Oswaldo Zapata Marín is writing a series of essays about the history of superstring theory at Spinning the Superweb. His first essay, On Facts in Superstring Theory, describes something that is very mysterious to me as a math person: the process by which conjectures in string theory achieve a status akin to fact.
Via Not Even Wrong.
Hm… as someone who is familiar with the theory (though not an expert), let my try to answer some of the strange claims made in this article. This turned out to be quite a long answer, so I might also post it on my blog.
Let’s focus on this one sentence from “A case study: the AdS/CFT correspondence”, because I think this is where much of the confusion lies:
“In the authors’ opinion the correspondence was still in the phase of gathering evidence. It was not yet established as scientific fact.”
This is quite a misleading statement, for several reasons. The correspondence is a mathematical conjecture — there is nothing ’scientific’ about. But more importantly, it is misleading in its implicit description of how physicists work these days.
It is important to recall that the ultimate goal in physics is to predict the results of experiments. As long as we reach this goal, anything goes. One example of this is the path integral. As far as I know mathematicians still don’t have a definition of path integration in any realistic theory. And yet this ill-defined tool has been successfully used for decades to predict experimental results.
Sometimes physicists face a situation where there is an interesting mathematical statement, which would be useful if true, but it is too difficult to prove.
What do they do in such a situation? This is the crucial point: They gather evidence. Mathematical evidence.
Let’s take an example that is unrelated to string theory: Seiberg duality. Roughly, this is a conjectured duality (isomorphism) between certain pairs of supersymmetric field theories. This is a conjecture — it has not been proven — but we have a lot of evidence that it is correct. For example, there is a certain calculation one can make in the two theories (calculating about ten numbers), and if the theories are isomorphic then the numbers must come out the same. Well they do come out the same, and while this doesn’t prove that the duality holds, you can see why this is compelling evidence. It increases our confidence that the conjecture is correct.
So far, Seiberg duality has passed all the tests thrown at it, so physicists are quite confident that it is correct. Of course, it’s still a conjecture, not a fact. But you see, the more evidence we have, the more we become confident that this is an interesting conjecture worth researching.
This is where the ’sociological’ effect comes from: As time goes by, some conjectures (such as Seiberg duality) pass more tests, and our confidence in them grows. Others fail a test and are thrown out. So there really isn’t much sociology at play here.
Again, our goal isn’t to prove Seiberg duality. It would be nice if we could of course, but the more interesting thing is what it might teach us about strong coupling limits of realistic theories. This is the real goal. And again, this has nothing to do with string theory!
Now the same goes for the AdS/CFT conjecture, which is a conjecture in string theory. At first it seemed like an interesting conjecture, and as time went on more and more evidence was gathered, and it was all consistent. So we are more confident that AdS/CFT is true today than we were several years ago. It’s still not a fact, and no one I know treats it as a fact. This I can say from my personal experience, working with people in the field.
At some point in the article it is claimed that this method doesn’t apply because string theory isn’t “empirically verifiable”. Well this is just nonsense, but let me not get into that.
Finally let me address the question of whether string theory is a theory of quantum gravity. Again we have good evidence that this is true, and as far as I see the article ignores one important piece of evidence — the calculation of the black hole entropy. This quantity was calculated semi-classicaly long ago by Bekenstein and Hawking. This means we know what the answer should be in any theory of quantum gravity — even without knowing the theory. Reproducing this result is a non-trivial test that any theory of quantum gravity must pass.
String theory reproduces this result, as was shown using the AdS/CFT correspondence. As a result of this calculation, confidence in string theory as a theory of quantum gravity of course grew. It is not a matter of fashion or of sociology, just of cold hard evidence.
Guy
On the level discussed in the first article (I haven’t had the strength to wade through the subsequent ones), Zapata Marín is simply wrong.
There’s an old theorem, due to Weinberg, that any unitary theory of an interacting massless spin-2 particle (in flat space) has, as its low-energy limit, Einstein gravity.
The argument is simple: start with the free theory of a symmetric tensor field, h. To remove the unphysical polarizations, you need to postulate a gauge symmetry which looks like an infinitesimal diffeomorphism. To couple h to matter (or, for that matter, to itself), you find that the gauge transformation needs to be modified by nonlinear corrections. Those, in turn, require modifying the action for h… Iteratively, you build up both the Einstein action, and the full nonlinear diffeormorphism symmetry.
