A few quick items before the holiday:

- I hear that Luis Alvarez-Gaumé will be the next Director of the Simons Center, starting next Fall, taking over from John Morgan, the founding Director. My understanding is that the hope was to have the directorship alternate between mathematicians and physicists, and with the hire of Alvarez-Gaumé, they’ve managed to achieve this. His early work on supersymmetric path integrals and the index theorem (see here) was characteristically lucid and this remains one of the great points of intersection between modern mathematics and the quantum theory. One of the best relatively short introductions to QFT is this one (with a shorter arXiv version here). I think he’s an excellent choice.
- In physics blogger news, Tommaso Dorigo reports that he has found a publisher for the book he has been writing: Anomaly! – Scientific Discoveries and the Quest for the Unknown, and it should appear next year. I’m very much looking forward to seeing a copy. His insightful but irreverent take on experimental HEP I’m sure will make this a fascinating read for anyone interested in the subject.
- Matt Strassler’s blog has been dormant for a while, but he has now been heard from. After a couple year visiting position at Harvard, he says he’s now “employed outside of science”, but working on a book about particle physics for non-experts.
- Jim Holt has a review in the latest New York Review of Books of my colleague Michael Harris’s Mathematics Without Apologies.
- By some accounting, today is the 100th anniversary of Einstein’s GR field equations, which he presented November 25, 1915 at a lecture in
~~Gottingen~~Berlin. This anniversary has been celebrated in many places, in many ways this year, so there’s not any need for me to chime in. Among many excellent treatments of the topic, there’s also an unfortunate tendency of some to use Einstein to grind their particular axes. Sean Carroll I suspect has Einstein spinning in his grave, using the PBS NewsHour to enlist Einstein as a multiverse fan:

The ability for seemingly constant things to evolve and change is an important aspect of Einstein’s legacy. If space and time can change, little else is sacred. Modern cosmologists like to contemplate an extreme version of this idea: a multiverse in which the very laws of physics themselves can change from place to place and time to time. Such changes, if they do in fact exist, wouldn’t be arbitrary; like spacetime in general relativity, they would obey very specific equations.

Perhaps Carroll could enlighten the public by writing down these “very specific equations” he’s advertising, for comparison to the Einstein field equations.

If I were to grind my own ax here, it would be to note that Einstein’s great breakthrough came about through close collaboration with some of the best pure mathematicians around, adopting difficult but deep ideas about geometry. Without the mathematicians, I’d guess that the theory of general relativity would have taken many more decades to come to fruition. Maybe there’s a lesson there…

`Perhaps Carroll could enlighten the public by writing down these “very specific equations” he’s advertising, for comparison to the Einstein field equations.’

As if the public (as in “PBS”) were enlightened even by Einstein’s equations.

Warren,

It seems I was being too indirect. The point is that there are no “very specific equations” for the landscape, so Carroll is moving beyond axe-grinding into being intentionally misleading here. At this point no one knows what the space of configurations of a full string landscape theory might be, or what dynamical equations on this space might be the right ones. What exists are just some conjectured approximations in some very specific Rube Goldberg-esque constructions (eg KKLT), and even those are very complicated.

I think even the unsophisticated can get the basic gist out of the simplified expressions of Einstein’s field equations one typically sees in popular treatments (or on tee-shirts). I’ll never know the full power of the tensor maths embedded therein, but the “matter tells space how to curve, space tells matter how to move” aspect, and the impact of the modern inclusion (as well as Einstein’s mistaken one) of lambda has, is appreciable on a superficial level. Not sure if I would be able to form sound judgments if one stuck the universe of Einstein next to a multiverse, expressed in equations. I am wise enough to know how useless the latter is to science unless it makes some testable predictions, which it hasn’t, and very likely won’t, ever. Juxtapose that fact with the successes of GR, and I should hope the depressing reality multiverse mania would be obvious to any interested layperson. What’s sad is the lack of interest many in the media show in being hard-nosed about the facts, which are simply GR is a spectacularly successful theory, and the anthropic multiverse is utterly bereft of value until it makes even one testable prediction that isn’t utterly trivial or tautological. Which it hasn’t. And likely never will.

In the words of Einstein :

“Nobody who really grasped [the general theory of relativity] can escape from its charm, because it signifies a real triumph of the general differential calculus as founded by GAUSS, RIEMANN, CHRISTOFFEL, RICCI AND LEVI-CIVITA”

“On the General Theory of Relativity” (submitted 4 November 1915, published 11 November 1915) from http://einsteinpapers.press.princeton.edu/vol6-trans/110.

