# On String Theory from a String Theorist

Bret Underwood, a friend of mine from my time in Madison, WI, saw my post on String Theory, and took issue with my statement that it wasn’t testable. I’m still standing behind what I said, but let’s address what Bret has to say.

I don’t understand your argument above for why string theory is untestable. In fact, it seems to me you just outlined the best possible case for string theory! What you said above is that if I have a string theory construction of a phenomenon (say, the Standard Model or Inflation), which uses a set of parameters X, and makes some predictions, then I can find another set of parameters Y that gives a different set of predictions. Wonderful! This means I can determine the parameters (either X or Y) by making measurements, and rule out models and parameter sets!

I don’t think that’s wonderful at all; I think that’s a very dangerous analogy. Why? Because string theory has too much “wiggle room” to be scientific. String theory isn’t at all predictive in this sense. How many possible values for the string vacua are there at this point? The typical estimate that people cite is about 10500, according to the string landscape. For comparison, the number of subatomic particles in the entire Universe is somewhat less than 1091. There are far fewer than 10500 parameters describing our entire Universe, so people argue that one of those models is likely to match with the Universe. And when we find out which one it is, then we can figure out everything.

But that isn’t a scientific theory to me, not as I understand science. A scientific theory makes definitive predictions that are unique. But string theory doesn’t do that; at least, not for any prediction that I know. Most models of string theory predict a negative cosmological constant, for instance. But we don’t say that this means string theory is wrong, we say that this rules out those models, because we see a positive one. String theory gives you a 10-dimensional Brans-Dicke theory of gravity; we observe a 4-dimensional one with a Brans-Dicke parameter of infinity. But somehow, we don’t say string theory is wrong, we say that we just need to get rid of 6 of those dimensions and make that parameter be infinite. We don’t say how, we just say somehow. Most models of string theory predict small tensor modes, but most models of inflation do, too. What does string theory predict that’s unique to string theory? Other than “everything is made of strings,” I don’t know of one. Until there is one, and one that can be tested, I can’t be comfortable calling it a scientific theory.

The nightmare scenario for me is the following: suppose I describe a phenomenon (Standard Model or Inflation) in string theory with a set of parameters X, which gives some predictions. Then I consider another different set of parameters Y that give the same predictions. Thus, predictions are not unique, so I cannot distinguish models!

But what’s even the point of distinguishing models if there’s no observation I can make or experiment I can do that validates string theory? Maybe I can find one (if you’re lucky) or more than one (if your nightmare comes true) set of parameters that agree with all the laws of physics in our Universe. But what can you tell me that I don’t already know? That’s what I mean by untestable.

I’m not saying that people who are interested in this shouldn’t work on it. But I’m saying that if string theory is going to bill itself as being science as opposed to mathematics, it needs to address the issue of “what does it predict that nothing else predicts?” I don’t know of any test that’s ever been devised, even in principle, that can test it. Do you?

FYI: I downloaded a talk by Michael R. Douglas at Rutgers, a string theorist who’s actually optimistic about string theory being a predictive theory. He asks the question: “Are there testable predictions of string theory?” He says yes initially, but then admits the following:

…none of the ideas which have been suggested so far are guaranteed signatures of string theory.

Yikes. Sorry, Bret, but that means I place it into the category of an untestable hypothesis at the present time. If you can’t validate it and you can’t falsify it, it isn’t yet a good scientific theory.

April 18, 2008

I tend to agree with you, Ethan, though there is one way to interpret their statements which makes it more okay.

If string theory with parameter set X predicts exactly the same outcomes for all conceivable experiments as non-string theory Y, then those two theories are mathematically equivalent. Either is an equally valid description of our universe, and whether you take whatever baggage either one brings (e.g. extra dimensions) as “real” or just mathematical leftovers is the part that’s not science. Gell-Mann initially thought quarks were a purely mathematical construction, but he was still entirely sure the quark model worked. Many quantum numbers seem to have “real” meaning without representing anything physical.

It may just be the gusto that seems typical of string theorists that causes consternation, since in most things I’ve read, they insist that such constructs ARE real within string theory, and don’t write about them as pure mathematics that just happen to be part of a description of the physical laws.

2. #2 ethan
April 18, 2008

There’s an example of what you’re saying that’s pretty famous, the Wess-Zumino-Witten model. Wess and Zumino found a solution to this for a quantum field theory problem related to Ward identities, but it was very messy. Witten found an elegant solution more than a decade later, but it used an extra (fifth) dimension. Both are physically equivalent; Witten’s is mathematically nicer. But it doesn’t provide any evidence for a fifth dimension.
But nobody believed that Feynman diagrams were physical descriptions of what’s happening on a quantum level when they were first instituted. Now, many physicists do (although I still don’t). But yes, that part isn’t even science at this point.

