Over at sci.physics.strings there’s the scary sight of Lubos Motl agreeing with me in a posting about “Stringy Naturalness”. Well, maybe he isn’t directly saying he agrees with me, but “It would be too difficult for me to pretend that I disagree with these Woit’s remarks” is pretty close. Lubos is criticizing the new sort of “naturalness” critierion advocated by Miichael Douglas in a preprint reviewing his recent work on the “Landscape”. By this criterion a low energy effective QFT is more “natural” when there are more supposed string theory vacua that have this low energy limit. As Lubos points out, the danger with this criterion is that it tends to lead you to the conclusion that the most “natural” effective field theory is the one that is least likely to be able to predict anything new.

The posting immediately before Lubos’s is from Michael Douglas himself, responding to an earlier thread. In it he explains the goal of his work as follows. He wants to estimate N_SM, the number of vacua consistent with the observed known Standard Model behavior, then

“Based on this information, we can decide whether we should continue the search for the right vacuum directly (appropriate if N_SM <= a few), look for additional principles to cut down the number (if N_SM is large), or give up and start making anthropic arguments or whatever (if N_SM is ridiculously large)." The posting immediately before Douglas’s asks for “what would cause string theory to become nonviable and abandoned”, but hasn’t gotten any responses. An obvious response would be that if it becomes clear that string theory has so many consistent vacua that it can’t ever predict anything, the theory would have to be abandoned. Neither Douglas nor others working on the Landscape seem willing to mention this possibility in public, the closest he gets is the line about having to “give up and start making anthropic arguments or whatever”.

>This behavior of a perturbation series isn’t mysterious

Well, at least it is to me. But I admit I haven’t been studying this problem in details. I guess this has something to do with what Connes and Kreimer are doing.

Presumably the perturbation series for QED is divergent but asymptotic. This means that, while you can’t get an exact result at finite coupling by summing the whole series, if you take the first few terms of the series you get something which approximates the exact result more and more accurately as you take the coupling to zero. This behavior of a perturbation series isn’t mysterious. The exact result is not analytic at the point you are trying to expand about (zero), so the power series expansion doesn’t converge. You see the same thing in simple QM examples with the quartic potential.

In QED, for small coupling, the perturbation series gives quite accurate results for most everything you want to calculate. People doing string theory like to believe that perturbative string theory is a good asymptotic expansion for some quantitities (e.g. giving a graviton and reproducing GR at low energies), but not others (e.g. they would like to believe that it fails to describe the vacuum state). As far as I have ever been able to tell, this is purely a matter of wishful thinking and string theorists are promoting perturbative string theory when it gives them what they want, ignoring it when it gives them something they don’t want.

>More accurately, one can show that the terms in >the perturbation series for QED are finite and >well-defined at all loops

But the series does not converge, does it ?

It is still a wonder to me how the first few terms of a divergent series can give the right experimental results to 16 decimal places or something like that. Could it be that the perturbation series is not really self-consistent and would be made so only by including quantum gravity effects ?

More accurately, one can show that the terms in the perturbation series for QED are finite and well-defined at all loops, for superstring theory this has only been shown up to two loops, although people hope it is true for all loops.

Non perturbatively, you can rigorously define QED with an ultraviolet cutoff (e.g. the lattice), but the evidence is that when you take the continuum limit, the renormalized charge goes to zero, and you end up with a non-interacting theory. This doesn’t happen for QCD (related to why Gross-Politzer-Wilczek got a Nobel prize this week). QCD can be perfectly rigorously defined with a cutoff, and all evidence is that you get exactly the physics you expect when you remove the cutoff (although there is no rigorous proof of this).

Non-perturbatively, no one has even a good conjecture about what the definition of non-perturbative superstring theory or M-theory is. It’s a very different situation than QFT, not only can’t you prove anything, you don’t even know what it is you would like to prove.

It’s my impression that perturbative QED and perturbative string theory are about equally well-formed mathematically – they both exist as formal series but there’s no proof of convergence. But I’m not sure how the dualities, branes, “11-dimensional limit”, etc., rate.

