After the incredible response to two of our recent posts (Krauss on Intelligent Design, Religion (and String Theory); and From the Sublime to the Ridiculous), Sean, JoAnne, Clifford, Risa and I asked Lawrence Krauss if he would be interested in submitting a post summarizing his views on the issues raised regarding string theory, religion, and the popularization of science.
Lawrence is an extremely well regarded member of the physics community, whose research, popular writings and remarkable efforts to defend science against pseudoscience and political distortion have earned the respect of all of us. We were therefore delighted when Lawrence agreed to make time to do this and we welcome him as Cosmic Variance’s first guest blogger.
We look forward to a high level of discussion regarding this post and, since it might need saying explicitly - keep it polite please folks! Here is Lawrence’s post.
__________________________
The contributors asked me to write and clarify some of my thoughts, especially since in one way or another I, and my writing, have been the subject of a few blog threads. I have already tried to respond; eventually hopefully clearly, within the threads to the concerns, but perhaps a single reasonably cogent monologue bringing some of these ideas together may be worthwhile. We will see:
On popularizing: the most important thing to attempt to get at is the difference between what we know, and what we don’t know; and how we can tell the difference.
On String Theory: A mammoth and very deep and original enterprise which, to date, has not been particularly successful, in my opinion. While string theory has been a fruitful stimulation of new mathematical ideas, as a search for physical theory it hasn’t been productive. This is not to say that it one day will not be so. It simply hasn’t achieved the goals it originally had, and thus far has not been able to make contact in any useful way with either experiment or observation, nor has it yet explained any of the fundamental theoretical puzzles that drive particle physics. Is it interesting? Yes! Should theorists continue to investigate it? Yes! Might it be of vital importance if it leads anywhere? Yes.
Is it worth talking about to the general public? I am not sure. As a study in the kinds of things that physicists sometimes like to think about, and why they think about them, yes; and that is what I have tried to talk about in my most recent book, and no doubt others have as well. As a demonstration of what is likely to be the underlying reality beneath what we observe in the world today, no; namely I personally do not think there is any compelling evidence that these ideas are going to be correct. Nor do I think it fair to place the large set of ideas that are currently being explored under the single banner of a “theory”. What seems clear is that as these ideas are explored in greater depth, the mathematical complexities increase and the possible connections to the world we measure seem to have decreased. I don’t know where things are headed, but frankly I see no reason for great optimism. And, as I try to emphasize to popular audiences, it is important to realize that most theoretical ideas, even great ones, are wrong. So in some sense it is important to keep that fact in the back of one’s mind whenever any new ideas are being discussed.
The good news is that ultimately science has been able to determine which ideas are wrong, and one hopes in the case of string theory this might be possible too, although, as Ed Witten himself has pointed out, it may turn out to be impossible for string theory to make any contact with the measurable world. It is also vitally important that those who are going to devote most of their productive years trying to work on an idea have faith that it is going to pan out. There is nothing wrong with that - it is required to keep up one’s motivations - but it might not pan out. That is the way it goes in science. It was in this context that I think the example of the dual-string model and QCD, which so irked Clifford, is relevant. It is not to make fun of infinities; rather it (a) demonstrates some of the subtleties of mathematics, which lord knows is a difficult subject to try and popularize, and (b) it illustrates what I said in one of the blog comments, namely “My point was not to use infinities to argue against anything.. but to point out that canceling infinities, as the dual-string did, was not by itself a guarantee that it was right, but that a completely different theory ended up coming along and replaced it.. as could easily happen again… I didn’t use it to argue that anything was flawed.. but merely that it is a mathematical problem that needs to be solved, but not every solution of it needs to correspond to reality.”
On String sensitivity: I understand that young people who currently work on string theory probably feel that they work under an undue burden, placed upon them by the original hype associated with the remarkable results in the mid 1980’s, which has continued and sometimes escalated since. I also understand that they may be entranced with various aspects of the ideas that have been developed. That is fine. But it simply is not yet on a par–in almost any sense–with any of the other significant, successful, and well-defined theoretical and experimental developments in physics in the past century. That is neither a bad nor a good thing; it is a fact. And relating one’s own excitement is fine, and good, but it should be tempered with a dose of realism, especially when discussing things to a popular audience, which cannot discern science from pseudoscience in general, much less the finer details of particle physics.
It is bad for science to give the impression that we know more than we do. Moreover, I hope this explains some of the sensitivity of others who do not work on string theory - namely, there are truly great and wonderful developments in theoretical and experimental physics that have simply been far more important and successful at describing nature and which have, in addition, led to technological advances. There have also been concrete discoveries, like dark energy, that are astounding and about which we currently have no clear understanding, so that other areas where we may have little understanding, such as the inconsistencies between GR and quantum mechanics, while important, are perhaps not the most overpowering immediate concerns.
On Extra Dimensions: I continue to remain neutral, if skeptical, here. While the notion of large undetectable extra dimensions is fascinating, and the fact that they can exist and have remained undetected is really fascinating, my own impressions, based on my understanding of particle physics data, is that they don’t smell right as a solution of the hierarchy problem. The apparent unification of couplings, large top quark mass, etc, provide at least suggestive evidence to me that there really is a large scale involved in unification, and also that supersymmetry seems to be suggested at some level. The research I did for my new book also made me frankly more skeptical from a theoretical perspective as well; namely, if I think about what the ground state of M-theory might be, the likelihood of some single, relatively isolated, relatively flat brane on which we live existing embedded in a higher dimensional and large space, seems unlikely to me. But we shall see.
On ID and Science: As many of you know who have followed any of my writing in this regard, the reason I took up this cause a bunch of years ago, and have spent many unfortunate hours defending science against attacks rather than doing what I prefer to do, which is getting people excited about science, is that I viewed the attack on evolution as an attack on science as a whole. The more I learned, the more I saw this as a campaign that was based on fear of the fact that God is not an explicit part of the scientific method. For some, this implies that science itself is immoral, and if you read much of the literature, in particular from the Discovery Institute, you will see this expressed explicitly. I also saw this campaign as not merely one by well-meaning but misinformed individuals, but rather by people who were very well schooled in public relations, who had a mission, and wanted to achieve it however possible. And since scientists, by nature, tend to be miserable at public relations, it seemed important to try and counter this in whatever ways possible.
My own awareness for the necessity of being respectful of religious beliefs has increased tremendously during this process. It has also become more clear to me that scientists tend to, whether they want to or not, appear patronizing about this, and also tend to make the philosophical leap from the fact that science deals with natural causes and effects to the statement that there can be no purpose in the universe. Whatever one’s personal perspective on this, and I see no evidence for purpose myself, this is a personal philosophical or religious notion, not a scientific one. In my piece in the NYT in May - the one that provoked the wrath of the Cardinal, Archbishop of Vienna - I used the example of Lemaitre and the Big Bang to point out that science functions independently of questions of purpose.
Now, how does all of this relate to string theory and the source of all the concern in one of the blog posts and the resulting comments? Well; it is the point I mentioned at the end of one of them, when responding to Clifford. I paraphrase: “the context in which I referred to ID was actually to make a point that I am beginning to think is actually relevant… namely that when physicists refer to ’string theory’ it is in the context of ‘field theory’… namely as a technical replacement of one physical and mathematical framework for dealing with relativistic quantum mechanics with another.. but unfortunately in the context in which we complain about IDers saying Evolution is ‘just a theory’, the popular use of the term string theory is unfortunate.. because ’string theory’ is not a theory in the context in which we claim evolution or general relativity is… i.e. something that has been tested time and again against experiment and observation.. calling it the string hypothesis would not be inappropriate in this sense..”
