I have a long-percolating post that I hope to finish soon (when everything else is finished!) on “Why String Theory Must Be Right.” Not because it actually must be right, of course; it’s an hypothesis that will ultimately have to be tested against data. But there are very good reasons to think that something like string theory is going to be part of the ultimate understanding of quantum gravity, and it would be nice if more people knew what those reasons were.
Of course, it would be even nicer if those reasons were explained (to interested non-physicists as well as other physicists who are not specialists) by string theorists themselves. Unfortunately, they’re not. Most string theorists (not all, obviously; there are laudable exceptions) seem to not deem it worth their time to make much of an effort to explain why this theory with no empirical support whatsoever is nevertheless so promising. (Which it is.) Meanwhile, people who think that string theory has hit a dead end and should admit defeat — who are a tiny minority of those who are well-informed about the subject — are getting their message out with devastating effectiveness.
The latest manifestation of this trend is this video dialogue on Bloggingheads.tv, featuring science writers John Horgan and George Johnson. (Via Not Even Wrong.) Horgan is explicitly anti-string theory, while Johnson is more willing to admit that it might be worthwhile, and he’s not really qualified to pass judgment. But you’ll hear things like “string theory is just not a serious enterprise,” and see it compared to pseudoscience, postmodernism, and theology. (Pick the boogeyman of your choice!)
One of their pieces of evidence for the decline of string theory is a recent public debate between Brian Greene and Lawrence Krauss about the status of string theory. They seemed to take the very existence of such a debate as evidence that string theory isn’t really science any more — as if serious scientific subjects were never to be debated in public. Peter Woit agrees that “things are not looking good for a physical theory when there start being public debates on the subject”; indeed, I’m just about ready to give up on evolution for just that reason.
In their rush to find evidence for the conclusion they want to reach, everyone seems to be ignoring the fact that having public debates is actually a good thing, whatever the state of health of a particular field might be. The existence of a public debate isn’t evidence that a field is in trouble; it’s evidence that there is an unresolved scientific question about which many people are interested, which is wonderful. Science writers, of all people, should understand this. It’s not our job as researchers to hide away from the rest of the world until we’re absolutely sure that we’ve figured it all out, and only then share what we’ve learned; science is a process, and it needn’t be an especially esoteric one. There’s nothing illegitimate or unsavory about allowing the hoi-polloi the occasional glimpse at how the sausage is made.
What is illegitimate is when the view thereby provided is highly distorted. I’ve long supported the rights of stringy skeptics to get their arguments out to a wide audience, even if I don’t agree with them myself. The correct response on the part of those of us who appreciate the promise of string theory is to come back with our (vastly superior, of course) counter-arguments. The free market of ideas, I’m sure you’ve heard it all before.
Come on, string theorists! Make some effort to explain to everyone why this set of lofty speculations is as promising as you know it to be. It won’t hurt too much, really.
Update: Just to clarify the background of the above-mentioned debate. The original idea did not come from Brian or Lawrence; it was organized (they’ve told me) by the Smithsonian to generate interest and excitement for the adventure of particle physics, especially in the DC area, and they agreed to participate to help achieve this laudable purpose. The fact, as mentioned on Bloggingheads, that the participants were joking and enjoying themselves is evidence that they are friends who respect each other and understand that they are ultimately on the same side; not evidence that string theory itself is a joke.
It would be a shame if leading scientists were discouraged from participating in such events out of fear that discussing controversies in public gave people the wrong impression about the health of their field.
Damn! I missed making the 400th comment!
Gina, I have to say that I have to disagree with your comment that “there are very good reasons to say that string theorists are the theorists … There is something special about string theorists.” I think it’s clear that there are brilliant people in all areas of theory, and all areas of science, and all areas of human endeavor in general.
In one of his popular books, Feynman talks about almost getting into a bar fight, but then tensions are smoothly defused by another patron. “Every area has its geniuses,” Feynman says. (Or something like that: I’m relying on memory again.)
amused, I had decided not to point out that your strong-coupling expansion scheme didn’t make sense, but I’m happy to see that you noticed it yourself.
Now if only certain others posting here had similar powers of introspection …
Dear Thomas:
I got confused by your previous post #396. That is why I made my remarks. I’ll think some more about the last few comments.
Thomas,
I took a look at your paper math-ph/0603024, which in comment #28 you say contains a “no-go theorem for string theory”. Elsewhere, you’ve complained that this paper has been ignored.
Curiously, neither the abstract nor the conclusions of this paper even mention string theory. The abstract begins, “A local gauge symmetry can not possibly be a mere redundancy of the description, provided that 1. charge is nonzero.