The definition of M-theory is not “a little vague”, it is non-existent. “Something which is 11d supergravity in some limit” is not a definition, it is an expression of a hope that there is a definition. QFTs can be mathematically rigorously defined, although in interesting cases it is difficult to rigorously prove that they have all the properties one would hope for.

What I think would be helpful is to have a taxonomy of field theories, broad enough to include M theory. Then we could see its place in relationship to the other possibilities. It appears to be a deformation or extension of 11-dimensional supergravity. Can we say what *sort* of deformation or extension? And do other theories of the same sort exist, but derived from simpler field theories? Do they feature objects considered to be uniquely M-theoretic, like D-branes or T-dualities? Can we say anything a-priori about the possibility of such objects appearing outside of the M-theory framework? Etc.

I take your point about M theory’s definition (founded on the union of the moduli spaces of the string theories) still being a little vague. But it’s not as if the existence of most ordinary QFTs can be demonstrated rigorously either.

This would be a lot more plausible if anyone actually knew what M-theory was. So far the existence of a theory anything like what you are describing is just wishful thinking.

I think of M theory as the “Monster Group” of field theories. Finite simple groups are famously classifiable into a number of infinite families, with 26 ‘sporadic’ groups left over, of which the Monster is by far the biggest. The Monster has a little bit of everything in its makeup, so if you are trying to identify an unknown simple group and know just a few generating relations, there would be a reasonable chance that it looked like some part of the Monster. In the same way, M theory is a sort of field theory (under a generous definition that includes topological field theories, noncommutative field theories, etc.), and it features so many sorts of excitations that perhaps ‘most’ field theories resemble some M-theoretic vacuum.

So I’m sympathetic to the critical tone of this blog. I don’t think we should *presume* that M theory is the final theory, when its bare empirical adequacy has not yet been demonstrated. However, if it does turn out that the landscape’s bounty is so great as to render the theory almost unfalsifiable, I think it will still warrant much more respect than it gets here. It will depend on how many *other* (non-stringy) field theories are *also* capable of reproducing the Standard Model. If there are lots, then yes, M theory will not be so special. The capacity to include gravity might be decisive here (there’s obviously an infinity of non-stringy field theories containing just the gauge forces). If LQG, the Visser/Sakharov ’emergent gravity’ program, or some other approach to quantum gravity pans out, that will be a blow to string theory’s proclaimed uniqueness. If the other approaches falter, that will strengthen the position of M theory. Even if there are a million distinct ways in which M theory might give us the world we see, it would then still be the favorite, no matter how unhappy we might be with that epistemic situation.

But this is all cart-before-the-horse. First let’s do the job of seeing whether M theory can describe reality at all; if it can, let’s find out all the ways that it can; and once we’ve done that, then let’s have this discussion again.

*Any* framework capable of reproducing the Standard Model (i.e. capable of predicting “anything we can observe”!), even one made of gremlins, warrants interest, simply because it might be the truth.Mitch, is string theory really capable of reproducing all aspects of the standard model? No unbroken low-energy supersymmetry, no new long-range forces (massless scalar particles associated with moduli), no new gauge bosons, an extremely long-lived proton? And a small and positive cosmological constant.

Would you rather a soccer ball for describing the universe?

http://www.hep.upenn.edu/~max/wmap3.html

Chris W – wonderful post.

There is another argument (third?) against string theory that doesn’t get any attention. I call it the “prima facie preposterous” argument. String theory is not only wrong, it’s

wrong-headed. The fact that it can’t predict anything, that it can’t reproduce the simplest physico-mathematical structures, that its most ardent practitioners are willing to resort to anti-scientific arguments and polemics, and that a sterile hermaphrodite is held up as a “theory of everything that will enable us to see God, and give him football betting tips”, are all symptoms of having taken seriously a ridiculous idea. I can’t think of ANY example in physics history in which a ridiculous idea was seriously considered. The orbs of Kepler actually led him to right answers, and the epicycles of Ptolemy represented a sane theory in its day, even an esthetic one.*Any* framework capable of reproducing the Standard Model (i.e. capable of predicting “anything we can observe”!), even one made of gremlins, warrants interest, simply because it might be the truth.