Unfortunately, string theory and extra dimensions are often held up as examples of science being indistinguishable from religion. I have tried, even in my last NYT piece, to explain some of the differences, but in a statement I made elsewhere that got someone very upset, I do believe that saying, other than tongue-in-cheek, that the current ideas are so beautiful that they must be correct–without any recourse to empirical data, is almost indistinguishable from religion.
Lawrence, thanks for chiming in. It’s only a matter of time before you have a blog of your own, I’m sure.
Too many interesting things going on here, so let me just register my own quick reactions to your main points:
– Whether or not string theory has been successful to date depends both on what you think its goals are, and how much progress one should expect. Of course it has not made direct contact with the real world, and it’s still hard to tell how it ever will, and that’s the ultimate test. Maybe it won’t, and we’ll move on to something else. But we have learned an incredible amount, working under the difficult situation of having very few experimental clues. The theory could have led nowhere, but it keeps leading us in surprising new directions — certainly more than enough progress to keep people from giving up.
– As far as achieving goals is concerned, I think the primary goal is obviously to quantize gravity, no matter what people say in their more excitable moments. And in that direction, string theory is by far our best current idea, well worth pursuing on that basis alone.
– I agree that separating what we know from what we’re speculating about is one of the most important goals of talking to the public. At the same time, I think it’s perfectly clear that we should be talking about string theory, and being honest about what we know and don’t know about it. Successful or not, the ideas behind string theory are both deep and incredibly exciting, and more importantly are what a large number of theoretical physicists today are actually thinking about. Why should we hide our work from the public until it’s all finished? We should trust them to be able to understand when we explain the speculative ideas we are thinking about.
– I’m never sure what is meant by “respecting religious beliefs.” Personally, I don’t agree with such beliefs, and I firmly believe that scientific reasoning ultimately comes squarely into conflict with them. And I’m not reluctant to say so, since I think it’s the truth. At the same time, I think we should be very respectful of the individual people who have such beliefs; no reason not to have a rational discussion. I think there is overwhelming reason to believe that there is no purpose in nature, and it would be patronizing to not admit this just so we didn’t hurt people’s feelings.
– I completely agree that saying that an idea is so beautiful that it must be correct is just silly, even if the silliness is coming from people who are much smarter than me. I tend to think that such utterances are in the spirit of Einstein expressing that he would have felt sorry for the Lord if general relativity hadn’t been correct; somewhat tongue-in-cheek. Hopefully.
To me the key aspect of string theory, whether its present lines of development prove to be correct or incorrect is to transcend the notion of point particles (zero dimensions) and theorize that there is at least one if not more than one dimension to the fundamental constituents of the universe. Doesn’t this conceptual shift actually put the theory (or one of its descendants) in a better position to remove infinities from equations describing these fundamental phenomena?
Elliot
As an example of why Lawrence might have a problem with some of the current attempts to promote string theory to the public, see the following news article about an event held in Princeton yesterday:
http://www.dailyprincetonian.com/archives/2005/11/14/news/13792.shtml
as well as some commentary about this at my weblog. I don’t think this kind of thing does anything to help the public understanding of physics, quite the opposite, and I know of very few people besides Lawrence who have been willing to publicly criticize it.
Hi Lawrence,
Thanks for preparing the post. I very much agree with much of the caution (tested vs not tested) that you express, and have said many similar things several times on this blog.
As to your second and fourth paragraphs, I am sure that it is important to talk about this to the public. This is why I was disappointed that you did not say those careful things in your public presentation, (and in fact it is very dangerous not to be careful when discussing such thing) and hence my earlier post, and the summary I gave in comments here , here and here.
Here’s hoping that some of the people who were at that presentation will read your careful words here, and thus get closer to the correct story. Also, I’m glad that this discussion means that several new people (readers of this blog) will see this, rather than the more misleading (intended or not) statements discussed previously.
Best Wishes, and thanks again.
-cvj
Hi Peter,
I note that the article that you pointed us to ends with the following:
About his other analogies, I can’t comment. I don’t fully understand them!
But he does seem to allow for (and clearly point out) the possibililty that the enterprise may come to naught. Is that not significant? The extracts on your blog’s post don’t mention these lines. I’m puzzled about that. Please help me.
Cheers,
-cvj
The problem is the presentation of the problems of Einstein’s theory, coupled with strings as the only possible solution.
I think it is frankly inappropriate to present string theory as “solving the problems of Einstein’s theories”, when to date it has done exactly nothing for our understanding of the physical universe. Mathematical contributions, sure. But no physical contributions at all, really.
This is what annoys people who don’t work in string theory, and it happens again and again. String theory is presented as somehow correct, a physical theory, a solution, when to date at least, it is none of those things. At this stage, it is a speculation with no supporting evidence, based on extrapolations of known physics. It is inappropriate to include it next to Einstein’s theories, which had rapid and complete experimental verification.
Hi Clifford,
I don’t think it’s difficult to understand what the analogies were trying to explain (perturbative superstrings better behaved than perturbative quantization of GR as a QFT in the ultraviolet), or that they were unlikely to actually transmit any information about this and would instead just confuse people.
In my posting I did quote Foster’s line that “Superstrings may be purely philosophical and may have no measurable contributions to our universe”, and commented that this is highly misleading and gives people the wrong idea about what science is. If superstring theory ends up involving “no measurable contributions to our universe”, it’s not “purely philosophical”, it’s wrong.
The last line that you quote is something the reporter says that she copied off the final slide, it would be interesting to hear in her words what she thought it meant. I actually think it is again quite misleading: as your well aware, the existence of supersymmetry does not imply the existence of superstrings (although I’ll readily agree it would be some evidence that superstring theory might be on the right track).
So I take it you have no problem with this kind of performance and think it should be encouraged?
Peter
Whoops, I see a flaw in the last sentence…. susy does not imply strings, of course. that is certainly wrong.
Cheers,
-cvj
Ah,… just came back from your blog….. where I posted the above comment, and did not see yours here before I repeated my post here. Sorry. Indeed, susy does not imply strings, and he is wrong about that. Very wrong.
But I do think that he was clear to state that strings may not be correct….
And I think that “purely philosophical” in this context is universally understood to be the same as “wrong”.
It would be nice if he was more accurate in his comments, I agree. I don’t see him being misleading about what other people’s research is about though. That would be bad. If he makes an analogy between this research and something that is not at all science (and in fact is damagaing science) and then does not explain the analogy, that would also be bad. If he claims (I can’t see it in a quick read) that string theory is the only solution to these problems, then he is also wrong to do that, since we don’t know that…… but if he is just trying to give some analogies about what is going on in string theory research and what sort of research people are doing with that field, then it is fine.
I don’t think wrong statements should be encouraged in general, no.
Cheers,
-cvj
If origins science sticks with what we know, then we live in a finite expanding, yet flat universe and I’ll buy that from day-one without assuming inflationary theory nor a cosmic singularity either.
