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.
Somewhere in the above mass of comments, the owner of this blog made some basic comments about gauge invariance without mentioning charge conservation. This seems very odd to me.
-drl
Dear Sean,
Thanks for your comments and thanks also to everyone for the high level of the discussion. Thanks also for your supportive comments about alternative approaches to quantum gravity. But I believe you miss the key point, which is that there is good reason to believe that any acceptable quantum theory of gravity must be background independent. Those of us who work on “alternatives” do so because we find the arguments for background independence compelling, whatever the approach.
You mention that we don’t understand what string theory is. I find it compelling that any complete formulation of string theory must be background independent, and it does indeed seem to be possible to make progress in this direction. For years it has puzzled me to no end why it is not obvious to everyone in string theory-as it is obvious to those who pursue virtually every other approach to quantum gravity-that any quantum theory of gravity must be background independent. On top of this, there is an obvious reason special to string theory, which is that we know different solutions correspond to different backgrounds, so any theory they are solutions of must make sense prior to the specification of a background. The fact that, after huge investments of effort, both AdS/CFT and the matrix models have been only partly successful supports this. Very recently it occurred to me that we in quantum gravity base our conviction about background independence on arguments that may never have been spelled out in a context where string theorists could encounter them. So I’ve written a paper making the case for background independence that I’m about to post on the hep-th. Since I regard the arguments I’ve reviewed in the paper as compelling, I would be very interested to hear if some readers don’t.
So I would insist that the reason to support alternatives, is not just because it is the ethical thing to do. The only hope for string theory itself is to go in the direction that LQG, CDT and other background independent approaches have pioneered. In fact, contrary to your implication that these directions “soon get more or less stuck”, there are important recent developments in both LQG and CDT regarding hard problems including the emergence of classical spacetime. Even given the far fewer people and resources available for work in this area, progress since 1986 has been steady and cumulative, and never has been as rapid as now.
As for predictability, in spite of the good work being done on the landscape, it must be emphasized that it is a BIG DEAL to give up on the main claim and main goal of a theory, in this case uniqueness leading to a unique explanation of the standard model and unique predictions for future experiments. One can rationalize it, but I would hope only after serious reflection on the possibility that a theory that fails to deliver the goal for which it was pursued is just simply the wrong theory. The point of the formulation of the landscape that I gave many years ago was that a theory with many vacuum states could still be explanatory and predictive, but only under certain conditions, which I spelled out in my book and papers on the subject. Let’s be clear that the burden is on us, when we advocate a theory, to propose falsifiable and doable experiments, and to take them seriously, so we are prepared to abandon the theory if the experiments go against it. Otherwise, there is no possibility to settle the truth of the theory by rational argument from evidence, and nothing to prevent the scientific community from splitting into quasi-religious communities of true believers.
On Lubos’s comments, there are new proposals for unification within LQG. Crane et al have made some speculations in this direction. Look for new work coming soon, about this (already announced at several conferences) by Markopoulou and myself.
Finally, there are experiments in progress that probe the Planck scale, such as AUGER and GLAST. Does string theory make precise predictions for what these experiments will see, when they report in the not too distant future? I know of no paper that claims so, although naively one would expect string theory to predict that Poincare invariance is unmodified and unbroken. Do the experts agree that this is the prediction?
Lee Smolin
Fred(erik)
Sorry for mispelling your name earlier (I went with the french version), feel free to mutilate mine next time we meet. Nice post above, but I have to admit I for one am lacking a sense of crisis, maybe I have my head in the sand. If we had a very large number of realistic vacua (to start, non-supersymmetric ones) I might start getting worried…
(reminds me of a Woddy Allen line, on his death bed , to his wife, “we could have made love more often, or maybe once…”)
Of course, no way of knowing without looking, as you say.
Peter,
My comments about predictions were in the context of soft scattering etc., it has been a while since this thread started…
best,
Moshe
If you are trying to make friends and influence string theorists, Sean, two cheers is not nearly enough. Check out our friend Lubos, for example. String theory demands complete dedication – sort of like being in Stalin’s entourage. The first guy to stop clapping is the next guy on the train to Siberia.
It’s nice that string theory “predicts” gravity, but in the old days only stuff we didn’t already know counted as predictions.
Background Independence considered harmful (in obvious homage to Edsgar Dijkstra)
In response to Lee Smolin’s post emphasizing the fundamental importance of Background Independence, let me suggest the contradictory proposition, not directly contrary, that all empirical evidence better supports the idea that a special flat class of background is realized in Nature. That is, despite the observational confirmations of General Relativity predictions and the success of Inflationary ideas, it still appears that we live in a flat universe. The fact that quantum mechanics is so hard to formulate in curved spacetime may be telling us that we live in a universe that is necesarily exactly flat, not just approximately flat, or accidentally flat. Perhaps the universe is not background independent, but rather requires a flat background. I think current astronomical evidence supports this position, or at least does not contradict it.