So, if you grant me that string theory is a consistent interacting quantum theory containing a massless spin-2 particle, it is necessarily a theory of gravity. Perhaps you don’t want to grant that. But Zapata Marín doesn’t assert that string theory is inconsistent. Instead, he goes on for paragraphs, arguing that an interacting quantum theory containing a massless spin-2 particle is not necessarily a theory of gravity.
At that point, I throw up my hands in despair, and move on. Life is too short …
I wasn’t aware of this theorem, thanks!
Guy: What would be the reception if I announced that I thought that Seiberg duality is false?
Jacques: That’s a very interesting result.
False always? Or false for particular values of Nf and Nc?
Seiberg duality (and related developments) represent a huge advance in our understanding of the low-energy dynamics of strongly coupled gauge theories. But it’s certainly not the last word on the subject. In particular, if you discovered some feature of the low-energy dynamics that would distinguish between the two gauge theories, whose behaviour Seiberg says is identical, that would be interesting …
I’m not sure it’s that “interesting.” In some sense, it’s pretty obvious.
In any case, it’s the sort of result one would be expected to know, if one were writing essays on this subject…
Walt: I’m not getting email alerts when someone comments on this thread, hence the late response. Of course Distler said it but let me answer anyway.
If you had evidence that Seiberg duality was wrong, people would be very interested in your results. I’m guessing it would quickly become the “hottest” topic on hep-th, until the implications of your results were worked out. For example it would be interesting to understand whether you invalidated all the isomorphisms or just some of them.
You would certainly not be ignored simply because what you say goes against current belief. High energy theorists are interested in the truth, just like other scientists.
I’ve never said otherwise. High energy theorists are interested in the truth, but conjectures exist in a gray area.
So what if it’s just my opinion that Seiberg duality is wrong? I don’t have a counterargument; I just find the existing evidence not very compelling. What would be the reaction then?
(Just to be clear, I have no opinion on Seiberg duality.)
…but conjectures exist in a gray area.
Most of theoretical physics, indeed most of science, exists in such a gray area. There are very, very few results which can be said to have been rigourously proven.
At best, one can say that the preponderance of evidence (sometimes, an overwhelming preponderance of evidence) favours a certain conclusion.
In the case at hand, Seiberg and others have amassed a fair amount of evidence in favour of the conjecture. No single piece of evidence is particularly conclusive, but taken together, they have convinced most experts that the conjecture is correct.
I think a reasonable person would ask for an alternative conjecture for the infrared behaviour of N=1 SQCD. One that passes all of the consistency checks that Seiberg’s does.
But that is what I would call a sociological process — the process that I was curious to hear explained. In one society, a reasonable person would ask for an alternative conjecture, and the opinion of experts is considered decisive. In another society, skeptics owe believers nothing, and while the opinion of experts counts for something its weight is very small. For example, the circumstantial evidence for the Riemann Hypothesis is pretty strong, and most experts think it’s true, but this doesn’t weigh very heavily.
And this isn’t like the normal physics versus mathematics cultural difference — if physicists can predict the outcome of thousands of experiments, the fact that they don’t have a rigorous proof is a minor nuisance. A conjecture about a theory that at the moment only exists inside human heads really is a gray area in a way that Feynman diagrams are not.
I’m not saying that the mathematician’s attitude is the right one. If Seiberg duality is true, then any amount of skepticism is a waste of time. I’m just curious, as an outsider, how the culture of theoretical physics works.
I doubt things work quite the way you describe.
Per your example, I doubt there’s much effort devoted to developing mathematical structures that would be relevant or interesting, only if the Riemann Hypothesis turned out to be false.
Someone working on a topic, sufficiently far-removed from the behaviour of N=1 SQCD, can afford to be agnostic about whether Seiberg’s conjecture is correct, just as someone, working in a branch of mathematics far removed from any implications of the (truth or falsity of) the Riemann Hypothesis, can afford to be agnostic about it.
Someone working in a more closely-related subject has no such luxury. And such a person would be foolish, indeed, to predicate a significant amount of their own work on the “contrarian” premise that the conjecture is false.
There are other kinds of evidence, besides experimental measurements.