If, as it appears, the goal of the big bang was an aboslutely flat and perfectly symmetrical structure, then it barely missed, but every action since then has increased the ongoing the effort “toward” *apparent* purposeful goal of absolute equilibrium.
It requires an unfounded leap of faith to assume beyond what we know that humans can be here for any other purpose and our actions clearly demonstrate that we are very good at satisfying it.
Sticking to what we know, my observation has been that we’ve carried a problem that never got resolved into higher physics under the assumption that this would resolve itself later, and this still seems to be the mentality.
Nobody understands why antiparticles have postive mass.
Nobody resolved the negative mass solutions for GR, but particles that comprise a negative pressure vacuum give the appearance of negative mass, due to the “anti-gravity” effect that comes from having less pressure and less density than matter.
Won’t the wave functions in this background affect the expansion of the field and the corresponding creation and annihilation operators?
Doesn’t this process require the condensation of vacuum energy before you can have a high-energy photon interaction to make it real?
Won’t the rarefying effect of condensation increase negative pressure and cause vacuum expansion?
Doesn’t the offset increase between positive mass-energy and negative pressure hold the universe flat as it expands?
How can we just skip over a resolution between Relativity and Quantum theory if we carry this flaw into QFT and beyond?
Sticking to what we know… the anthropic principle has VERY strong thermodynamic implications in only the observed universe.
Quickly before I will have to run: I really enjoyed reading this piece and feel grateful for Lawrence for taking time to write it. On first reading I cannot see anything I particularly disagree with… and to one of the points, maybe string theory being called the string framework or string activity or something is not a bad idea, this will also emphasize the fact that it is not really one idea (that is being carefully guarded by the believers) but a diverse and interesting process that is still developing.
Hope things run smoothly here, ‘fraid I will have to decouple now…
LK wrote:
Why is science worth doing? One has only so much lifespan, so many waking hours, so many working hours - why do science in that small period? I do not think there is a scientific justification for doing science; it boils down to personal perspective. Yes, there is the survival of the species, future generations, etc., but to the extent one is free agent, why should these matter? Then, if we are into respecting extra-scientific personal perspectives, then any religious-type perspective that does not attempt to dictate the content of the universe ( e.g., “any number assertions in the Scripture to the contrary will not make fire cord”) is also worthy of respect?
Is it worth talking to the general public
Why would it not matter what the building blocks of nature are to us?
on Sean’s point
I think Lee spoke to this as well….yet he was not satisfied either by it’s success, although success has been implied by use of string theory? Did it lead to other scientifc avenues in regards to technologies developement?
By it’s theoretical nature does “extra dimension” not imply the way evotvos handles it procedures? This also is a comment to the ideas of “theory” as a establish process in scientifc dealings. If you cannot adhere to this process, then those looking over your shoulder and reading, will have been mislead by the the words chosen?
Does this go to the susy comments brought forward here? Statements about a superfluid as misleading?
A couple comments more directly about what Lawrence had to say, my earlier comment was somewhat tangential.
1. I’ve been thinking a bit about his question about string theory: “Is it worth talking about to the general public?” As far as my own blogging goes, this doesn’t really come up since my concept there is to write assuming I’m talking to professional colleagues, although with the hope that interested members of the public will sometimes tune in and get something out of it, even if they find much of it mystifying. The people here at Cosmic Variance are trying to directly engage the public, which is great, but it seems to me they do need to seriously think about Lawrence’s question.
I know some string theorists disagree, but I think an accurate characterization of particle theory these days is that it is a victim of its own success, with no promising ideas about how to get beyond the all too successful standard model. Absent the usual pattern of important new clues coming from experiment keeping theorists honest and on the right track, a certain degree of dysfunctional behavior has emerged in the way particle theory is being pursued. Do you really want to invite the public in to see this? As an analogy: if your kitchen is a complete mess and family members are having a loud, ugly argument about what to do about it, do you really want to invite the neighbors in to show them around? One possible tactic is to keep the kitchen door closed, show off the incredibly beautiful and elegant front rooms (e.g. the standard model), and tell people that you’re working on the kitchen, things aren’t going that well, so it’s in no shape for public viewing. Another is to throw the doors open, invite them in to see the mess and hear all the arguing, hoping that they’ll appreciate your family’s openness and straight-forwardness.
I can see arguments for either of these tactics, but I think the tactic that many have actually adopted is a third and indefensible one: to keep people out of the kitchen while claiming everything is going just great in there, showing off drawings of what you wish your kitchen looked like, and giving the misleading impression that you’re making progress toward getting the kitchen to look like the drawings. The problem with this is that sooner or later your neighbors are going to find out what has been going on, and you will have lost all credibility with them.
2. While I agree with just about everything Lawrence has to say, I have a different perspective on the point he makes here and elsewhere that saying a theory must be true because it is beautiful is not distinguishable from religion. Of course this is true: he’s right that what finally makes something a tested scientific theory is to confront it with experiment. But at an earlier, more exploratory stage when you can’t yet do that, picking one idea over another because it is more beautiful is actually a very rational, scientific way to proceed. Occam’s razor is important, and one should be looking for simple, elegant, beautiful ideas in preference to complicated, ugly ones, unless experimental evidence makes the ugly ones unavoidable. The problem with string theory is that it is no longer a beautiful idea about how to unify the standard model and gravity. All constructions that even partially reproduce the standard model are hideously ugly, with no experimental evidence to back them up. What is happening these days is that an increasingly large number of string theorists, in desperate attempts to get the standard model, have ended up working with increasingly hideous constructions.
Sean wrote…
…and I think he’s right. “respecting religious beliefs” in the context here (this overall discussion) really means respecting and not patronizing a well-meaning person who professes religious belief.
However, if it was the case that someone’s religious belief was that the world is flat (literally, not in the Thomas Friedmann sense) then I don’t think that belief is worthy of respect. Perhaps he or she is just a well meaning person who is mis-informed (and in this case woefully so). If also they attempted to present flat-earth geology as an viable alternative to geology then no respect is accorded.
Whenever I get to riled up thinking about the ridiculousness and idiocy of some religious people attempting to have ID taught in science class or saying that Dover PA now voted itself onto God’s “pay-no-mind” list, I think that there are also people like my parents who are religious, well-meaning, but just not informed and are un-interested in the way science works. They’re not active pro or anti ID people, but just don’t think much about it or don’t have the time to. This is why public outreach about science is so important, because they are open to learning about it.
Now, whether I still attend Mass on Sunday is something they DO worry about…
Hi,
I agree with most of what Lawrence said. But since I was mentioned, I should clarify why I and most people who work on quantum gravity, apart from string theorists, find it impossible to agree with Sean’s statement that string theory is “by far our current best idea” about quantum gravity.
-Any acceptable quantum theory of gravity must incorporate the basic lesson of GR that the geometry of spacetime is dynamical and defined without reference to any fixed background-hence background independent. String theory has as yet no such formulation. Furthermore, there are several theories that provide precisely such a theory, such as loop quantum gravity, spin foam models and dynamical triangulation models, about which many non-trivial results have been proven.
- Even at the background dependent level GR is not recovered because all backgrounds on which consistent propagation of worldsheets have been shown are static in that they have timelike or null killing fields. So, there is no evidence that string theory exists even on backgrounds that are time dependent, which is the generic case in GR. We know that the Einstein equations on the target space are (up to higher order terms) a neccessary condition for consistent worldsheet propagation. But sufficient conditions include also canceling the tachyon instability. In all known cases this imposes another condition which is worldsheet supersymmetry (or something equivalent) which in turn requires that the background be static. So it is not true that string theory predicts or incorporates GR as a low energy limit, because all solutionis to GR seem to be ruled out as giving inconsistent propagation except static ones.