`If I were to grind my own ax here, it would be to note that Einstein’s great breakthrough came about through close collaboration with some of the best pure mathematicians around, adopting difficult but deep ideas about geometry. Without the mathematicians, I’d guess that the theory of general relativity would have taken many more decades to come to fruition. Maybe there’s a lesson there…’

Funny how it is that some of the best pure mathematicians around HAVE BEEN and ARE collaborating with physicists about deep and difficult ideas about geometry, topology, etc. They work on mathematics related to string theory (Kontsevich, Yau, Morrison, Donagi, Morgan, Freed, Donaldson,…).

The deepest ideas in mathematics and the deepest ideas in theoretical physics have been intertwined for centuries (Newtonian dynamics/calculus, Maxwell theory/fiber bundles, Einstein gravity/Riemannian geometry,…).

String theory has been the source of some rather deep results in mathematics over recent decades (monstrous moonshine, elliptic genera, homological mirror symmetry, Seiberg-Witten theory, …). The flow of ideas in both directions has been stimulating for both fields.

The cognitive dissonance of your love of mathematics and your antipathy toward string theory is simply breathtaking … and telling. Maybe there’s a lesson there…

Nature has a story this week about his collaborations

http://www.nature.com/news/history-einstein-was-no-lone-genius-1.18793

Peter, I thought Matt is a tenured prof at Rutgers.

shantanu

Emil,

My criticisms of string theory have never been about its effects on mathematics. That’s an extremely interesting subject, but one of great complexity, beginning with the fact that “string theory” is now a pretty ill-defined term. Eliminating actual content and complexity by claiming all sorts of very different things as “related to string theory” is just a tedious ideological debating point.

If you’re interested in what I think, and not in a dumb string theory rules/sucks argument, you could start by noticing that my complaints have always been about the effect of “string theory” on physics, not on mathematics. You write about collaboration between mathematicians and physicists on “deep and difficult ideas about geometry, topology, etc.”, which is quite accurate. What you don’t mention is such collaboration on deep and difficult ideas about physics. The string theory unification picture of the world has degenerated into a hideous pseudo-scientific story about the “Landscape” (do you think there is deep new mathematics there?) and wishful thinking that the LHC will see some evidence for SUSY (any collaboration with great mathematicians on making LHC predictions about properties of superpartners?).

There’s a wide array of wonderful deep mathematical ideas behind fundamental physics and lots of very good mathematicians that would like to think about them. If physicists would admit that string theory unification has been a failure and abandon empty, dead ideas, there would be even more opportunities for new interesting overlaps of the two subjects.

Shantanu,

Strassler resigned his position at Rutgers a couple years back.

Peter,

Did Strassler explain why he resigned? I would think Rutgers was a very good position, low teaching load, don’t know how good the department is in physics (it’s very good in math) but you are certainly near plenty of great people in Princeton and the city. Was he just sick of physics? Not if he took a visiting job at Harvard, I wouldn’t think. Did he think a few years at Harvard would get him a better gig?

Jeffrey M,

I have no idea why Strassler left Rutgers (which has a very good physics department), you’d have to ask him. He has continued to be active in physics research, no evidence this was because he’d lost interest in that.

Emil, there are also great mathematicians working at the interplay between geometry and physics, and not interested that much in string theory, e.g. Connes. There might also be a lesson here.

martibal,

On the topic of Connes and string theory, it may not be 100 years, but 10 years ago I posted this

http://www.math.columbia.edu/~woit/wordpress/?p=313

The story about string theory and Chicago is rather funny, perhaps Emil knows who it refers to.

All, actually there was nothing at all about string theory in this posting. I’d like to encourage discussion of any other topic than that.

Peter,

In providing context for his failed grant applications, Strassler says: “U.S. government cuts to theoretical high-energy physics groups have been 25% to 50% in the last couple of years”. Is this correct? I had no idea.

Einstein sought guidance from good mathematicians on how to mathematically formulate his ideas about how to solve certain problems in physics. Again, the initial ideas were

about physics, and they were his ideas, with some inspiration from people like Ernst Mach.S. S. Chern saw this clearly, and discussed it in a an edited collection of symposium talks published following the Einstein centennial year of 1979. (See pages 271-287.)

As of now we lack physical ideas of comparable fruitfulness in confronting the current problems in fundamental physics. We have no lack of mathematical ideas, but we don’t know how to select which ones we need, or clearly identify the kind of new mathematics that might be required. (I’m inclined to believe that the problem is primarily one of selection and reformulation; the array of available mathematical ideas is already vast.)