The most recent overview of string phenomenology that I read (from late last year), says (page 7) that no-one has yet exhibited a string model manifestly capable of giving the right values for the fermion masses and CKM matrix elements. Researchers are apparently busier exploring the many paths to *qualitatively* reproducing the Standard Model (e.g. the gauge group). These debates about the phenomenological fecundity of the string landscape, and whether it invalidates string theory as science, may be a little premature.

To Mitch P: Peter is making a methodological and epistemological point, not an ontological one. He isnotsaying that “Since string theory can generate millions of models that resemble our observations, the world can’t have a string-theoretic foundation”.He is saying that the theory in its current form appears to be effectively immunized against refutation, other than by observations that would also refute its predecessors (the Standard Model and general relativity). If someone makes new observations that are inconsistent with one string-theoretic model, then theoreticians can trot out another model accounting for the observations in question, which they might well claim to be equally consistent with the basic principles of the theory. Those principles are thereby insulated against any possibility of being contradicted by observations. The models take the fall instead, and no one worries much about it because there are so many of them to choose from.

That is, no one worries if they think the theoretician’s objective is to be always ready with another model (derived from his favored

mathematicalframework) whenever previous models have trouble accounting for observations. This makes sheer mathematical richness a virtue, and indeed the mathematical richness of string theory is often proclaimed as an important source of its fascination.However, physics and science generally are not simply exercises in applied mathematics, ie, in mathematical model building. In his early years Einstein was quite suspicious of mathematical formalism, and even in later years lamented having to respond to the ideas of people who in his words “can calculate but can’t think”. He was trying to get at fundamental principles, and it was vital to him that those principles be lucidly expressed and subject to empirical refutation as directly as possible. Ensuring that this is the case depends in part on a methodological commitment to avoid immunizing stratagems. This is tricky — one mustn’t give up on a theoretical idea too easily — but it is arguably the most essential aspect of doing science.

To many people string theory continues to “smell” right. The question has become, “exactly how does it smell right; what are its central and distinguishing

physicalprinciples, and what are their unambiguously testable consequences?” In the 1980s it was often said by Witten and others that, unlike general relativity, string theory’s central principles remained obscure, and a major goal of research in the field was to elucidate them. This goal seems to have dissipated, or to have degenerated into much aimless wandering in a vast mathematical wilderness.Peter: You said, “The standard model QFT can predict anything that we can observe, using only of order 20 parameters.” In the context of this discussion I feel compelled to amend this to the following: “The standard model QFT can account for anything that wehaveobserved, using only of order 20 parameters.” Presumably (one hopes!) there are observations we will make someday that the Standard Model cannot account for, over and above the values of the 20 parameters themselves, whose inexplicability motivates so much recent effort to go beyond the standard model. However, I think we can be rightly suspicious of the notion that there are a vast profusion of such observations yet to be made which require a far richer theoretical framework to understand. String theory appears to be just such a framework. I suspect that much of it will ultimately prove to be irrelevant to fundamental physics. I hope that in the midst of it (and in loop quantum gravity) are the outlines of a few key ideas that will prove essential and lasting.GremlinsIf we did not consider the alternate view of what the spacetime fabric could be, how would we ever consider step off points for consideration?

In quantum mechanics, the vacuum of space is not a vacuum; rather, it is field with virtual particles, such as the graviton. Light passing through this field of virtual particles is refracted, just as it is when passing through water or any medium.The graviton, being the essence of gravitational force, would interact with (or slow down) those particles with greater gravitational potential. With mass directly proportional to energy, as expressed in e=mc2, photons of higher energy have greater gravitational potential than lower-energy photons — as if they “weigh” more.

The highest-energy photons would therefore travel through space more slowly than lower-energy photons. (This does not violate the constancy of the speed of light, for light travels at the same speed only in an absolute vacuum.) To detect the very slight difference in photon speed, one needs an extremely distant source emitting extremely high-energy photons: that is, the gamma ray burst.http://www.astronomytoday.com/cosmology/quantumgrav.html

A “theory” that doesn’t predict anything isn’t a scientific theory, and if you spend your time studying a theoretical framework that is inherently incapable of predicting anything you’re not doing science.