Thus, while there is talk about string theory on time dependent backgrounds there are no actual examples. Given the importance of supersymmetry in consistent string dynamics, it is plausible to me that this is because there is only consistent worldsheet propagation on static backgrounds.
-The precise matching of black hole thermodynamics to string states is impressive but only seems to work for special black holes that have positive specific heat (and are hence near extremal.) This is because no black holes are involved at all, instead what is counted are states of non-gravitational systems of branes in flat space with gravity turned off that have, by virtue of BPS symmetry the same quantum numbers of certain positive specific heat black holes. This can’t work for negative specific heat black holes because they are not BPS and because they can’t have the same thermodynamics of orindary systems with positive specific heat. There is no evidence string theory can describe precisely generic negative specific heat black holes. I suspect this may be because there is no consistent worldsheet propagation on backgrounds with horizons-because they do not have global timelike killing fields.
-On top of this, while there is very non-trivial evidence for all orders finiteness, it is still not proved (please don’t jump on me again about this unless you have a new paper with a full proof.)
-Since Sean’s statement is comparative, it is important to say that background independent approaches exist, and many key results have been shown about them. LQG, in its spin foam formulation, continues to advance and is now, in my view, the “best model.” There were recently big advances on the hardest problem, that of getting known physics form the low energy limit announced in talks by Rovelli, Freidel, Markopoulou and others at the loops05 meeting (now with talks on line at http://loops05.aei.mpg.de/), and there were predictions for corrections to the CMB described in the talk there by Hofmann. Elimination of both black hole and cosmological singularities has recently been shown in related models. This is on top of proofs of uv finiteness and the fact that the theory is background independent. Black hole entropy is understood for real negative specific heat black with real horizons.
In my view the second best model is the Loll-Ambjorn causal dynamical triangulations model, with stunning recent progress described by Loll at loops05.
If string theory overcomes the problems mentioned I would be the first to cheer But for the present I believe that the background independent appraoches are moving faster and are more worthy of our time.
Thanks,
Lee
[...] There’s an interesting guest posting from Lawrence Krauss over at Cosmic Variance. I think I’ll turn off the comment section on this posting here, since if people want to discuss this, it is probably best done over there. [...]
Kaku told in a recent interview that he believes that if Einstein had not invented GR, it wouldn’t have been invented by others before 1970. This is because, as Wald explains in his textbook, the obvious way to write down a relativistic theory of gravity is using retarded potentials in a flat spacetime. The idea that spacetime could be anything else than flat would not have entered the heads of physicists anytime soon.
To me theories like string theory, LQG etc. look more like naive contrived attempts to come up with a TOE, similar to what would have happened had GR not been discovered by Einstein.
I think there continues to have two different threads embedded here. 1) Is string theory the best existing approach to quantum gravity? and 2) how do practicing scientists most effectively communicate to the lay public what is “going on” in fundamental research in physics? I’d like to humbly suggest that although they are deeply interrelated, they are really two different questions. I like Peter Woits kitchen analogy but it appears that there is no clear consensus on whether of not the kitchen is clean or dirty or if it is better for the family to clean it up or call in a cleaning service or demolish it.
Elliot
So, upon further reflection, would Prof Krauss agree that there is in fact nothing in common between the string theorist’s “fascination with things unseen” and religious sentiment? That they are in fact utterly different things which the magic of the English language [yes, folks, ONE set of words can have TWO meanings, incredible as that seems...] allows ignorant people to confound? That a great deal of florid “popular science writing” is nothing but the raising of such simple confusion to an art form?
Look at the Princetonian event which Peter Woit described. Everyone laughs at idiots talking about quantum pasta. But nearly all of the popular writing about science I see is just as idiotic. Prof Krauss, remember that dancer waving her arms around and claiming that some deep insight into “space” was being vouchsafed? Pretty silly, wasn’t it? But is it really much more silly than seeing analogies where none exists?
Okay, maybe just quantum gravity then?
Would this make everyone happy? As far as keeping out of the kitchen, I don’t think so. If you had taken your synoptic views in book form to the public, what would make you think they could not come for a closer look and see what you are doing?
Oh! Maybe targeting specific readers are you? About 1% of the population, this should make you really rich?
That should cuts sales down quite a bit, if you think you are selling to a select few who you think are in the kitchen?
So what are the problems that exist then? For the lay person a historical perspective.
The opposing view is that background-independence is fundamental, and quantum mechanics needs to be generalized to settings where there is no a priori specified time. The geometric point of view is expounded in the classic text Gravitation, by Misner, Wheeler and Thorne.
The two books by giants of theoretical physics expressing completely opposite views of the meaning of gravitation were published almost simultaneously in the early 1970s. The reason was that an impasse had been reached, a situation which led Richard Feynman (who himself had made important attempts at understanding quantum gravity) to write, in desperation, “Remind me not to come to any more gravity conferences” in a letter to his wife in the early 1960’s.
http://en.wikipedia.org/wiki/Quantum_gravity
Thanks, Lawrence, for a thoughtful and well-written article.
The significant question about which there is disagreement appears to be: Should physicists be talking to the public about string theory?
I believe that, in the light of Lee’s posting, it is instructive to consider the question: Should physicists be talking to the public about causal dynamical triangulations, and about loop quantum gravity?
More specifically, when the public are told about string theory, should they be told about possible alternatives? And if not, why not? And if so, why hasn’t that been the case so far?
Lee,
> In all known cases this imposes another condition which is worldsheet supersymmetry (or something equivalent) which in turn requires that the background be static.
Can you please elaborate why supersymmetry requires the background to be static?
Regarding Lee Smolin’s comment in #17, even if string perturbation theory is defined on arbitrary background spacetimes, what can we get other than S-matrix elements? Is that all the content of a quantum theory of gravity?
Hey guys, I have a few minutes before dinner, so I have to be quick. I disagree with lots of what Lee mentioned above as statements of fact about string theory (many other issues are simply a matter of individual judgement).
Since the subject is close to me heart, let me only concentrate on the sentence “there is no evidence that string theory exists even on backgrounds that are time dependent”, which is incorrect on many levels. There is a lot of work on string theory on such backgrounds, which tend to be singular and therefore interesting…
In particular we have AdS/CFT and it is complete and non-perturbative definition of string theory in spaces with a negative cosmological constant, this includes each and every physical question one may dream up, time dependent or not. So I am not sure what Lee means exactly.
His evidence cited here is a technical point about string perturbation theory, (which is only one corner of the subject) which I believe is misguided, worldsheet (unlike spacetime) SUSY and the resulting absence of tachyons have nothing to do with spacetime Killing vectors, and therefore does not require spacetime to be static. (in fact worldline SUSY is a beautiful structure which arises when you try to describe in this language any particle with spin, nothing to do with string theory…).
I am not sure you guys want this thread to concentrate on this issue, maybe there will be a better time and place for this…
Any acceptable quantum theory of gravity must incorporate the basic lesson of GR that the geometry of spacetime is dynamical and defined without reference to any fixed background-hence background independent.