2. we also consider divergent gauge transformations, whose brackets with local transformations contain global charge operators.”
I believe you have made a mathematical error in your discussion of Yang-Mills theory. The error consists of working on R^3 without specifying boundary conditions at infinity. Without boundary conditions, the theory is ill-defined.
We can supply boundary conditions by working on T^3 or S^3 (or any other compact manifold). Then the divergent gauge transformations are not present, because there is no r->infinity limit where they can diverge. Also, only the zero-charge sector exists; I cannot put a single electron on a compact manifold, because there is no place for its electric field lines to end.
So neither your first condition (nonzero charge) nor your second (divergent gauge transformations) holds when boundary conditions are supplied by working on a compact manifold.
“I think it’s clear that there are brilliant people in all areas of theory, and all areas of science, and all areas of human endeavor in general.”
Of course, I agree, Mark, and I even said so. Something special about string theorists is the required abilities (from the bulk of them not just the very best) to master so many things. One especially annoying aspect of the critique on string theory, in my opinion, was the fundamentally unfair critique of string theorists and the string theory community.
Mark, I agree that my no-go argument is not a theorem in the mathematical sense. There are also some tacit assumptions, e.g. that the gauge generators act as well-defined operators (possibly the zero operator) on a well-defined Hilbert space, something which presumably is not true in interacting QFT.
And yes, I ignore boundary conditions, but I don’t believe that the essential physics resides on the boundary. Besides, you may object to CFT on similar grounds. If you fix boundary conditions at infinity on the complex plane, it does not seem to be a good idea to apply conformal transformations with singularities there. This never stopped anyone from using the full Virasoro algebra.
Thus, I only have a heuristic argument, but it does suggest the existence of anomalies. That such anomalies are then found strongly suggests that my argument was essentially right in the first place.
Note that the Kac-Moody-like anomaly does not arise in QFT, because it is proportional to the second Casimir rather than to the third; the two types of extensions are contrasted in eqns. (12) and (13). It does arise in QJT, however. The reason is that in QJT, we quantize not only the fields but also the observer, and the relevant anomalies in all known representations are functionals of the observer’s trajectory.
It may be noted that the higher-dimensional affine algebra has appeared in string theory with a different physical interpretation, cf. hep-th/9511185. They also describe what happens globally and on the group level, something which I am unable to do.
Mark, thanks for giving me the chance to find that mistake on my own. (As a feeble excuse, my main interest in this stuff was with anomalies and index theory in the lattice model, and I never gave much thought to the more practical continuum limit issue before.) Related to this I have a physics question which maybe you or someone else can help me out with. What is the current status of the continuum limit issue in lattice QED? (It seems unrealistic to hope to get anywhere with the continuum limit issue in lattice formulation of the SM without properly understanding the lattice QED case first.) Lattice QED has two phases – a weakly coupled Coulomb phase and strongly coupled confining phase. So I guess the places where one could try to take a continuum limit are at the two boundaries of the Coulomb phase, namely e -> 0 and e -> e_c where e_c is the critical coupling separating the Coulomb and confined phases. I seem to remember reading somewhere that there is a possibility to take the continuum limit at e -> 0. But that seems wrong, since for small coupling we can use perturbation theory to find that the bare coupling e(a) as a function of the lattice spacing flows *away* from 0 for a -> 0. (This is the opposite of the situation in lattice QCD and is due to the fact that the leading term in the beta-function has the opposite sign.) That seems to leave e -> e_c as the only possibility for taking a continuum limit, but I never saw this possibility discussed in the literature… maybe there is some reason why it doesn’t work and lattice QED doesn’t admit a continuum limit?
Gina wrote:
“Something special about string theorists is the required abilities (from the bulk of them not just the very best) to master so many things.”
They are not alone, definitely.
Cosmologists for instance have to embrace almost every branch of physics, sometimes even chemistry and some other disciplines. Some cosmologists even embrace string theory besides all that. 🙂
There are multidisciplinary scientists who work in many disciplines in order to investigate a given problem.
But, yes, string theory deals with a lot of mathematics, if that is what you meant.
Christine
Gina wrote:
“There is something special about string theorists.”
Exactly! The question so hotly contested is whether that something special is good or bad for physics.
Mark asks (302), “The question I always come back to is, what if the landscape is essentially correct? That is, what if string theory is the correct theory of the world, that it has zillions of metastable vacua, and that inflation creates zillions of “pocket universes” (our universe being one of them), each with its own metastable vacuum?”