3. #3 nc
April 19, 2008

String theory is the opposite of mathematical physics. It’s not even speculation, because it ignores all the facts known, and builds constructions upon fanciful guesswork. If you build a non-speculative theory upon fanciful guesswork, where is the physics?

If you have a ‘theory’ which isn’t even an ad hoc empirical model for known facts, which is defended by ignorant arrogance and censorship/bigotry towards alternative ideas like trying to incorporate gravity into the standard model and trying to work out a theory which actually predicts the parameters of the standard model based on factual evidence, then that ‘theory’ tells you that in order to work there must be 11 dimensional gravity floating like a surface on a 10 dimensional bulk, and 6 dimensions are rolled up into an unobservable Calabi-Yau manifold, why should you believe it?

It’s religion. It gets worse. To stabilize the 6 dimensions of the Calabi-Yau manifold into an unobservable size, you need Rube-Goldberg machines. Because you can’t see any of these epicycles, you don’t know what values they can take. There are about a hundred moduli or parameters describing the Calabi-Yau manifold’s six compactified dimensions, none of which are known. The resultant is 10^500 metastable vacua.

There is no evidence that any of them is the real world. It’s a worse situation than Ptolemy’s Earth-centred universe with its epicycles, because at least Ptolemy’s ad hoc model actually allowed accurate predictions of some things, even though it was physically incorrect and a mess.

String theory is the best example of groupthink failure after the examples of dictatorial regimes. It’s a case of excessive pride before a fall. They keep on hyping and saying how much a genius the theory is, without actually delivering the goods. Promises, promises.

The things that string theory claims to deliver are non-physics. A theory of black hole entropy or inflation or unification by coupling constants equalizing at the unobservable Planck scale, or what have you, isn’t physics unless it is empirically convincingly checked.

What a theory needs to deliver are checkable predictions, explanations for the coupling constants, mixing angles and masses in the Standard Model, and other checkable stuff such as self-consistent quantum gravity which approximates to general relativity on the classical limit (large scales).

The kinds of really imaginary or philosophical ‘problems’ that string theorists are proud of tacking neglect the real physical problems that remain ignored because they can’t compete with the spin machine of string, they have no funding, they get censored by so-called ‘peer reviewers’ (string theorists), and so on.

4. #4 Luboš Motl
April 19, 2008

Crackpots like you or NC clearly have no chance to understand the tiniest portion of theoretical physics. You are just far too limited.

Bret Underwood who knows these things roughly 10^{501} times more that all of your crackpots combined explains you extremely clearly, and in a very simple way that the smartest kids from a kindergarten have to grasp, that string theory is extremely constraining and extremely predictive because most things one could design at the beginning simply cannot be realized anywhere on its space of vacua and the combination of theoretical constraints and observed evidence usually reduces the number of possible candidate vacua dramatically.

You prefer not to torture your brain because it would hurt, wouldn’t it? You prefer to write down the number 10^{500} that scares you – because you are scared by virtually all numbers higher than 10, much like everyone else at your intellectual level.

10^{500} may be a large number and we don’t know for sure which of these vacua is the right one, matching the Universe around. But even all those 10^{500} vacua share many powerful and very general features that are universal predictions of string theory. And once all these things are understood more completely, the number clearly drops to a very small number and eventually one.

Also, the number 10^{500} is much smaller than 10^{10^{infinity}} which is the a priori number of theories and models we would have to consider if we didn’t have string theory. But you’re not interested in science and you don’t want to torture your brain. You are happier if idiots like you share your hatred against numbers greater than ten with you.

5. #5 ethan
April 19, 2008

NC,

I think you’re being a little unfairly harsh on string theory. It’s not that there’s anything wrong with the mathematics that they’re doing or the inelegance of the theory; to be completely fair, there is no other self-consistent framework to unify gravity and quantum mechanics. This includes frameworks like “loop quantum gravity,” which doesn’t unify gravity and quantum mechanics.

The question is, how is it relevant to our Universe? Even at this point, I think, if someone were to write down all the true values for string vacua on a piece of paper and slip them to Ed Witten, I don’t think there would be any definitive new predictions that would come of it. If that’s true, then I don’t see how it has the potential to be scientifically predictive. If that’s untrue, though, then I’ll have to recant what I said, because then restricting the parameters is a way to lead to definitive, unique predictions, and that’s my one gripe with it.

Lubos,

What on Earth do you mean by constraining and predictive? What physical parameters has string theory ever constrained? Other than string theory parameters, none. What unique predictions about the low-to-intermediate energy world has string theory made? Also, none. Even if you were able to solve string theory mathematically, essentially unifying gravity and quantum mechanics in a solid mathematical framework, unless you could make quantifiable predictions about observable phenomena, I still wouldn’t care, any more than I cared what the 45th Mersenne prime was.

