Model of particle physics — is simply incoherent. It just doesn’t make logical sense. It is very easy to ask questions to which we don’t know the answer: “What is the gravitational field of an electron?” For that matter, since the Sun is made of elementary particles, we can’t even sensibly talk about the Sun as simultaneously a source of gravity and as a source of light and heat. This is not acceptable. Our goal as scientists is to understand how the world works, and relying simultaneously on theories that are deeply incompatible with each other is nothing to be happy with. Even if it won’t help us make a better TV set or understand the mass of the proton, we need to have a coherent theory of quantum gravity.
Recently there has arisen another sense in which string theory purportedly makes no predictions, associated with the “landscape” of possible string vacuum states. Just as in quantum field theory, the observable spectrum of low-energy string excitations and their interactions (that is to say, particle physics) depends not only on the fundamental string physics, but on the specific vacuum state in which we find ourselves. String theory predicts more spatial dimensions than we directly observe, so one of the characteristics of our vacuum is the way in which the extra dimensions are hidden from our view. It now seems quite plausible that the number of possible ways for this to happen is enormous — perhaps 10500 or so. If true, this puts a damper on the hope that string theory would predict a unique vacuum state, and we could explain (for example) the ratio of the muon mass to the electron mass from first principles.
Well, too bad. It would have been great to make such predictions, but the inability to do so doesn’t render string theory non-scientific. The appropriate comparison for string theory is not to “the Standard Model of Particle Physics,” it’s to “quantum field theory.” Nobody complains that there are a huge number of possible quantum field theories, and we actually have to go out and measure the properties of actual particles rather than calculating them using pure thought. If string theory turns out to be the same way, that’s life.
My own view is that string theorists have been a victim of their own characteristically aggressive form of optimism. Not only, we are told, is string theory a consistent theory of quantum gravity, but it’s a theory of everything, gives us wonderful new insights into gauge theories, and possesses a mathematical beauty that is so compelling that the theory simply must be correct. These kinds of arguments just don’t carry that much weight with the non-converted. If I were in charge of the string theory public-relations machine, I would be emphasizing over and over again the basic feature that we’ve understood for a very long time: it’s the most promising way we know to quantize gravity. If there were multiple very successful ways to quantize gravity, it would be important to distinguish between them experimentally; but so long as the number of successful models is less than or equal to one, it makes perfect sense to make every effort to understand that model.
Which is not to say that we shouldn’t also pursue alternatives. I’m all in favor of supporting research on loop quantum gravity, dynamical triangulations, causal sets, and whatever else smart physicists might personally find promising. As long as we don’t know what the correct theory is, individuals need to use their own judgment about what clues to follow. String theory, starting as it usually does from talk about perturbative excitations propagating in a background spacetime, will not seem especially compelling to someone who thinks that background-independence is the most profound feature of gravity. It’s certainly good to support plucky Apples and Linuxes in the face of the Microsoft-esque dominance of the string theory approach; you simply can’t tell ahead of time when someone will hit on a brilliant new idea.
On the other hand, string theory has thus far been fantastically more fruitful than any other idea. When you get into string theory, one of the things that keeps you going is that you don’t get stuck — the rate of progress waxes and wanes, but the progress is very real. It didn’t have to be true that the five string theories studied in the 1980’s would turn out to all be part of one big theory, but they are. It didn’t have to work out that the entropy of a black hole calculated from semiclassical gravity ala Hawking would be equal to the entropy of a corresponding gas of strings and branes, but it is. It’s clues like these that keep the believers moving forward, hoping to understand both the inner workings of the theory and its ultimate connection with what we observe. We interested outsiders should be cheering them on.
Bob,
First of all, I’m not talking about QFTs as effective field theories. Non-abelian gauge theories with a small enough number of fermions have perfectly consistent high energy behavior, and make sense at all energies. I understand perfectly the standard ideology these days about renormalizability not being a fundamental criterion and that QFTs are only effective theories valid at low energies for some more fundamental non-QFT. I just think it’s probably misguided.