If everyone doesn’t mind going back to this, I would like to make two comments. First this is two hypotheses. String theory could have a vast landscape of metastable vacua whether or not eternal inflation is true. The first question, how do we do science if string theory-or any other candidate for unification- gives a vast ensemble of vacua, was the question I asked in my first book, Life of the Cosmos (1997). I agree with you, this is a key question. I think the answer, as developed in that book at length, is that we are still obligated to falsifiable predictions by which we can test our theory. I showed in that book and related papers that this can be done, in the context of the cosmological natural selection scenario (CNS).
Your second hypothesis is that eternal inflation is right. So far, when combined with the string landscape this does not yield any falsifiable predictions. I have explained in detail in that book and again in TTWP and recent papers why it cannot. Thus, I believe that while the string landscape may be true, its development within the eternal inflation scenario is problematic, because if there are no falsifiable predictions.
Nothing that has happened since publication of LOTC in 1997 has changed or challenged the conclusions given there. CNS is still the only cosmological scenario within which it is possible to make falsifiable predictions (and btw its predictions remain unfalsified.) Alternatives based on the anthropic principle have failed for exactly the reasons I explained they must in LOTC and papers since.
Now, you advocate, “strive to narrow down the possible string vacua that are compatible with the Standard Model (as amended, if necessary, by whatever is found at the LHC), and then to look for predictions common to this class.” My expectation would be that there are no interesting further predictions for accessible accelerator experiments, because I know of no reason the landscape should not evenly populate the space of standard model and post standard model parameters. The reason is the hierarchy problem itself. I see no reason why constraints imposed to get consistency at the Planck scale should imply any constraints on gauge groups, choices of fermion and scalar representations, and parameters of low energy effective field theories, apart from those that could be deduced by the principles of effective field theory, without string theory or quantum gravity. Nor is there any reason for eternal inflation, taking place at grand unified scales, to lead to probability distributions that favor any particular fine tunings in the standard or post standard model parameters.
One can always hope, but this seems to me a faint hope. Better I would think to spend our time investigating cosmological scenarios that immediately leads to predictions for standard model parameters.
Thanks,
Lee
Lee, and anyone else still here: What do you think of “modal realism,” the idea that every “logically possible universe” exists (or, that “existing” is not rigorously definable in any non-circular way anyhow, etc, as argued by Frank Tipler and apparently, Max Tegmark.) In such a case, there is no point in talking about string theory or any other such foundational business, since our world is just one of the infinite platonic universes…. However, there is a Bayesian self-selection problem that we would be unlikely to live in a possible world that had such consistency even if friendly to life, for there are “more” possible universes where the descriptions no longer follow the preceding order (just like there are more possible pixel arrangements that start out orderly, like a recognizable face, but then deteriorate into a mess, than the very few that are entirely recognizable.) Letting “everything” exist is more of a mess for that an other reasons, than its proponents realize or acknowledge.
Dear Christine, what I meant to say (but perhaps did not succeed) is this: String theorists individually and as a group are extremely impressive even if string theory itself will eventually somewhat disappoint us. (Yes, yes, cosmologists are great as well!)
Similarly, LHC is an amazing piece of technology and a great human achievement even if the outcomes will be somewhat disappointing. (And yes, yes, the Hubble space telescope is great as well!)
Dear all, crossing the 400 comments line is perhaps a time for some foundational issues. (In addition to a most welcomed discussion on the Cosmological natural selection scenario.) Do we really have a public debate as the title of Sean’s original post suggest? Below is some very indirect evidence for a negative answer. My argument is based on a (very preliminary) comparative study of two cities in California, Gilroy and Santa Barbara.
Gilroy is referred to as the “Garlic capital of the world”, indeed when you pass through Gilroy there are big signs stating precisely this. In Gilroy, you smell garlic everywhere you are offered garlic food at every corner, even garlic ice cream. It is not universally accepted that Gilroy is the garlic capital of the world: I heard of a city in Ohio with similar claims and I would not be surprised if some cities in Russia China or India can also be regarded as contenders to this highly desired title. Yet it seems that garlic is of central importance to the people of Gilroy as every visitor immediately realize.
I expected something similar in Santa Barbara when I visited there as a tourist some years ago. I expected big signs “Santa Barbara the physics capital of the world!” or at least “Santa Barbara – the land of the asymptotically free”. I expected to smell physics everywhere in Santa Barbara. I expected to be offered “QCD-ice cream”, to see “string bars” instead of the traditional “noodle bars,” or at least to see “open strings pomodoro” or “brane-lasagna” dishes in local Italian restaurants. In turn, the only thing remotely related to physics I saw in the whole one afternoon touristic trip to Santa Barbara was the sign on the highway: UCSB next exit.