Woit,

Could you elaborate on Einstein working with great mathematicians? I’m not an historian on the subject, but I believe Einstein worked a little bit with Marcel Grossmann to understand some Riemannian geometry, but that except for this collaboration, he developed his theory quite independently.

PS:Chern’s essay (originally a talk) may have been republished elsewhere as well, perhaps in a volume of his collected papers.ronab,

That’s somewhat of an exaggeration. The DOE HEP theory budget numbers recently are

FY2013 66.3 million

FY2014 64.3 million

FY 2015 59.2 million

FY 2016 60.3 million (proposed)

Given inflation, and some of this an increase in Lattice QCD, there definitely has been a decision to decrease the amounts going to theory groups. Because of the details of how these grants work, some of the decreases have been large. For some discussion of the subject see

http://www.math.columbia.edu/~woit/wordpress/?p=6701

and this

http://www.usparticlephysics.org/sites/default/files/webform/p5/calamity.pdf

Justin,

Grossman was crucial in introducing him to modern geometry and the techniques he needed to formulate the theory. Around the time he announced the field equations, Hilbert found the variational form of GR, and other very well-known mathematicians (for example Noether and Weyl) made contributions to the understanding of the theory.

It seems a little inaccurate to mention Weyl as an afterthought or to put him alongside Noether, who I am not dissing here – it’s just that Weyl was one of three people who really got it right off the bat – with Eddington and Einstein. Noether’s theorem did not play a role in early geometrical ideas about gravitation and was not published until 1918. It was Weyl who first understood the physical problem of the GR action and conservation laws stemming from it, which work also came in 1918. I am pretty sure that Noether and Weyl did not meet until Weyl was at Goettingen, about 10 years later. So her work likely had no influence on Weyl when he was working on his generalization of Riemannian geometry. (Weyl of course had found special cases of Noether’s theorem. Nevertheless his intent was physical and he wondered if conservation laws could be found at all. I could be wrong. See “The Dawning of Gauge Theory” by O’Raifeartaigh. And certainly, he was greatly influenced by her in his later work on electron theory.)

-drl

Do these “very specific equations” also change from point to point by some yet another set of “very very specific equations”? . Maybe there is even more general set of “very very very specific equations” that govern the “very very specific equations”? Maybe there is an infinite sequence of equations like that? And then there may be equations that govern the whole infinite sequence.

That somebody takes ideas like that seriously is beyond me.

Einstein did his greatest work when he had solid experimental (or observational) evidence and followed it to the end. Yes, GR is a triumph in its mathematical sophistication, but he had the Perihelion precession of Mercury as a guidance.

In later years Einstein followed beautiful mathematical ideas and deep connections – you all know what the outcome was.

I would hope that those who know the particulars of this history will chime in and correct or expand as needed, but I think part of the physical argument arose in the context of whether or not the energy momentum tensor was a true tensor versus pseudo tensor. Also, I believe Einstein spoke of the equations for gravitational waves as being nonlinear several years before formulating the field equations themselves, and it was the task of separating gauge degrees of freedom from physical ones that led Hilbert to enlist Noether’s help. (“With Einstein’s theory, one of the many paradoxical consequences of this failure of energy conservation was that an object could speed up as it lost energy by emitting gravity waves, whereas clearly it should slow down.)

http://arstechnica.com/science/2015/05/the-female-mathematician-who-changed-the-course-of-physics-but-couldnt-get-a-job/

I’ve never been sure as to whether or not Mach’s principle is a philosophical argument, a physical argument, or an attempt to impose boundary conditions that was never really fulfilled. Also, I’ll second the motion that Weyl is grossly under appreciated by physicists today.

@Chris:

Exactly, and just to add that before GR, the anomalous perihelion of Mercury was attributed to … unseen matter- the planet Vulcan.

But I guess unseen (or dark) matter was always a very convenient solution…

@Peter:

I think Einstein has no grave 🙂

“… Einstein spinning in his grave …” Einstein does not have a grave. His body was cremated and his brain was removed at autopsy and preserved in formalin.

https://en.wikipedia.org/wiki/Albert_Einstein%27s_brain

Peter,

I wouldn’t say that string theory (removing the scare quotes) is an ill-defined term; rather that it is a somewhat inapt designation for a circle of ideas about fundamental physics, given that the primacy of strings is now understood as an artifact of perturbation theory. And the fact that all sorts of very different things (from finite simple groups to K-theory, to name but two examples) are related to string theory is not so much a ‘tedious ideological debating point’ as it is an indication that this circle of ideas has the depth and richness that one would hope for in a fundamental theory.