When QED was first formulated in the late 1920s, it immediately explained very well a huge array of experimental data. No one knew how to handle loops, but as any experimentalist can tell you, you don’t need to calculate loops to get highly accurate approximate answers for just about anything they can measure. So, from the time it was written down, QED was a theory with very strong grounding in experiment. You could worry about its problems of principle and people did, but nature had told us incontrovertibly that there was something very right about the theory. It took twenty years to figure out how to handle higher order calculations, but during much of that time the physicists involved were not working on this, but either trying to save their own skins or figure out how to incinerate cities. I think any analogy with string theory is ludicrous. After more than twenty years of full-time work by thousands of physicists, there is still not a single connection to experiment, and people are now devoting their efforts to more and more convoluted excuses for this situation.
I know perfectly well what the tree-level amplitude in perturbative string theory looks like. I just don’t think this allows you to say anything about what amplitudes for the conjectural full non-perturbative M-theory look like. It seems to me you’re trying to tell me it’s a “prediction” of string theory that you can ignore non-perturbative effects in this case, although you hope you can’t ignore them in determining the vacuum state of the theory. This doesn’t make sense.
Hi Ann,
I’ve always been careful to not “disparage the whole enterprise”, but to distinguish between those parts of string theory that have been fruitful (AdS/CFT, connections to QCD, mirror symmetry and other applications to mathematics), and those which have been complete failures (attempts to unify gravity and the standard model in terms of a 10 or 11 dimensional supersymmetric theory of strings, branes, etc.). The problem here is that the part of string theory Sean is promoting is the part that has failed.
While string theory has led to new insights about QFT, there has been a huge opportunity cost. Do you really believe that if Witten and thousands of others had devoted the time they have spent thinking about string theory thinking instead about QFT they wouldn’t have come up with something interesting?
I’m not interested in making it hard for string theorists to get jobs, but in making it possible for smart, young, mathematically sophisticated people who don’t believe in string theory to be able to get a job if they decide to pursue a non-string theory topic. While phenomenologists and string theorists can get jobs, I don’t see much place in the field these days for people with more formal, mathematical interests who don’t want to do string theory.
You say you wouldn’t “defend every paper” I’m supposedly using to disparage the whole field. Presumably we’re talking about the Susskind et. al. landscape stuff. What about not defending every one of them, but acknowledging that these things are not science?
The big problem with string theory is that it predicts a whole lot of things (most notably supersymmetric particles, branes and extra dimensions) for which we have little or no evidence, while predicting few things which we can compare to practicable experiments.
String theory does, as noted earlier, also suffer from being oversold. String theory has most definitely been sold as a means of determining fundamental particle masses in the standard model from first principles. Indeed, one of the main reasons people are driven to look for something deeper than the standard model at all is that abundence of constants that seem to have some sort of relationship, but precisely what that relationship is, isn’t terribly obvious. String theory doesn’t appear to have made meaningful progress on that front.
In contrast, quantum gravity theories that are focusing on backgrounds — the loop quantum gravity people, the dynamic triangulations people — are making at least comparable progress without a lot of the ugly sides of string theory. These provide quantum gravity paradigms in which a 4D macrouniverse emerges naturally, without having to use supersymmetric particles, maybe even without having to have a graviton at all. Those theories are just starting to develop, just a string theory is still not a really mature theory, but they seem likely to have more testible predictions. LQG proposes that neither the Big Bang or Black Holes are true singularities, and most of the background oriented theories call for a non-abelian gauge field that for sub-Newtonian effective field strengths at short ranges, and super-Newtonian effective field strengths at very long ranges (in a bit of an analogy to QCD). These are things we can be tested macroscopically, and one would expect that a quantum gravity theory, be it stringy or not, ought to have so macroscopic manifestations. In the same way, while QED occurs at tiny scales, you can do simple inteferrence, oil slick rainbow and tunnelling experiments that tease out its distinctive properties.
String theorists also come across, rightly or wrongly, as remarkably tone deaf to developments to other fields of physics that could be pointing us in the right direction. Where are the string theorists pointing us to places to look for CP violations? Where are the string theorists explaining in advance that neutrinos must have mass?