I leave it to the experts to determine what this implies for String Theory vs. Quantum Gravity, but to me it appears to favor the String Theory approach.
Jim Graber
Nice quip, CIP, but note that it predicts not just gravity’s existence, but the fact that gravity is *quantum mechanical*, and a manner in which this can come about. This solution to one of the biggest problems of the 20th Century is one we did *not* know already.
Cheers,
-cvj
The key reason why quantizing gravity is hard is that people don’t understand the projective representation theory of the relevant diffeomorphism symmetry. There are many analogies: to quantize spin, you need to understand the reps of SU(2), in special relativity you need Wigner’s classification of Poincare irreps, in 2D phase transitions you need the irreps of the Virasoro algebra, etc.
This was a key motivation for my discovery of the generalization of the Virasoro algebra to several dimensions, and its lowest-energy representations. The reason why such reps had not previously been constructed is that one needs to resolve essentially the same problems as in quantum gravity; how to avoid infinities arising from ordering effects, how to single out a privileged energy direction in a diff-invariant way, etc.
What has prevented the acceptance of this discovery is the widespread belief that since the diffeomorphism symmetry is gauge in general relativity, only the trivial rep matters. People like Lubos Motl and Jacques Distler charmingly expressed this as “A gauge symmetry is a redundancy of the description, you idiot”, or something to that effect. But of course this is not true in the presence of anomalies. What is really funny is that the simplest counterexample can be found in the most elementary chapter of the string theory bible; it is explicitly stated in chapter 2 of GSW that the free, subcritical string is consistent despite the conformal anomaly c = 26 – D. Check it out for yourself.
The free string is of course very relevant to gravity, since it is nothing but 2D gravity coupled to scalar fields.
I wonder if many string theorists are unaware that the no-ghost theorem explicitly allows for consistent theories with conformal anomalies.
James, current experimental evidence implies that our universe is NOT flat at all, in fact quite the opposite, it looks DeSitter.
As for String theory, correct me if im wrong, but I always got the impression it was said the formalism was background dependant not necessarily b/c it was that way deep down, but rather it was merely the fact that it was perturbative at this time, read an approximation around a classical saddle point. If it didn’t admit such a thing, then its game over. Other than that, it is perfectly background independant in the sense that the metric is a dynamically varied variable in the action (indeed that has to follow since it is simply Einstein’s gravity + scalar fields + corrections)
The good thing about string theory is that upon quantization hard consistency checks seem to come out -ok- when different metrics are inserted, and the same fundamental forms of the solutions appear. In fact it might be surprising that those checks *do* come out correct at all, even when the nonperturbative regime is obscured.
The idea I guess would be similar to such a such a field theory being gauge fixed, where lorentz symmetry is not manifestly apparent (even if its there deep down), one has to work hard to show it.
Thanks for the interesting discussion. I am a niave experimentalist. I hope
someone can help me answer the following two questions:
1) What experimental or observation will invalidate string theory?
2) What are the unsolved problems in string theory (please answer this for
non-experts) and how will string theorists know that they have finished their
job of making a unified theory of all forces?
Shantanu
Lee– Thanks for commenting. The relative merits of LQG is another thing that I have non-expert opinions about, but it deserves its own discussion rather than to be subsumed by the string theory thread. My desire to support alternatives was not based on ethics, but on the desire to get the right answer, and the appreciation that string theory may not be it. I also am sympathetic to the need for background independence, but (as I mentioned in the original post) every road to quantum gravity has problems, and how we prioritize them is a matter of judgment. Hopefully we’ll find time to get to it properly soon.
Peter,
I don’t mean to imply that everyone should be studying String Theory. Just that even without immediate experimental tests it’s a subject worthy of in-depth study and it seems reasonable to devote a non-trivial amount of resource to it. It seems to me that whatever mathematical equipment we need to do Strings is likely to be similar to what we need to do all kinds of other things with quantum systems, and that even if no successful physical theory comes of it we’ll be in a better position to solve other problems of value.
I would like to repeat the question asked by Levi:
> A short question. If, as rumored, experiments show that gravity weakens
> at small distances, would this be a serious blow to string theory?
Perhaps Lubos, Jacques or some other superstring expert could answer it ?