In summary, my thesis is that this debate on string theory is not really a public debate and it is of interest just to a small part of the already very small academic swamp. In some sense, it is the projection of the serious and deep scientific debate within the string theory and high energy physics community itself on its shallow boundaries. (For a real public debate, we can try garlic.)
Dear Neil B,
I agree with you and deeply disagree with what you call modal realism, because I do not believe that mathematical objects and systems exist, in anything like the same meaning of existence that the physical universe exists. So I am a Platonist neither about mathematics or physics. I believe there is a lot of confusion generated by mixing notions of mathematical and physical existence, which has affected the notion of time in physics as well as notions of probability and possibility. This further corrupts how people try to think about the landscape, because they are tempted by the Platonic fantasy of timeless probability distributions on timeless spaces of mathematically possible universes. Eternal inflation restores the eternal timeless universe fantasy that GR superceded and suggests this confusion of mathematical and physical possibility. I suspect that these eternally static and infinite spaces of possible universes will come to be seen as quaint and theological as we now see medieval diagrams of the Ptolemeic universe with earth at the center and heaven above the stellar sphere. I very much admire Max Tegmark’s recent work about this because he takes to the logical reducto ad absurdum everything that I suspect is wrong with the Platonic notion of mathematical reality. My current project, with the philosopher Roberto Unger, is to sort this all out and give time, change and evolution central roles in cosmology.
Thanks,
Lee
Hi Gina,
I expected to smell physics everywhere in Santa Barbara.
This is funny 🙂 What do we learn from that? Strings don’t smell? When I was in Santa Barbara, I’ve been repeatedly asked if I know any Nobel prize winner, and if I’m working on that string stuff. I can’t say it happened all that often, but it happened (should stop reading papers at Starbucks). I have to say though that KITPs public outreach isn’t really impressive. This discussion is in so far public as that Peter, Bob and Paul from next door (and yes, also Alice) suddenly think they need to have an opinion about string theory and string theorists. When it comes to string theory, I find that not bad at all, it’s an opportunity to raise interest in theoretical physics generally. When it comes to string theorists, the issue among physicist is not whether or not the discussion is ‘really’ public, but how public they think it is – this does of course affect the way arguments are made, starting with complete denial of any problems, and is generally not beneficial for having calm discussions. I have to say that I don’t think blogs are really useful in this regard, neither do I think writing books is. I mean, seriously, what’s the next thing to happen? Regarding String Kings – someone is going to write a book praising the string community and deconstructing Loop-lers? Come on, that’s not going to work, we should really try to find a better way to deal with the present problems in research funding. Best,
B.
So you disagree with Sir James Jeans, who for decades in the first half of the twentieth century was credited with the false ‘discovery’ that the solar system was formed by massive tides in the sun. Jeans wrote in his book The Mysterious Universe (Cambridge University Press, 1930, reprinted many times) that God is a mathematician:
It’s then an small step for a Harvard string theorist to write sixty years later to claim: ‘Superstring/M-theory is the language in which God wrote the world.’
However, the problem for Jeans was that the special atomic numbers he lists aren’t special for reasons of pure mathematics. Those numbers aren’t primes or anything. Instead they come from quantum mechanics, with the way electrons are arranged in orbits according to phsyical effects like the exclusion principle. Jeans’ claim about radioactivity being just due to the atomic number being 83-92 was a complete deception.
Professor Eugene Wigner argued:
The role of maths in string theory contrasts with Wigner’s account of why mathematics is useful in physics generally. String theory spectacularly successful in explaining unobservables in terms of other non-observables: an example is how Nobel Laurate Brian Josephson was able to use string theory concepts without a single equation in his paper unifying ESP and what he calls the ‘special mental vacuum state’ used by string theorists when doing their mathematics, see: http://arxiv.org/abs/physics/0312012
Is there anybody else out there that believes that the reason for the existence of the landscape and extra dimensions is due to the fact that string theory starts with a classical object which is then quantized? The role of compactifcation is to eliminate these classical degrees of freedom. Perhaps if we had the correct quantum starting point rather than modeling things on a classical string + quantization+compactification, we would be free of the landscape. Presumably, this correct starting point would correspond to one of the string vacua, and we would be able to see how it is special if we ever find it.