We’ve had some of the brightest people in the world looking at the math for thirty years without much in the day of conclusive answers. This is the sort of thing that doesn’t happen unless a piece of the puzzle is missing.
Extraordinary claims require extraordinary proof, and string theory definitely makes extraordinary claims while offering little by way of proof.
String theories also, and the original post here is no exceptions, have done a poor job of pinning down what the theory says so far. One of the sociological reasons that the standard model has taken such prominence in the minds of educated laymen is that it has offered up a “small catechism” of what it does say, in the form of a big “periodic table” style document, the Feynman diagrams, and a fairly spare theoretical framework.
If String theory is to get wider acceptance with the educated public, it needs to be able to offer more of a catcheism of central points that string theory has established, rather than simply saying “its great and beautiful and it does everything, trust me.”
Hi Peter
I am saying it now seems just as silly to say one “doesn’t believe in” string theory as it is to say one doesn’t believe in QFT. It is such a demonstrably useful tool that I would indeed be suspicious of a formally inclined theorist who refused to use it as some matter of principle. To say one doesn’t believe in all the nonsense ond hype of the 80’s about how one will use string theory to calculate all the parameters of the standard model and make predictions about what lies beyond is different, but practically noone does believe in that stuff anymore. Some people still think a supersymmetric extension of the standard model will be verified by LHC, but that is a perfectly testable and scientific theory. It does mesh well with how some people think string theory will unify gravity, and I view that model as a spinoff of string theory, not the most interesting but reasonably well motivated. Personally, I think “believing in” speculative ideas which do not yet have sound experimental evidence is nutty, but I think one can and should do research on them.
( I must admit I pretty much agree with you, (and Lubos!) about the papers on ‘predictions’ from the landscape. Such papers are not a big part of string theory however, despite the impression one might get from reading your blog, and in particular, hardly any young people are involved.)
Ann
“When QED was first formulated in the late 1920s, it immediately explained very well a huge array of experimental data. No one knew how to handle loops, but as any experimentalist can tell you, you don’t need to calculate loops to get highly accurate approximate answers for just about anything they can measure.”
But you knew you *should* calculate loops, and that if the theory made sense then so would those calculations. There were plenty of examples in QFT where loop calculations seemed to not make sense. Should everyone have been willing to overlook that? Now, I know that QED also agreed with a lot of observations (all of them), and it was data and not an appeal to unifying gravity and quantum mechanics that buoyed the hopes of researchers trying to reconcile the obvious applicability of QED with the mathematical uncertainty of the techniques it entailed. But if all you had was tree level QED, would you be satisfied with that? I thought we were talking about quantum field theory.
“It seems to me you’re trying to tell me it’s a “prediction” of string theory that you can ignore non-perturbative effects in this case, although you hope you can’t ignore them in determining the vacuum state of the theory. This doesn’t make sense.”
I haven’t made any claims about predictions, with or without quotation marks.
But I don’t understand your argument here. There are plenty of physical processes in field theory that are described perturbatively, and there are other phenomena in the same theory which are inherently non-perturbative. Are you saying that if there is any question for which non-perturbative physics is important, then I should be suspicious of all perturbative results in that theory?
If your argument is that we should never do theory in any energy range beyond those we can probe in the immediate future, then fine. We can agree to disagree.
Bob
Hi Ann,
I agree with you that it doesn’t make sense to just say one “doesn’t believe” in string theory. It certainly is a non-trivial and interesting structure, with important connections to QFT and mathematics. But it does make sense to say one doesn’t believe in the specific conjecture that launched the whole business in 1984 and that has been hyped continuously since then. This is the conjecture that, at a fundamental level, the world is decribed by a superstring in the critical dimension (10), or its extension to M-theory.
I don’t think the people working on the landscape are fools, abandoning science for no good reason. I think they’re doing it because that’s the corner they’ve been backed into by the conjecture they refuse to give up on. Over the last couple years, I’ve found it incredibly shocking to see the lengths to which smart people will go rather than admit than something doesn’t work, one reason I’ve gone on about this quite a bit in the blog. String theorists desperately need to change the way they do business, starting with an honest evaluation of where the subject is, what works, and what doesn’t.