If superstring theory is the only consistent quantum theory of gravitation,
then the effective potential should be known at least qualitatively.
Holy cow, been away for the weekend and I will need the whole week to catch up…
Two comments: Regarding strongly coupled strings: Unfortunately, 11D sugra is not enough as this is only the low energy limit like 10D sugra is the low energy limit to string theory. Doesn’t tell you anything about high energy scattering (for two reasons: It misses the higher modes, whatever they will be and it is not renormalizable, two sides of the same model). And this is worse than in low energy QCD, where one in priciple can compute on the lattice which captures non-perturbative effects. But there is no lattice string field theory (preferably for closed superstrings 😉
Regarding gravity getting weaker: This is bad since naive extra dimensions predict that at short scales Newton’s law goes like 1/r^(2+d) for d extra dimensions and thus gets stron faster for r->0. So, if the effect is real, it cannot be plain vanilla extra dimensions.
Lee Smolin:Finally, there are experiments in progress that probe the Planck scale, such as AUGER and GLAST. Does string theory make precise predictions for what these experiments will see, when they report in the not too distant future?
While I had notice these points also, I would like to say, such thoughts linked to my website would be one in which bulk consideration might warrent inspection to perspective views about that bulk?
Leading to graviton production seems a inevitable consequence, and Gia and those that would test the mirrors on the moon, help to exemplify these issues would they not?
Model consumption in string/M theory would have benefited those who saw more this way?
Wow Sean,
If tenure were to be granted based on one’s ability to generate meaningful discussion of mankind’s efforts to understand nature, you might have fared far better at the UoC! But thanks for making it possible for us amateurs to observe, as you professionals discuss the merits, and lack thereof, of the most advanced thinking on the planet.
I can almost imagine the reaction of an extra terrestrial type, from a more advanced civilization that long ago discovered how to explain the existence and properties of radiation, matter, and energy: “You guys are making this thing way more complicated than it needs to be!” he would probably exclaim. “Holy cow, the first thing all this confusion should tell you is that you are never going to get there from here. Go back to the beginning and start over.”
I also imagine that he would think that Smolin’s comment here is the most relevant, Sean, not the least relevant. His comment doesn’t have so much to do with LQG per se; it has more to do with the conjecture “that amounts to saying “string theory is the correct description of quantum gravity.” The relevant point is that Smolin understands that the background dependence of string theory is the issue that trumps all others. All this fuss about the landscape of possible vacuum states on the one hand, and the cheering for the “prediction” of “a [theoretical] massless two-spin particle, whose properties turn out to be that of a graviton,” on the other hand, become tempests in a teapot, when one understands that no background of space and time exists upon which it all must be based.
ET’s admonition to go back to the beginning and start over may be impossible advice for you erudite professionals, but for all of us uncommitted researchers, it’s most compelling. A space-time background is as essential to the formulation of classical and quantum physics as a floor is to a dancer. Take it away and we might as well sit down or go home. Perhaps, the time has come to realize that we can’t dance without Fock space and, therefore, must either find a new, background-independent, quantization, as Smolin et. al. have done, that comes with its own state space, or just sit down (or, alternatively, give Larsson’s ideas a try and seek a covariant way out.)
However, IMO, the background-independence issue is only symptomatic of the real problem with the quantum theory of spacetime. Afterall, the reason the current formulation is background-dependent is fundamentally grounded in the goal of Newton’s original research program: focus on the forces in order to describe nature in terms of a few interactions among a few particles. This goal itself assumes that the universe is best described as a container of matter, which has naturally lead to an exhaustive analysis of the container and its contents: the container of matter is filled with an aether, it’s a continuum of locations, it has 3+1 dimensions, it has 26 dimensions, it has 11 dimensions, etc. (BTW, has anybody read Chen’s 3+3 papers, “Equations of Motion with Multiple Proper Time,” (quant-ph/0501034,0505104,0506176))?
Chris W. recently wrote that he would find it interesting to read a “thoughtful exposition on the philosophical presuppositions underlying the string theory program,” which he found unlikely to emerge any time soon. However, going back to the beginning means going back to examine the “philosophical presuppostions” underlying Newton’s program, which is even less likely to emerge at this point, but Chris points to the crux of the matter at any rate:
“This intersects in my mind with the issue of how to evaluate and interpret quantization methods. Here again is a subject for which thoughtful philosophical discussion could be most illuminating. One might wonder why the formulation of a quantum theory should depend on “quantizing” a classical prototype at all. A key notion appears (to me) to be that in our currently accepted understanding of quantum theories, discreteness is a feature of certain solutions, and does not really reside in the fundamental assumptions shared by quantum theories in general. Indeed, quantum field theory is supposed to largely explain the origin of the discrete substructure of matter that was taken as a given* in 19th century and early 20th century physics. (* ..with notable exceptions, of course.)”