Insert sound of Aaron banging his head against the wall here.
“Any acceptable quantum theory of gravity must incorporate the basic lesson of GR that the geometry of spacetime is dynamical and defined without reference to any fixed background-hence background independent.”
Insert sound of Aaron banging his head against the wall here.
Sorry about that — the comment system was acting funny.
And I still haven’t seen any computation of black hole entropy in LQG that doesn’t pretty much assume that the answer is proportional to the area. I’d be happy if someone could point one out to me.
But that does bring to mind a point I’ve been wondering about. Do LQGers expect that LQG is only consistent with that bizarre value of the Immirizi parameter? If not, what physics is described by the other consistent background independent theories of whatever?
moshe,
I just thought that for any symmetrical breaking action it would need to break from something much purer? Is there no such thing as supergravity?
I thought such a thing as a superfluid, would be quite beautiful, and a place for such bubbles to emerge.
So Lee you talk about “new” theoretical developement. Here is something to contrast it. Your point of view?
Sir Michael Atiyah
Anyway Lawrence, is there anything you would like to say so far about the discussion?
Hi,
Thanks very much for the comments. Let me begin by answering Wolfgang’s questions and then address Moshe’s and Aaron’s comments. As I said before, lets try first to agree on matters of fact. Perhaps I’m not aware of a result, in which case I look forward to being educated.
“Can you please elaborate why supersymmetry requires the background to be static? ”
The basic reason is to expect so is that the algebra of supersymmetry transformations closes on the hamiltonian, which is the generator of time translation symmetry.
Now on to Moshe’s comments:
“There is a lot of work on string theory on such backgrounds, which tend to be singular and therefore interesting…â€
I agree there is interesting work, but that is not the same as there being explicit examples of consistent quantum world sheet propagation on time dependent backgrounds. Am I wrong that there are none?
“In particular we have AdS/CFT and it is complete and non-perturbative definition of string theory in spaces with a negative cosmological constant, this includes each and every physical question one may dream up, time dependent or not. So I am not sure what Lee means exactly….â€
AdS spacetime has 10 global symmetries, so that is not a counterexample. Nor is the issue that we can’t ask time dependent questions on a time independent background. We can also argue about which version of the AdS/CFT conjecture is supported by the present results, but it is certain that the very strong form in which “each and every physical question one can dream up, time dependent or not†can be answered by measuring something in the dual CFT is a conjecture, not yet shown. The non-perturbative existence of N=4 SYM is also an open conjecture as there is still, so far as I know, no known lattice regulator that preserves supersymmetry.
“His evidence cited here is a technical point about string perturbation theory, (which is only one corner of the subject) which I believe is misguided…”
String perturbation theory is one part of the subject, but it is the only part where one can compute explicit quantum gravity corrections to ordinary processes.
“…worldsheet (unlike spacetime) SUSY and the resulting absence of tachyons have nothing to do with spacetime Killing vectors, and therefore does not require spacetime to be static….â€
I agree in principle that worldsheet supersymmetry does not imply spacetime supersymmetry. But tell me, are there explicit examples with worldsheet supersymmetry on a time dependent background? If not we should try to understand whether there is a reason. If there were an example, would it imply the existence of a killing fields in the induced metric on the worldsheet, but not on the spacetime from which the metric was induced? If so this could not be generic.
If I am wrong about this I would be happy to be educated. Or maybe there is an extension of string theory to time dependent backgrounds that does not have a perturbative description in terms of worldsheets. But if this exists it has yet to be constructed.
“in fact worldline SUSY is a beautiful structure which arises when you try to describe in this language any particle with spin, nothing to do with string theory…”
Certainly, I’ve nothing against SUSY as a mathematical structure, and I’ve devoted lots of time to it myself, but no one is claiming that worldline supersymmetry leads to a consistent theory of particle physics or quantum gravity.
Re Aaron’s point: “And I still haven’t seen any computation of black hole entropy in LQG that doesn’t pretty much assume that the answer is proportional to the area” None of the calculations usually cited (Ashtekar, Baez, Corichi, Krasnov and others….) make that assumption. Please read the papers, these are careful people and they state their assumptions explicitly.
But I agree with your worry, Is “LQG … only consistent with that bizarre value of the Immirizi parameter? ” I’ve been wondering about this too.
Thanks,
Lee
The problem of quantum gravity is so fascinating that young people can not help try attacking it and thats what I also wanna do. And unless people come up with more ideas about it quite a few people will keep working on strings.
That said, one must take a course on astrophysics from LK to get the feel what it means in science when we say something is well tested (in contrast to Motl’s belief system), and how is it to work in a field where you are confronted with numbers to comapre your theory with on a daily basis.
There probabaly is something in the physics popular writings that the common people ussualy dont have a clear idea of the real accomplishments of physics. For example, they would put the general big bang theory and the brane world scenario into the same category of speculation, on part of phycists, whosse job is to come up with new and marvelous ideas anyway. (Sure its just my personal expereince of talking to freinds, and does not have real statistical significance)
Ofcourse there is nothing wrong with coming up new beautiful ideas. As I understand , Eienstien wrote GR based only on his theoretical insights and demanding some general properties for a theory of gravity ( relativistic invariance, equivalance principle ect) and then looking for internal consistencies. Probabaly string theorists find themselves in same situation. But the thing is that people would have not belieived in it as a hard fact of nature if there were no mercury’s prehilion shift and solar eclipse tests.
I am not so sure as Sean, and most everyone else here seems to assume, that the goal of the string framework is to arrive at a theory of quantum gravity. As far as I can tell the “goal” of the programme (if programmes and not just individual theorists can be said to have goals) has been to explain masses, coupling constants ect in the standard model and that the apparent existance of gravitation in the framework is merely a highly motivating factor for study within the programe. Finding quantum gravitational correction to known processes seems very impractable as the corrections are so small that they likely will never be observed. So, assuming the overall hope is for a connection with experiment, that the goal would then be to calculate the parameters of the SM. It would be interesting to hear from the string theorists reading this blog, if they considered the goal to be one or the other( or if they even make a distinction). As most of them seem to think of themselves as particle physics I expect that they are more concerned with explaining the parameters of the SM.
Lee, worldsheet SUSY (which is usually needed for classical stability) does not imply that the spacetime has to be static. This is the technical point I was making in response to your post, and it is actually correct. So this leaves the possibility of string backgrounds that have worldsheet SUSY but are not static, and indeed there are many, too many to mention here, various orbifolds of flat space and coset constructions are a few such examples. They are stable classical backgrounds (=worldsheet theories) of the superstring. Incidentally there are also consistent (indeed solvable) classical string backgrounds that include horizons (Witten’s black hole is an example, but there are many more).
But, again this is just one method of investigating string theory. Another one I mentioned is AdS/CFT that requires you to fix the asymptotic geometry to be AdS, but in the interior of the geometry absolutely anything is allowed to happen, time dependent or not. So for example one can calculate dynamical quanitities like various transport coefficients in strongly coupled gauge theory using the gravity dual.