Bob,
Of course I’m not saying one shouldn’t do speculative work on things which we can’t test experimentally in the near future. Hey, I work in a math department and happily spend lots of time thinking about stuff that has no possible connection to experimental physics. I’m not a phenomenologist like Ann, and I think what particle theory needs is to encourage people to spend time thinking more deeply about QFT, not worrying for a while about how to connect up to experiment. String theorists are encouraged to do this kind of thinking and have come up with interesting things because of it. But if the road to progress beyond the standard model requires deeper insights into QFT that don’t have anything to do with string theory, we’re not going to get there as long as only string theorists can get jobs doing speculative work.
But when one chooses what speculative idea to work on, one needs to have something that tells one when one is on to something. In the case of QED, the fact that tree-level worked so well meant that speculating about the full theory was a very well-motivated thing to do. Speculative work in string/M-theory hasn’t been able to get any evidence from experiment that it’s the right direction to be going in. This seems to me reason to be skeptical that it’s the right direction, and seeing how things have gone the past twenty years appears to me convincing evidence that it’s a wrong direction.
My comments about perturbative string amplitudes have to do with Sean’s original claim that they are a “prediction” of string theory. I just don’t think such a claim is consistent with the whole string theory research program, in which the idea that there is some unknown non-perturbative version of the theory that will explain low energy physics plays a large part.
Peter
It makes no sense to say that one believes in or doesn’t believe in “the conjecture that at a fundamental level, the world is decribed by a superstring in the critical dimension (10), or its extension to M-theory.” There is no way to test that conjecture as it stands because the physics implied by that conjecture at experimentally accessible energies is nearly infinitely non-unique. Everyone admits that now.
One can however, formulate more extended versions of the conjecture, with some specifications of what is to be done with the extra dimensions, the supersymmetry, the role played by branes, fluxes etc. Perhaps one can use very early cosmology to motivate some such extended version. In the end one has some effective field theory which one can test. I’m not a huge fan of such “string phenomenology” but I admit the resulting effective theories of physics beyond the standard model are sometimes interesting in their own right, particularly when they involve concepts like supersymmetry or D-branes that particle theorists otherwise would not have thought of. If some such model turns out to be verified at the LHC I would not view that as evidence for string theory, but rather as vindication of string theory.
So one cannot test “the conjecture”, unless it turns out that the string scale is much lower than the Planck scale , or that some superstrings are observable cosmic strings, or that decoupling actually fails in some subtle but observable way. It is not a useless conjecture however, since it has inspired some good ideas. The fact that it also inspires some bad ones isn’t really the fault of string theory. There are many more bad ideas out there which were not string inspired.
You could blog about the bad papers some people are writing in any subfield of theoretical physics.
Man, you try to go do some work and people fill up your blog with comments. Most of which are great, by the way, thanks. Bob has done a good job of expressing the perspective of a real string theorist, Ann has put her finger on why a phenomenologist might be impressed with string theory, and Peter W. as always mounts a staunch critique with good points. The one sociological point of Peter’s with which I might completely disagree, which I don’t think has yet been challenged by anyone, is the idea that “many of the people doing it have become discouraged or even left the field.” That hasn’t been my experience at all — people will grumble good-naturedly that things have been relatively quiet and it’s about time for another “revolution,” but seem largely still just as excited and optimistic as ever. Probably we have been interacting with different string theorists.
As far as substantive points are concerned, I guess I need to clarify my point about making predictions about scattering. As Bob mentions, string amplitudes differ in being “softer” in their high-energy behavior than point particles. (Joe, yes there are explicit expressions here; I’m not really the one to give you a relevant example, perhaps a real string theorist will help you out.) My point was that in principle you don’t need to go to “ten times the Planck scale” to see these differences; with arbitrarily precise experiments, you could see them at low energies. Such precision is completely out of reach, of course, but that’s not string theory’s fault.
I don’t really understand the harping about non-perturbative effects. They might indeed be important in choosing which vacuum we live in, just as they are in field theory. That doesn’t mean we can’t make any predictions that are safely within the purview of perturbation theory. Scattering well below the string scale would seem to be one example.