The standard model QFT can predict anything that we can observe, using only of order 20 parameters. Present day string theory predicts absolutely nothing at all, using a much more complicated theoretical framework than that of Standard model QFT. It’s looking increasingly likely that this is because the string theory framework is inherently vacuous: to get the standard model out of it as a limit you have to assume the existence of such a wide range of vacuum states that you can’t predict anything at all beyond the standard model (which is put in by assumption). All you have is a complicated way of parametrizing an infinite variety of possible extensions of the standard model. Unless you can figure out some way to use this to predict something, whatever you are doing, it isn’t science.

What if I believe in gremlins and said that my theoretical framework is that everything is determined by the gremlins and that’s all we can ever know. When you complained that my gremlin theory can never predict anything and never be checked, I could answer you:

“This doesn’t make sense. There are a million ways that a gremin-theoretic world might look like the one we inhabit – therefore we don’t live in a gremlin-theoretic world?”

Just describing the world in terms of fanciful abstract entities is not doing science. Finding a simple set of abstract entities that can predict new things we didn’t already know about the world is.

“if it becomes clear that string theory has so many consistent vacua that it can’t ever predict anything, the theory would have to be abandoned”

This doesn’t make sense. There are a million ways that a string-theoretic world might look like the one we inhabit – therefore we don’t live in a string-theoretic world? therefore we don’t think about whether we live in a string-theoretic world?

A similar argument could have been used to rule out “quantum field theory” as illegitimate. “You can make a QFT do just about anything – what sort of scientific theory is that?”

Well, I don’t think its entirely fair to criticize String theory quite yet. As with all new work in progress theories, there is still room for deeper principles that may eliminate all sorts of degenerate vacua. Brian Greene gave a lecture here a few weeks ago where he *optimistically* thought there was still room for different formalisms that could solve things in a more elegant fashion.

Michael is entirely in his right to publish papers exploring statistical values on the landscape. And how much fine tuning/philosophizing ultimately such a distribution would require. If you want to follow the math, then follow it wherever it may lead. It may end up actually falsifying what you set out to do.

More interesting to me, is that I have yet to see a convincing phenomenological model that actually reproduces a stable Standard model with even one single handpicked choice of vacua. That is, without the appearance of to many hard to believe artifacts. Say one that adequately satisfies bounds on proton decay lifetimes and with the desired suppression of flavor changing neutral currents. Jacques Distler had a blog about that some time ago.

I think the idea is if you can get close enough to SDM physics, than you can argue that there probably exists some similar, but different enough choice that does give the proper suppression. Then again, Distler said that even that was probably quite difficult (something to do with R-parity appearing only in very isolated parts of the moduli space)

Imagine if string theory dies a painful death and gets “defunded” shortly after the LHC experiment goes online and rules out low energy supersymmetry. It would be hilarious if 70 years passes away, some future particle/gravity theorist stumbles across string theory by “chance” and resurrects it again as a viable quantum theory of gravity with no “living memory” of it’s previous incarnations. (70 years into the future, all of the proponents of today’s string theory would be either dead or retired with very little to no influence in physics research).

String theory then becomes like the Energizer Bunny which keeps on going and going and going … and refuses to completely die!

Or, to put it more starkly (and a bit sarcastically), string theory will become nonviable and deserving of abandonment when it becomes clear that its practitioners are unable to specify any other conceivable circumstances (logical or empirical) under which it would become nonviable. At that point it would be abandoned because, as a physical theory, it has become a bore, ie, it is no longer interesting as a basis for an empirical research program, and most young physicists are looking at alternatives (and are being encouraged to do so).

That situation has not arrived, but it has become worth worrying about for anyone who sees lasting value in the ideas and accomplishments of the field.

Actually, I am not that surprised. As you yourself pointed out some time ago, ignoring his rhetoric like “superstring theory is the language God wrote the world” and all that, he is actually very sensible.

Although I personally don’t think string theory is ever going to explain particle physics, I do enjoy, and often learn from, Motl’s observations, who I believe is a reincarnation of Pauli. Maybe just as Pauli was proven wrong on the utility of Yang-Mills theories (massless gauge bosons; confinement and SSB unknown to him), he may be wrong on LQG, despite some pretty good observations on the field.:)