According to what ET tells me, Chris is right on. The idea of discreteness MUST reside in our fundamental assumptions of quantum theory, but the trick is, he says, don’t try to force this assumption into a substructure of space-time in the context of quantum gravity, but be smart and recognize what is staring you in the face: space and time don’t exist as a container (background); they are simply the reciprocal aspects of motion, nothing else.
What’s more, he tells me, you don’t need a background to define motion, you only need to understand that space progresses in the same sense that time progresses, and that the joint progression of these two are only the reciprocal aspects of what actually does exist, a universal motion. Start with this, he says, and you will find an absolute reference system of motion that will provide the background-independent state space you need.
Honestly, if we had been in a bar and I were a woman, I would have asked him to buy me a drink, and if he had demanded to know first, if I were going to have sex with him, I would have sworn that it was Feynman. I thought to bring up the subject of harmonic oscillators, but I was just too tired. This stuff plain wears me out, you know?
Well, with that, I guess the discussion is over. But 80 or so good comments is a heck of a run. It’s the best discussion of string theory I’ve seen so far on the net.
Robert,
I agree with your statement of course:
> naive extra dimensions predict that at short scales Newton’s law
> goes like 1/r^(2+d) for d extra dimensions and thus gets strong
> faster for r->0.
So do we have a test of string theory here ?
By the way, if M-theory/string theory is indeed a consistent quantum
theory of gravitation, then I would expect a stronger statement than the
naive argument. At least you should be able to state how much
(and at which scale) the effective potential deviates from Newton.
Again, I would expect that Jacques, Lubos or somebody else could
answer this question …
Levi, Wolfgang, and Robert
About If those experim experimental showing that gravity weakens at small distances. I will say next is not rigorous but is semiintuitive argument
Ignoring possible dependence on relative velocity, one obtains strong effective gravitational interaction to shorter distances.
Taking like good the rule 1/r^(2+d) for d extra dimensions (some recent RS brane model introduces Yukawa like exponential correction from extra 5th dimension), we can observe that smooth behavior is obtained formally with
d -2 for r –> 0 imply formally elimination of divergencies on (1/r^2) force strengh.
Message truncated by use of ilegal characters!!!!!
I repeat the basis of my reasoning
If experimental experimental showing that gravity weakens at small distances is correct we can derive it at least formaly from.
d negative on 1/r^(2+d) for d extra dimensions. It is interesting the chossing d = -2 for short scales (dimensionality in string M theory is fixed but is not in other approaches) because
i) It is compatible with recent advances in triangulations quantum gravity (hep-th/0505154).
ii) d -2 for r —> 0 imply formally elimination of divergencies on (1/r^2) force strengh since (1/r^2) —-> (1/r^0).
Smolin’s new paper on background-independence is available here: The case for background independence
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Since you seem to be counting, just keep in mind that you have 97, not 102…
(I just wanted to bring this thread back to the Recent Comments line)
I agree with Fredrik that studying the Landscape is very important.
It would be nice to find a smaller number of vacua, so that
predictions are possible. But we would only find out if this number is large or
small if people
study models carefully and find more and more controlled constructions.
A large number of vacua is
the only explanation we have today for Lambda in string
theory. Hopefully we will have a better one soon, but since this is
the best we have, it should be studied and I am glad that excellent people
are studying it.
Because I have no original thought of my own, but still wanted to contribute a comment to this post (if only to push the count closer to the magic 100), I thought the following quote by a master from the past, Emilio Segrè, might be considered relevant and not entirely worthless. I suppose you could think of it as one part of the explanation of why a quantum theory of gravity is proving such a tough nut to crack:
“The ultimate goal of physics is to describe nature and predict phenomena. It is impossible to do this starting with a priori theories; we would be stymied after a few steps, and every error would be compounded and would send us further from the right path. On the other hand, using experiments alone, we would soon be lost in a bewildering array of disconnected facts without any hope of making sense of them. It is the combination of theory and experiment, brought about by the use of mathematics as a language, that permits the astounding results physics has attained. It is Galileo’s immortal accomplishment to have clearly understood the power of this alliance and to have indicated ways of achieving it.”
[p. 61, Chpt. 4, “From X-Rays to Quarks: Modern Physicists and their Discoveries”, Emilio Segrè, (1980)]
Excellent comment. A quotation to guide us all. Thanks Ijon Tichy! -cvj