I think I disagree with Ann’s pespective in the last post, although perhaps our disagreement is purely semantic. The thing that everyone admits is that it will be hard/impossible to uniquely derive a low-energy effective field theory from string theory. (Probably “everyone” is an exaggeration.) But I think there is some conjecture that amounts to saying “string theory is the correct description of quantum gravity,” which is either right or wrong. (And the correctness of which can only ultimately be decided by experiment, whether or not those experiments are ones we know how to do.) It’s hard to formulate precisely what the conjecture should be (at least for me), since we don’t understand string theory perfectly. I’m guessing that it would involve the stringyness of perturbative processes in quantum gravity. Any experts want to take a stab?
I hope that at least many people understood the connotations of the title of the post. It’s a variation on an essay by Steven Weinberg, “Two Cheers for Reductionism.” The point is that two cheers is a good number of cheers, but is not quite three cheers, which would be really good.
Hey Sean, first a user-interface complaint: I just wrote a comment, hit submit without first putting in my name, and e-mail. An error message then appears, and the comment vanishes irretrievably. Ah well, I’ll try again.
Ann,
I think there are two ways in which a conjecture can fail: it can predict something wrong or it can turn out to be vacuous and predict nothing. If you agree that the unification via string theory conjecture is consistent with just about any low energy physics, than my point of view is that is that it has failed for the second reason.
Honestly I know of no other scientific field in which leading figures are engaged in anything half as unscientific and bizarre as the landscape studies. This isn’t garden variety bad science, and I think the reason it isn’t is important and worth examining.
Sean,
Here’s a more specific version of my argument. Maybe I’m wrong about this, and if so would love to know why.
String theory perturbative scattering amplitudes are “softer” than field theory ones because they involve the exchange not of a single particle, but of an infinite tower of states with linearly rising mass. A field theory with a finite number of fields can’t reproduce this. But if you agree that the lowest energy state is determined by non-perturbative effects, shouldn’t this also be true of higher mass states? How do you know that higher mass states won’t turn into something inherently non-perturbative like black holes? But if this spectrum could be all sorts of different things, the scattering amplitudes also could be all sorts of different things. It seems to me that about all you can say is that they’ll probably somehow look different than field theory amplitudes. This isn’t much of a prediction….
Again, maybe this argument is wrong, but I’d like to know why…
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A few IMOs:
If one can live with the landscape in string theory, if that is just the way nature is, then one can live with fine-tuning in QFTs – that too, may just be the way nature is.
A good example to look at is a QFT that failed – SU(5) grand unification, I believe was quite pretty, predicted a rate for proton decay that wasn’t exactly experimentally accessible; but the experiments were done, no proton decay was found, and the theory was discarded. What is so perturbing about string theory is that I can’t see any way in which we can ever come to closure that it is wrong.
I don’t know enough of the history of physics, but I think the trend towards finding ingenious ways of retaining ideas that theorists loved but were not evident in nature started with supersymmetry. After that we’ve had a piling on of superstructure. Who knows, it may not come crashing down.
Peter,
I am not sure I really appreciate the problem, but let me try. String theory is calculable when the string coupling is small, and the volumes associated with compactification are large in string units. All recent models of flux compactification are of that category. When discussing the vacuum and its low energy excitations one is faced with the problem that all measurable quantities are extremely tiny compared to the fundamental scale (and furthermore they are model dependent). Therefore one is interested in tiny contributions such as non-perturbative effects (e.g to lift the moduli). This is very different from the vacuum structure in QCD where the coupling is large and non-perturbative effects are dominant.
In this scenario, if we had a luxury of collisions with stringy center of mass energy (or as Sean points out, sufficient accuracy), perturbative string theory has a definite qualitative feature which is universal- scattering will fall off exponentially with the appropriate kinematical invariant, rather than power law. This is of course only an approximation- the stringy tower will be truncated at high enough energies, and will consistes of narrow resonances rather than stable particles. However, these (perturbative and non-perturbative) corrections will be small. In this (really hypothetical) scenario one can falsify the whole class of perturbative string vacua all at once. In the real world one has to work harder.
best,
Moshe
“Bob has done a good job of expressing the perspective of a real string theorist,”
Actually, I just stayed at a Holiday Inn Express last night.