I hope the ad hominem attacks continue to work out well for you.

Best,
Ethan

6. #6 nc
April 19, 2008

“But even all those 10^{500} vacua share many powerful and very general features that are universal predictions of string theory. And once all these things are understood more completely, the number clearly drops to a very small number and eventually one.” – Dr Luboš Motl

Dear Luboš, please don’t just make more hand-waving claims (deceptions/hype/spin) that you can’t prove (or maybe you’ll need to look at a mirror before ad hominem comments about people studying alternative ideas).

At least people reading that closely will perceive that you are writing about your belief in what will happen “once all these things are understood more completely”.

However, you then change tense back to the present and try to make out that it is “clearly” the case that one vacua in the 10^500 landscape looks like the universe we inhabit.

What makes you think that with 100 unknowns that can give rise to 10^500 possibilities, mathematics will ever be able to rule out sufficient vacua to turn the remaining choices into a falsifiable experimental test?

Why should string be getting so much hype in advance of actually making any falsifiable physical predictions, let alone getting experimental evidence to confirm those predictions?

The bandwaggon of celebration of string theory has lasted decades and since it has been premature (to put it mildly), it’s maybe the time to look at other, more exciting ideas now.

7. #7 nc
April 19, 2008

‘… to be completely fair, there is no other self-consistent framework to unify gravity and quantum mechanics.’ – Ethan

Ethan, sorry but I’m far too stupid to grasp what you mean here. Your comment could mean that you’ve ruled out all alternatives to spin-2 graviton conjecture, or that you simply haven’t seen an alternative which has yet been proved to be self-consistent. There is quite a lot of censorship, and many people have ideas they can’t publish in the right journals or even on arXiv, because string theorists have so much power. This is the problem with string theorists: they are perhaps too self assured without bothering to even check alternatives carefully. Any alternative is ‘crackpot’.

8. #8 ethan
April 19, 2008

NC,

There’s no other self-consistent framework to unify gravity and quantum mechanics that I’ve seen in the literature. There’s interesting work that’s going on in string theory towards having it become a scientific theory, but it’s unclear as to whether that will ever be the case.

It’s a really hard problem, though, and a lot of people are afraid, as you rightly assume, to work on alternatives to string theory. Loop quantum gravity, which I mentioned above, doesn’t try to unify gravity with quantum mechanics. But it does attempt to describe how the gravitational force works on small (quantum) scales. There are “crackpot” alternatives out there, to be sure, but not every alternative theorist is a crackpot. Hell, I don’t think the people who work on MOND are crackpots, and I’m an expert on dark matter!

Don’t stress about Lubos. I choose to let him exercise his voice here, because I can take his attacks and I want this to be a place where people can express their ideas uncensored, even if I disagree with them.

And when I say “self-consistent framework” I’m talking about the problem of higher-order loop diagrams in quantum field theory blowing up; e.g., being non-renormalizable. This happens in all field theories, which is why they’re just good approximations of physics, but for gravity, it happens in the first term and just gets worse. But string theory solves this problem, and it’s the only method we know of that solves it. Don’t deny it credit for that; that’s a big deal mathematically!
Ethan

9. #9 nc
April 19, 2008

Self-consistency in a theory of unobserved spin-2 gravitons, unobserved unification at the Planck scale and an ad hoc number of unobserved extra spatial dimensions (but not observables) is not impressive because the inclusion of unobservables in string theory – for the purpose of making the theory internally self-consistent – lead to the need for the Calabi-Yau manifold and the landscape problem. E.g. the number of dimensions in string theory is partially fixed by the criterion of self-consistency. So it’s self-consistent not as a result of agreement with the world, but just because it was forced to be m mathematically self-consistent (to one or two loops, or however far the infinite perturbative expansion has been checked for the avoidance of infinities). At the end of the day, self-consistency isn’t even a basic requirement of a successful theory like QED, as Feynman explained lucidly in his book QED (1985):

‘The shell game that we play … is technically called ‘renormalization’. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It’s surprising that the theory still hasn’t been proved self-consistent one way or the other by now …’

What matters is not self-consistency, but agreement with nature.

10. #10 ethan
April 19, 2008

Well, and that last part, agreement with nature, is the holy grail of string theory. Feynman had different battles to fight, because he was pushing the “agreement with nature” argument while others (Schwinger, for instance) refused to work within his inconsistent mathematical framework. General relativity is both: mathematically self-consistent and in agreement with nature. String theorists are also hoping for both, and I don’t think that’s unreasonable. But until there is agreement with nature, I don’t think it’s reasonable to treat it as a physical theory.