In the context of AdS/CFT, I am not sure what is the distinction between “time dependent questions” and “time independent background”, because you see, AdS/CFT is *background independent*. The AdS space itself with its isometries is just the vacuum of the theory, one can ask questions about excited states as well, including time dependent questions. There is a large body of literature on the subject (Alex Buchel and Andrei Starinets are experts around you)
I am not motivated to enter into a discussion what is proven and what is not, since basically nothing interesting is proven to mathematical rigour, starting with QED with massless electrons. If there are some reasons to doubt AdS/CFT correspondence for specifically time-dependent questions that would be interesting to hear.
best,
Moshe
Again, dear bloggers, not sure you want us to divert attention from the main subject here, this is getting quite technical…I’ll be glad to postpone further discussion to a more appropriate time.
hmmm….
Lee says:
To which Moshe responds:
Even by some much lower standard of rigour, there is far more reason to doubt the nonperturbative existence of the Standard Model (a chiral gauge theory) than N=4 SYM.
A quick search of hep-lat (if Lee were interested) would turn up a fair-sized literature on N=4 SYM on the lattice (see, e.g. Catterall or Kaplan and Unsall). Crudely, fermion-doubling (the reason there’s no satisfactory lattice regulator for chiral gauge theories, like the Standard Model) is, in the case of extended supersymmetric theories, your friend.
And, of course, the very striking nonperturbative checks on S-duality by Vafa and Witten (among others) would be rather hard to understand if the theory didn’t actually exist nonperturbatively, wouldn’t they?
Re Aaron’s point: “And I still haven’t seen any computation of black hole entropy in LQG that doesn’t pretty much assume that the answer is proportional to the area†None of the calculations usually cited (Ashtekar, Baez, Corichi, Krasnov and others….) make that assumption. Please read the papers, these are careful people and they state their assumptions explicitly.
All the ones I read explicitly assumed that the degrees of freedom are located on the horizon. I have not seen any construction of a black hole state in LQG.
This thread in spr is relevant.
Lee, also apologies in advance for not being able to engage in a conversation in the next few days…mainly meant to quickly point out that one technical point, which I did…
Hello,
I’m not an expert in physics but nevertheless was wondering about this particular issue.
I’m very intrested in understanding why any quantum theory of gravity should necessarily be derived from a General Relativity framework.
Isn’t it possible to formulate a “relativistic” theory of gravitation on minkowski space-time and then try to quantize it as is done for the other field theories using canonical or path integral quantization ?.
Does this approach lead to inconsistencies and that’s why it has never be carefully examined or is there another reason why nobody cares to take a non-geometric approach to the quantization of gravity.
Lee,
insisting on background independende is a nice philosophical principle but not more. For the longer answer check here:
http://golem.ph.utexas.edu/string/archives/000621.html
Everybody agrees that gravity without symmetries is harder than with symmetries. This is not any different in string theory than elsewhere. For example I am not aware (but that might be my fault) of any analytical solutions to Einstein’s equations without symmetries. And all the textbook examples have Killing vectors. So, is that a problem of GR?
Re tachyons: The effective description of a ball on a mountain top contains a tachyon: The ball can roll down. Of course again, there is no inconsistency with balls on mountain tops it’s just that small deviations do not stay small. And situations with instable modes (aka tachyons) are slightly harder to analyse.
There are many things you can argue about string theory, but these ones are not too strong.
Unbroken target space supersymmetry means existence of a constant spinor. Existence of a Killing spinor implies existence of a Killing vector. But not necessarily a timelike one, as far as I am aware.
Robert,
> Everybody agrees that gravity without symmetries is harder than with
symmetries.
Sure. But Lee’s argument (as I understand it) is that the current superstring theory works only in highly symmetric (static) backgrounds and that there is a reason why this is so (insert his argument about supersymmetry here).
Ugo,
> Isn’t it possible to formulate a “relativistic†theory of gravitation on minkowski space-time
gravity is attractive, so you would have to consider a spin-0 or spin2 bosonic field
or a combination of both.
spin-0 alone does not reproduce some effects we know and spin-2 leads more or less straight back to GR due to consistency arguments.
Unbroken target space supersymmetry means existence of a constant spinor. Existence of a Killing spinor implies existence of a Killing vector. But not necessarily a timelike one, as far as I am aware.
That’s not the argument that Lee’s referring to. Essentially, in target space, the SUSY generators have to close on a time translation.
Jacques has already pointed out that there are recent papers on lattice constructions of gauge theories with high SUSY. See also hep-lat/0302017 and hep-lat/0307012.
There have also been attempts to formulate lattice constructions of chiral gauge theories, see hep-lat/0503011 and hep-lat/0510073. A proof of whether these truly work appears to be elusive, but perhaps they are a step in the right direction.
Lattices aside, does anyone really have strong doubts about whether asymptotically free gauge theories make sense?
Hi everyone, thanks for all the very useful comments. I’ll coment where I can, I’m sure someone will let me know if I get something wrong.
To Jacques, Thanks very much for the references for N=4 SYM on the lattice. Of course I’m interested, this is important progress. These were in the last year and I missed them, thanks for pointing them out.
To Urs, here is what I understand in 3+1 dimensions: A killing Weyl spinor gives a null killing vector. Two of them, as in a Dirac spinor make two null killing vectors, whose sum is a timelike killing vector.
To Aaron, Yes, the older LQG results about black holes assume the presence of an horizon and study the states that live on the horizon. That is recognized as a limitation. But this is not the same as assuming that the entropy is proportional to the area. There are a few recent works that explore going beyond that, for example, Husain and Winkler, gr-qc/0410125, gr-qc/0412039 gr-qc/0503031 , gr-qc/0505153.
To Robert, I agree its hard to write solutions to GR with no killing fields, but you can establish lots of properties of solutions we can’t write down. If string theory is a theory of gravity shouldn’t we be able to prove there is a consistent string worldsheet propagation on any generic solution? If not, why not? Shouldn’t there at least be consistent worldsheet propagation on simple spatially homogeneous models like Bianch IX or arbitary FRW?
Re tachyons, if you know the full non-perturbative definition of a theory and have proved stability and consistency, and then expand around a semiclassical state and find tachyons it just means that you are expanding around the wrong vacuum. But if you only have a perturbative description and it has tachyons you cannot be sure there is any non-perturbative formulation with a stable vacuum. For example, lambda phi^4 with the wrong sign of lambda does not exist in any dimension because there is no stable ground state. We don’t know if there is any full non-perturbative formulation of string theory, so we cannot be sure whether the tachyon rolls to disaster or to some unknown non-perturbative ground state.
On background independence, it is much more than philosophy, it has motivated a large body of results concerning approaches to quantum gravity that implement some form of background independence. I don’t need to convince you about the philosophy but I would like to convince you to take an interest in those results.
To Ugo, that approach of doing Feynman perturbation theory for gravitons on flat spacetime was thoroughly investigated and it was known definitively by the mid 70’s that it fails.
To Moshe, as you say, there have been studies of time dependent string backgrounds, orbifods of flat spacetime, coset constructions, linear dilatons etc. My understanding is that till recently, these either had problems with stability or either the string or Einstein frame metric was still static. Can you point us to the best case currently, so we can discuss that? So far as the AdS/CFT examples are concerned, I agree you can calculate many things, having to do with states propagating on an AdS X something background, we are not disputing that. By Witten’s black hole do you mean the large (positive specific heat) black holes in AdS? I wasn’t aware you could compute consistent string amplitudes on that, or for that matter on AdS X S^5 (generically, there are some results in extremal cases). If I’m wrong please give references.