Hi Moshe,
I understand that there is a regime of small coupling and large volume where you expect to be able to calculate reliably and thanks for the explanation, I see your point about the vacuum choice involving small energies. But given that you don’t know what the non-perturbative theory is, can you be sure that non-perturbative contributions are under control?
In any case, I guess I still object to Sean’s claim of having a string theory prediction. It seems to me that if you only have a reliable calculational method for this very special regime, you can’t claim that the results you get from such calculations are predictions about the real world, where the string coupling or compactification volume may be such that non-perturbative effects are not small.
“But given that you don’t know what the non-perturbative theory is, can you be sure that non-perturbative contributions are under control?”
Because, just as in field theory, the strength of the leading nonperturbative effects can be estimated from the growth of large-orders in perturbation theory.
In weakly-coupled field theory the h-loop amplitudes grow like g^{2h} h!, leading to the familiar (instantonic) e^{-1/g^2} effects.
In string theory, the h-loop amplitudes grow like g^{2h} (2h)!, leading to stronger nonperturbative effects, of order e^{-1/g} . This is stronger than in field theory, but still controllably-weak at weak coupling.
We even have a good (but not great) understanding of what those leading nonperturbative effects are in may weakly-coupled string theory backgrounds.
There is, by now, a rather large literature on the subject…
Hi Scott,
So, I’ll throw my 2 cents in on the matters you posed above…
>So I have a question about the claim that ST predicts gravity that “you just say the word “strings,” and gravity leaps out at you whether you like it or not.” Does it simply predict the existance of a 2 spin, massless, chargless, ect particle or does it also predict that all particles emit and absorb this graviton based on their energy and momentum as expected?Also does the existance of a particle that is also predicted by all the failed quantizations of gravity really a good thing for a theory to predict?
Well, that’s a bit odd – the reply engine ate the majority of my post. Maybe bowing to the East three times will appease the computer gremlins… Okay, that done, let’s try this one more time…
Hi Scott,
So I’ll throw my 2 cents in on the matters you posed…
“So I have a question about the claim that ST predicts gravity that “you just say the word “strings,” and gravity leaps out at you whether you like it or not.” Does it simply predict the existance of a 2 spin, massless, chargless, ect particle or does it also predict that all particles emit and absorb this graviton based on their energy and momentum as expected?”
Simple bosonic strings can be described by a field theory defined on the string worldsheet where the action is dependent upon the metric h_{mn} on the worldsheet, the 2-curvature R_{2} of the worldsheet, and a dilaton phi (a scalar field on the worldsheet). If we demand that the worldsheet field theory is conformally invariant (scale invariant), then the so-called beta functions must vanish (this is necessary for us to gauge-fix the metric to the conformal gauge). This only happens in 26 dimensions for bosonic strings. Incorporating supersymmetry results in a dimensionality of 10 for the beta functions to vanish. Now, if you look at the spectrum of states for this bosonic string you’ll discover that one of the states allowed for a closed string is characterized by zero mass and spin 2 – one is very tempted to equate this state with the graviton. Also, open and closed strings can absorb and emit these spin 2 states – this implies that these states can behave like gravitons – and the way these spin 2 closed strings propagate is essentially identical with the way small gravitational distrubances propagate in GR.
Now, if our theory seems to be predicting graviton states on a flat background spacetime, one would naturally ask what happens if the background spacetime is curved, since gravity in a theory implies a potentially curved space. If the background is curved, then it has a metric which enters the field theory on the worldsheet as a set of couplings between the string coordinates. When we demand our beta functions to vanish in this case, we discover that one of the requirements for this to occur is that the Ricci curvature of the background metric and the second derivatives of phi vanish, or R_{ab} + 2D_{a]D_{b}phi=0. This is Einstein’s equation for a spacetime with scalar field. So, the simplest version of string theory has Einstein’s equation jumping out at you almost immediately, yielding more evidence that gravity is hard-wired into the guts of string theory.