Hi Bee, we seem to have converged on more or less the same opinion…I like the way you phrased it, indeed everyone seems to be in urgent need of a strong opinion. For something you are not an expert on and does not have direct influence on your life, wait and see approach seems to me sensible, but I’m sure I’ll be corrected…
It is sad though that this endless ongoing debate derails almost any discussion of either funding structures or string theory content (the actual physics), by mixing the two subjects together, such is life…we can always discuss garlic.
amused,
The standard lore is that lattice QED has a quasi-continuum limit (I’ll say what I mean by that in a moment) for any lattice coupling e_0 in the range 0 0 is only possible if you also take e(k) -> 0; that is, you can only get free field theory in a true continuum limit.
More interesting is what happens if you start with e_0 > e_c, and approach e_c from above, in the confined phase. At least some of the people, some of the time, thought there was an interesting continuum theory here; I once heard Mike Peskin remark that perhaps this theory would be useful in technicolor models. But today I don’t think there is an interesting continuum limit. You would like to get a spectrum of mesons and lightballs, but there is no guarantee that their mass ratios stay fixed as e_0 -> e_c. I think the most likely possibility is that these mass ratios all become infinite, and that the continuum limit is a free field theory of the lightest meson/lightball (which presumably has spin zero). Not too exciting.
Thomas,
I agree that the essential physics does not lie on the boundary at spatial infinity, but that’s just where your argument puts it! A robust argument would also work on a compact spatial manifold, and yours (as far as I can see) does not.
Incidentally, the analogy with the conformal plane of the string world sheet is flawed as well. The conformal coordinate z is to be identified as exp(tau + i sigma), where tau is euclidean time, and and 0 < sigma < 2pi is the periodic coordinate along the string (for closed strings). Therefore, z -> infinity is the same as tau -> infinity, and we typically do not want to impose boundary conditions in the infinite future.
At any fixed time (say, tau = 0), the usual Laurent-Taylor expansion of the stress tensor into Virasoro modes corresponds to an expansion into plane waves on the sigma circle. Then, with L_0 identified as the hamiltonian (the generator of time translations), the Virasoro algebra fixes the time dependence as well, and this yields the Laurent-Taylor expansion in powers of z.
So I see no argument for new anomalies, no paradoxes, and certainly no reason to expect a “no-go theorem” for string theory.
oops, in my comment to amused, somehow several lines got lost. The first paragraph should read
The standard lore is that lattice QED has a quasi-continuum limit (I’ll say what I mean by that in a moment) for any lattice coupling e_0 in the range 0 0 is only possible if you also take e(k) -> 0; that is, you can only get free field theory in a true continuum limit.
Arg! It happened again! I now notice that the instructions above this box (rendered in a lovely light-gray font on a light-gray background) say that I shouldn’t use less-than and greater-than signs, even if they appear in the preview. Nothing like a user-friendly interface, I always say.
OK, once again, with feeling:
The standard lore is that lattice QED has a quasi-continuum limit (I’ll say what I mean by that in a moment) for any lattice coupling e_0 in the range 0 < e_0 < e_c. For any momenta k << 1/a (where a is the lattice spacing), we end up with electrons and photons interacting with a gauge couping e(k), computed via the (exact lattice) beta function starting at e(1/a) = e_0. This means e(k) < e_0, so if you want a particular e(k) at some scale k, you must start with a larger e_0. And you cannot go all the way to the continuum limit (that’s what I mean by there being only a “quasi-continuum” limit), because ka -> 0 is only possible if you also take e(k) -> 0; that is, you can only get free field theory in a true continuum limit.
Damn! I missed making the 400th comment!
Guys, Let’s keep the 500th for Mark!
@E # 416
Is there anybody else out there that believes that the reason for the existence of the landscape and extra dimensions is due to the fact that string theory starts with a classical object which is then quantized?
Yes, me.
If someone can convince me that the necessity for extra dimensions does not arise from quantization, please go ahead. If it does, let me ask, why do you trust it?
I edited some comments so that the < and > signs appear where they should. Glad everyone thinks our color scheme is lovely!
E, B, I’m afraid I don’t understand what you mean. There are certainly string theory vacua that are not all that close to the weakly-coupled, higher-dimensional strings. For instance, there are nongeometric compactifications. But the existence of these points in the landscape doesn’t make the other, extra-dimensional-looking points go away.
Maybe I should point out that points that are self-dual (and hence, in some sense, deepest in the interior of the moduli space) often have some enhanced symmetry. There was a paper by Faraggi suggesting that such points are really preferred vacua. But as far as I can tell no real mechanism to select such points was suggested, aside from some strange-looking (to me, at least) reformulation of quantum mechanics. A related, but more mainstream, idea is that beauty is attractive.