Thanks, Lee
Anonymous,
I don’t think there’s any reason to doubt that pure YM theory on the lattice makes sense: the lattice formulation is very straightforward, and there’s a lot of numerical evidence that the continuum limits exists and behaves as predicted by continuum perturbation theory.
Chiral and supersymmetric gauge theories are another story, since finding a lattice formulation with any hope of working is not at all easy. As far as I know, the various proposals out there are not particularly amenable to numerical simulation, so little is known about whether these proposals actually avoid the various problems one might worry about them having in the continuum limit.
This is getting far away from the original topic of this thread. In an attempt to bring things back to something related to the thread topic, I’ll mention that the unsolved problem of carefully understanding the non-perturbative behavior of chiral gauge theories has always seemed to me a good example of the kind of thing that hasn’t gotten the attention it deserves due to the way particle theory has been dominated by string theory for the last twenty years.
Elliot wrote:
I sure wish one of you leading experts (Clifford, Lawrence, Lee, Peter, others) would address Elliot’s incisive question. If you think that it’s possible that the public can understand and care about what physicists are doing in the kitchen, then maybe it’s important to listen to them as well as blab on in your own venacular, oblivious to their curiosity and keen desire to understand.
Sean writes:
Ok, then why not talk about it in terms of transcending the zero dimensional point particles and removing infinities. What is it that you have learned about transcending the zero dimensional constituents of the universe? That if you take those constituents and cook them into different kinds of pasta, they are no longer zero dimensional? Really, is your only choice to be so doggone condescending, or else to retreat into the netherland of professional jargon? Can you talk to us as if we had some brains for crying out loud, but without the use of your esoteric terms!
It’s not that hard. For instance, the natural numbers are like zero dimensional point particles, are they not? But when we interpret them as describing a relation between quantities, as a ratio, a vibration, lo and behold we transform them from 0D numbers to 1D numbers. The relation of two natural numbers, as a rational number, has dimension, the dimension of the signed integers; that is, n/m…1/2,1/1,2/1…m/n is the same thing as -n…-1,0,1…n, without the need for imaginary numbers.
Thus, a vibration, 1/t, transcends the zero dimensions of a point - we move from a point to a line, and the infinities are gone, because a line formed by a 1D vibration is bound, just as the number 1/2, interpreted as -1, is bound. Whoa, ok, that’s easy enough to understand, and it’s fascinating, but don’t stop there! Tell us, guys, what about 2D and 3D vibrations? What do they do for us? Is this one of the surprising new directions Sean is talking about? Tell us about these n-dimensional vibrations, please?
But don’t be condescending. Remember, just because we don’t have the specialized knowledge that you do, it doesn’t follow that we are stupid. We know that increasing the dimension of the integers leads to complex numbers, and then to quaternions and then to octonions. We also know that the octonions are not only three dimensional (four if you count the zero dimensional scalars), but that they are very curious too (we read also read Baez, you know).
What we really want to know is how this idea of yours, the vibration idea, plays with these numbers. Put down your colander and pasta, and pick up this vibrating octonion. Now this is really cool. The 3D vibration has the scalar, 1/1, three linear vibrations, three planar vibrations, and one cubic vibration, as a set, you say? All as one particle? What’s the frequency of this vibration? What’s its radius? Does it have an multiplicative inverse? Is the Clifford algebra of these n-dimensional vibrations, or rational numbers, commutative and even associative, due to the bi-directional nature of the vibrations?
Come on guys, talk to us. There are at least two of us (right Elliot?) who are keen to hear what you have to say.
Lee, have to go and catch a flight, so let us not raise new issues which may be interesting to discuss on some other occasion. You mentioned some specific issue to do with string worldsheet making sense only on static backgrounds (and w/o horizons) because of worldsheet SUSY. I think that technical statement is incorrect, and I would be eternally grateful if you will correct it wherever it appears.
Reference: Witten’s black hole is in two dimensions and is the classic paper
Phys.Rev.D44:314-324,1991; there are 788 follow-up papers also… You can also look at Tseytlin 1994 review hep-th/9410008 for an assortment of string vacua which are time dependent and exactly solvable. I don’t think most of them are static in either frame.
Finally, my point was that AdS (times something) is not chosen as a background to expand around, one describes in the CFT also all excited states as long as they are asymptotically AdS. So this describes also time dependent processes, and this is not just statement of principle, there is a large body of literatutre doing time dependent calculations in this framework. You should really talk to Andrei or Alex, they know everything there is to know about the subject.
best,
Moshe
Doug, just one small comment. I can’t see that any of the experts have been condecending here. In fact, your comment is one of the first in this thread that is a little insulting (”blab on in your own venacular, oblivious to their curiosity and keen desire to understand”).
Part of the reason we have this blog is public science education. We do a lot of it, and so I for one don’t appreciate your tone. If you’d like something answered, please feel free to ask, but don’t be rude; it brings down the level of the entire discussion.
To Aaron, Yes, the older LQG results about black holes assume the presence of an horizon and study the states that live on the horizon. That is recognized as a limitation. But this is not the same as assuming that the entropy is proportional to the area.
I guess everyone will have their own opinion on that point.
There are a few recent works that explore going beyond that, for example, Husain and Winkler, gr-qc/0410125, gr-qc/0412039 gr-qc/0503031 , gr-qc/0505153.
I don’t see any lqg in those papers. I don’t see any calculations of black hole entropy, either.
I will try to keep a low profile now in this conversation, but hopefully the foundational perspective you are sharing, has been caught here?
Thanks,
On the physical viability of static or stationary backgrounds:
SUSY backgrounds are interesting for particle physics phenomenology. For that purpose it should be fine if they are Minkowski in 3+1D since accelerators tend to be insensitive to cosmological scales.
I’d expect that a static CY x Minkowski SUSY background might describe the universe nicely locally, on the scale of accelerators, while it may be just a local approximation to a non-static non-SUSY cosmologically valid background.
(Just like we use Minkowski field theory to compute accelerator data even though we live in a world which is non-Minkowski on large scales.)
Even though everybody is talking about the “landscape”, I don’t have the feeling that cosmological issues are anywhere near tractable with current string technology. Please correct me if I am wrong.
Surely the statement is not supposed to be that SUGRA only has stationary solutions because some of the SUSY generators close onto the Hamiltonian constraint?
I think the question is rather if solutions that do not break all SUSY have to be stationary. So the question is if the _preserved_ susy squares to time translation. This is the case precisely if the solution has a Killing spinor that squares to a timelike vector.
Mark,
Point taken. Sorry, for letting that sentiment show. It’s just that only having the unintelligibility of the professional jargon on the one hand, or the oversimplified analogies on the other, is so frustrating.
Exact Supersymmetry can be mintained using Fuzzy regularization
Thanks Doug. I expect one of the string theory or LQG people will get around to addressing the point (I’m certainly not expert enough in these topics to do a good job). It’s not just jargon though. The issues involved in some of the topics here are highly technical and the language used is that suited to them. Explaining them in other terms can be very difficult. However, I think some of the questions, such as the one you mention, can be addressed in more simple terms.
I’ll let others take a real stab at it, but I would say that the extended nature of strings does mean that infinities are easier to deal with (are sometimes just absent) in string theory. However, we are already pretty happy with how we deal with some infinities in field theory (regularization and renormalization work well), and those infinities that arise in gravity (e.g. curvature singularities in black holes or the big bang) haven’t really been shown to be any easier to deal with in string theory yet. So while it’s a promising direction to head in, we don’t know if it helps yet. The fact that it seems to be a consistent theory of quantum gravity is, to my eye, the most important thing.