Now, string theory also makes a prediction on how Einstein’s equation behaves when one gets close to the string scale. Above, a certain step was hidden when we went from beta functions vanishing to Ricci curvature popping out. This step was the expansion of the string coordinates in a perturbation series in the string scale. The lowest-order terms in the string scale expansion give rise to the Ricci curvature and scalar derivatives when the beta functions vanish, and leads us to Einstein’s equation. If we include the higher-order terms we find that Einstein’s equation picks up contributions of order alpha(R^(2n)) where alpha is the string scale and n=0,1,2,.. This description is only really valid in perturbative string theory when the spacetime curvature is small in relation to the string scale.
Modified versions of gravity similar to this have been investigated for many reasons, one of those reasons being an attempt to explain the acceleration of cosmic expansion without appealing to dark energy or its cousins (see Mark and Sean’s papers atro-ph/0306438 or astro-ph/0410031). While the actions they use do not result in field equations of the form given above for the stringy corrections to Einstein’s equation, their results do illustrate that even small corrections to standard gravity can have pronounced effects.
So, in short, string theory (both perturbative and non-perturbative) predicts Einstein gravity to lowest order, it predicts a particle state with all the properties and behaviours of the graviton, it predicts this graviton interacting with other particle states as well as with itself, and it predicts higer-order corrections to Einstein gravity that could be experimentally verified or rejected.
“Also does the existance of a particle that is also predicted by all the failed quantizations of gravity really a good thing for a theory to predict?”
As for whether or not the prediction of a particle predicted by other “failed” theories of quantum gravity is a good thing I’d have to say yes. From our past experiences with the Standard Model and quantum field theory we have very good reason to believe that gravity is carried by a massless spin-2 boson. The fact that string theory automatically predicts such a particle state is a Good Thing for any theory that strives to be a quantum theory of gravity. Also, no nails have been banged into the coffins of the other contenders for a quantum gravity theory, such as loop quantum gravity (LQG), dynamical triangulations, causal sets, twistors, etc.. These other theories are still young, just like string theory, and have their own problems, just like string theory. Some of the concepts from these other theories (holography for example) have cross-polinated with those of string theory, to the betterment of all the theories involved. Granted, theories like LQG don’t claim to be Theories of Everything. LQG began with the modest proposal of quantizing Einstein gravity with the fewest assumptions and guiding principles and has resulted in a theory that has made predictions that have been confirmed by string theory, such as black hole entropy. One of the challenges for LQG (and the other TOE contenders) is to work in matter and the Standard Model gauge groups better, as well as fix the dynamics of the theory via a working Hamiltonian constraint so that one can start making predictions as to how quantum gravity affects Standard Model physics, if at all.
It’s like meeting someone, the first impression never really dies, though it may eventually be overcome. The thought that a physicist could ever think that the mathematics of a theory is so beautiful that we don’t need to test it, it must be right… C’mon, we’re engaged in the project of describing the universe, not someone’s mathematico-aesthetic senses. Pretty much this claim is what permanently destroyed the street cred of string theory for the non-string theorists grinding an axe, and since the string PR machine hasn’t stopped, this caraciture hasn’t had a chance to go away. If someone could please pull Brian Greene off the lecture circuit, that right there will calm things down a lot. If you can’t tell me a way that we can someday test some version of string theory, which I can then turn around and explain to someone who is badgering me because that person has heard that I’m in physics so “What do you think of string theory?”, then you’re full of crap. It’s really as simple as that.
I think SuSy would have been discovered without String theory. It seems to me its a rather logical refinement and generalization of the algebra used in field theory, as well as one of the few ways to escape the tight leash the Coleman Mandula theorem stuck phenomonlogists in. I have no idea if its ultimately relevant, but it is a relatively simple and elegant idea that im sure a smart phenomenologist would have eventually contrived.
No one doubts ST’s usefulness in studying Gauge theories, or that it has produced very interesting spinoffs. For that reason alone it should always remain an active research program.
But as a full theory of gravity, well, I don’t know anymore (and I would love if all those great claims came true one day). Its certainly worthy of having people work in it, but I partially see Peters point that it doesn’t deserve to have such a complete and utter stranglehold on the industry.
The landscape stuff, if it remains as is, pretty much kills in my opinion the greatest purpoted benefit the theory offered, namely ‘no continous adjustable free parameters’.
Thats precisely the reason why so few study qfts in curved spacetime anymore. The problem ultimately was intractable and unpredictive, at least in so far as what we currently understand with the available tools. Yet who among us doubts that such a thing exists?
John Chunko,
Why do you demand that the worldsheet field theory is conformally invariant on the quantum level? It is not necessary for consistency, see the first line in section 2.4 of GSW:
“Classical free string theory can be consistently formulated for any spacetime dimension, but quantization with a ghost-free spectrum requires D <= 26.”
So the no-ghost theorem rules out D > 26, but not D < 26 (for the free string).
In the presence of a conformal anomaly, the conformal symmetry is elevated from a gauge symmetry to a conventional symmetry quantum mechanically. The same thing almost certainly happens to general covariance in 4D gravity, see e.g. Roman Jackiw’s gr-qc/9511048, p 20:
“What does any of this teach us about the physical four-dimensional model? We believe that an extension in the constraint algebra will arise for all physical, propagating degrees of freedom: for matter fields, as is seen already in two dimensions, and also for gravity fields, which in four dimensions (unlike in two) carry physical energy.”
Hi Jacques,
Thanks for the argument, although before I completely buy it I’d have to look up exactly what sort of assumptions on the behavior of the full amplitudes are implicit in it.
But this question about bounds you can get in the limit of small coupling doesn’t really have anything to do with my original objection to Sean’s “prediction”. If the real world is governed by a string theory, you have no particular reason to believe that the coupling is arbitrarily small. It’s some finite number, and for that finite number, non-perturbative effects may dominate. By “predicting” that the world is in a region of small enough coupling to be able to control non-perturbative effects aren’t you like the guy searching for his keys in the dark who “predicts” that they’ll be under the lamppost. Do you think it is legitimate to call this a “prediction” of string theory?
Hi John,
You say string theory predicts higher-order terms that can be experimentally verified or rejected. You seem to be claiming that one can falsify the theory this way. What exactly is the prediction for a higher order term, such that one can do a specific experiment and see if it is there? Don’t these higher order terms depend on the details of your compactification, etc., so that it practice you don’t have a specific prediction, but could get pretty much any result you want?
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Let me clarify why I think that the subcritical free string is so important, and why it gives a very strong reason why both string theory and LQG must be wrong, at least as theories of quantum gravity. As is well known, the free string is 2D gravity coupled to other fields, and as such it is natural to try to learn about quantization of general-covariant theories from it. The most striking thing is what happens to the constraint algebra:
* In 1D gravity (point particle), there are no gauge anomalies.
* In 2D gravity (free string), there are some anomalies. They can be shifted between the Weyl and diffeomorphism sectors, but they cannot be removed.
* In 4D gravity things become even more complicated, and one strongly expects there to be many anomalies. This is how I read Jackiw’s paper.
Now, when you quantize the free, subcritical string, you automatically construct a non-trivial, unitary rep of the Virasoro algebra. Conversely, if you for some reason could not construct such a rep, you would be unable to quantize the subcritical string. I think everyone can agree about that.
The situation in 4D gravity is completely analogous. Successful quantization will lead to diffeomorphism anomalies. If you cannot construct non-trivial, anomalous reps of the diffeomorphism group, you cannot construct the correct Hilbert space of quantum gravity, because it must carry such a rep. No such reps appear neither in string theory nor in LQG, and hence these are not the correct theories of quantum gravity.
What about the theorem which states that there are no pure gravitational anomalies in 4D? Such anomalies cannot arise if you quantize the fields alone; one must also add an explicit representation of the process of observation, and quantize the observer’s trajectory in spacetime along with the fields. This is mandatory, because the relevant anomalies (“multi-dimensional Virasoro algebra”) are functionals of this trajectory. If you don’t introduce the observer’s trajectory, you cannot write down the relevant anomalies, and you are in the same position as people who try to quantize the subcritical string without conformal anomalies.
This is the technical reason why I don’t believe in string theory.