Cheers.
Doug,
“Removing infinities” is the wrong way to think about renormalization theory. A proper answer to your questions is way longer than would be possible in the comment section to this blog. I wrote a long post over on my blog, explaining why String Theory is the only viable approach to a theory of quantum gravity (in response to some of the comments, I wrote a followup post explaining why one frequently-cited “alternative” doesn’t work).
Perhaps these posts are still too technical; they were written with an intended audience of, say, a physics graduate student. But they’re probably a better start at an explanation than anything I could post as a comment here.
Peter wrote:
Chiral and supersymmetric gauge theories are another story, since finding a lattice formulation with any hope of working is not at all easy.
I didn’t claim otherwise. What I did claim is that I don’t think anyone really believes that an asymptotically free, or a conformal, continuum field theory in these cases is not actually well-defined. We don’t have a satisfactory nonperturbative definition of them, but it doesn’t cast doubt on whether they exist. It just means we don’t yet have an adequate toolkit for understanding these things. It seemed that Lee was insinuating that AdS/CFT isn’t really a nonperturbative definition of string theory on backgrounds with negative cosmological constant because the N=4 SYM (or related field theories for deformations of AdS) might not be well-defined. I think that 99% of people with experience in working with field theories would disagree with this statement. A theory like QED is nonperturbatively suspect because of the Landau pole, but QCD-like theories and conformal theories are not.
I’ll mention that the unsolved problem of carefully understanding the non-perturbative behavior of chiral gauge theories has always seemed to me a good example of the kind of thing that hasn’t gotten the attention it deserves due to the way particle theory has been dominated by string theory for the last twenty years.
Wow. I don’t think people have been ignoring this. I just don’t think anyone has a clue how to make good progress. Even for non-chiral gauge theories like QCD we don’t have much understanding of non-perturbative behavior. The lattice can only do so much, although it has made a lot of progress in recent years. I would say that the only 4D theories where we “carefully understand” non-perturbative behavior are SUSY ones, and string theory has been very useful in some of this.
Moshe,
Do we have to distinguish between solving the effective action (the GR-like equations) that arises from string quantization in a flat background versus string quantization in a general background?
-Arun
Gerard t’ Hooft:Quantum gravity and black holes if you travel down his webpage you will come across this reference.
Gepner point(?)
Of course to you season vets this may seem trivial?
and just so you understand that the division does not have to take place. People are coming around. This phrase below is distant memory although it indeed sets the course for what evidence is produced.
Lee Smolin
To Anonymous,
Your post raises for me an interesting point about the attitude we take towards problems which lots of smart people have tried and failed, over several decades, to solve. You say, “What I did claim is that I don’t think anyone really believes that an asymptotically free, or a conformal, continuum field theory in these cases is not actually well-defined. We don’t have a satisfactory nonperturbative definition of them, but it doesn’t cast doubt on whether they exist. It just means we don’t yet have an adequate toolkit for understanding these things.”
I have a background in quantum field theory and I certainly share the expectation that asymptotically free or conformal gauge theories should exist. But unlike you I believe we should focus attention on things like this where hard work has not payed of because, fairly often, it turns out we are all wrong. I was very influenced by Feynman who told me, when I was a grad student, that these kinds of cases are opportunities that good scientists exploit by exploring the possibility that what everyone has expected, but failed to show, might be wrong.
At the very minimum, I think we must always maintain a clear distinction between what has been shown and what we hope will be true. And I certainly think that doubt should always be cast in cases like these. Doubt if free, whereas certainly about things that turn out to be wrong can be very costly.
Thus, you misunderstand me when you say,
“It seemed that Lee was insinuating that AdS/CFT isn’t really a nonperturbative definition of string theory on backgrounds with negative cosmological constant because the N=4 SYM (or related field theories for deformations of AdS) might not be well-defined. I think that 99% of people with experience in working with field theories would disagree with this statement….”
No, I was simply saying that to my knowledge N=4 had not been non-perturbatively defined. I was not expressing any view about the likelihood of this being done, nor was I insinuating anything. I was glad to hear from Jacques that progress was recently made about this and I will study those papers.
But science is not a democracy and whether 99% of people believe something is not an argument. If anything, if so many good people believe something they have failed to prove, it suggests that something is being overlooked.
Thanks, Lee
Urs,
{Q,Q}=2H and the existence of Killing vectors coming from Killing spinors is the same. If psi is a Killiing spinor, you can form
j_m = psi-bar gamma_m psi
(for some nice version of ‘bar’) and that is a Killing vector. If psi were a physical field, j would be its current. So It should better have the same mass (in terms of representation theory ot the Poincare group) as psi has. If psi is Weyl it means it is chiral, so it has to be massless. So j has to me light-like. If psi is Dirac and has positive mass then j points along the flow of that particle and thus has to be time-like.
Anonymous,
I see Lee has responded to the first part of your last comment. As for the second part, about the non-perturbative formulation of chiral gauge theories
“I don’t think people have been ignoring this. I just don’t think anyone has a clue how to make good progress.”
Sure, no one has a clue how to make good progress on this. But neither does anyone have a clue about how to make good progress on other major problems. The fact that no one has a clue how to make progress on the fundamental problems of string theory doesn’t mean people have stopped working on string theory. Instead they do what they can: they try to learn more about the problem by doing calculations that won’t make good progress but that they hope might teach them something that will allow them to make good progress. I see a huge amount of this kind of work on string theory, very little of it on chiral gauge theory.
Lee wrote,
No, I was simply saying that to my knowledge N=4 had not been non-perturbatively defined. I was not expressing any view about the likelihood of this being done, nor was I insinuating anything.
Sorry for misunderstanding your point.
Lee also wrote,
But unlike you I believe we should focus attention on things like this where hard work has not payed of because, fairly often, it turns out we are all wrong.
Here you misunderstand my point. I don’t say that we shouldn’t focus attention on such things. I was just emphasizing that, while a proof is lacking, there is a large amount of substantive information that suggests that we do have a nonperturbative definition of string theory on asymptotically AdS backgrounds. Of course putting this on a better footing is worthwhile, and understanding gauge theories nonperturbatively is (in my opinion) even more worthwhile. But I think almost everyone in the field would agree that understanding gauge theories nonperturbatively would be a huge advance. Many people chip away at this problem all the time in small ways. The lack of a major breakthrough isn’t, I think, because people are not trying. It’s just that it’s really hard.
Similarly, Peter wrote:
The fact that no one has a clue how to make progress on the fundamental problems of string theory doesn’t mean people have stopped working on string theory. Instead they do what they can: they try to learn more about the problem by doing calculations that won’t make good progress but that they hope might teach them something that will allow them to make good progress. I see a huge amount of this kind of work on string theory, very little of it on chiral gauge theory.
I just don’t agree. Maybe people don’t specifically focus on chiral gauge theory, but as I said above, the non-chiral case is not well-understood either, and there is a huge amount of effort directed at understanding QCD. Many people working on stringy things are doing it with the goal (or at least a goal) of better understanding nonperturbative aspects of gauge theories, and there are all sorts of non-stringy