If your notion of deep and difficult ideas about physics is restricted to a narrow set of issues in particle physics, then no, mathematicians are not who one should run to for help. But fundamental physics is so much more than that. Einstein taught us the deep interconnection between geometry and gravitation, a notion which has been extended by the central role of gauge theory in the other fundamental forces. A useful role for mathematicians in this enterprise has been and remains to help develop the geometrical/topological/algebraic ideas that might be of use in constructing a physical theory. Sometimes those ideas are already at hand when the time is ripe for an advance on the physics side (e.g. Riemannian geometry was available to Einstein), sometimes mathematics is the beneficiary of developments in physics (e.g. quantum mechanics leading to developments in algebra and representation theory). String theory has been both beneficiary and benefactor of mathematics, for example K-theory was available to help understand brane dynamics, while properties of string worldsheet dynamics have led to developments in algebraic geometry such as mirror symmetry and quantum cohomology.

As for the so-called landscape, I regard the whole discussion as premature. A certain segment of the community is piling speculation upon speculation, and not really getting anywhere. It is useful to recognize that there is always going to be an issue with quantum cosmology — that the universe we inhabit had substantial quantum fluctuations early on, and we are now in one decohered branch of the wavefunction; and so what to make of all the other branches out there, and the question of how many are there. To make progress on a problem, one needs the tools to do so. Most of the analysis of the landscape is based on an analysis of effective field theory and the seeming existence of a plethora of solutions to the effective field equations. People spun their wheels for twenty years trying to solve the Hawking paradox using the same methods, without success.

We now understand that black holes are consistent with quantum mechanics in specific examples in string theory, yet we cannot point to the dynamical process which supersedes Hawking’s analysis of horizon dynamics in effective field theory. I suspect that making progress on cosmology (i.e. global dynamics) will have to await a better understanding of such local dynamical questions. One of the least understood aspects of string theory is dynamics.

As for your desire for physicists to “admit that string theory unification has been a failure and abandon empty, dead ideas”, good luck with that. People actually working in the field will pursue the directions they deem most promising, regardless of your little diatribes here.

Peter: thanks to the link to your previous posting. The quote of Connes is still pretty accurate ! Regarding the french CNRS that offers stable job at young people, there would be things to say (in my opinion, it has turned now into a “there is only a short interval of time after the PhD in which one has a chance to get a stable job, at PhD+ 5 one is already out”, which has many perverse effects), but that is another story 🙂

Emil,

One thing that strikes me is that you decided to comment here in response to an item I wrote, completely ignoring what that item was about. I’m curious: do you really think it’s all right for physicists to go on PBS and tell the public that the multiverse is “Einstein’s legacy” and that there are “very specific equations” describing it? If it isn’t, who should be saying something about this? If not me and my “little diatribes” (that’s what this one was about, not string theory), who is or should be taking on this job?

The argument for string theory that, while we don’t know what it is (other than a “circle of ideas”) various different kinds of mathematics have turned out to be useful to analyze some of the complicated structures that have turned up, isn’t a very convincing one. Yes, this circle of ideas that grew out of string theory has led people to wander around in some mathematically rich areas, raising questions and finding interesting things that would not otherwise have turned up. That’s great, and a perfectly good argument for pursuing this circle of ideas if you can’t think of anything else to do. It’s not an argument though for the 10d superstring (or related circle of ideas) as having anything to do with fundamental physics.

Back in 1985, at the beginning of your (and my, we were educated in exactly the same era) career, the idea that something like the heterotic string could unify physics was a reasonable one to try, but it’s now thirty years later. The idea that you could predict something, anything, this way has collapsed, giving us multiverse pseudo-science. The idea that higher energy colliders would find SUSY, giving experimental clues pointing towards this scenario, has also pretty much collapsed, with the final part of that story to happen over the next year or two. Given this, I think there’s a very strong argument that you and others need to face facts as scientists, admit failure, and move on. You can dismiss this as a “little diatribe”, dismiss any evaluation of the current state of string unification efforts as “premature” (with the right time to consider admitting failure only when you’re no longer around) and try and prop up a failed idea by hyped connections to mathematics, but I don’t think you’re doing the subject any favors this way.

Ronab, Peter,

While the total DOE high-energy physics budget hasn’t gone down by much percentage-wise, the cuts haven’t been distributed equally. Some large collaborations at certain universities received much larger percentage cuts than this average (I don’t know of any place that received anywhere near a 50% cut, but possibly Strassler does.)

I was reacting to the last paragraph of your original post (which I quoted in my initial response). So my response was a comment about the interaction of mathematics and physics, and that some of the most fruitful interactions of this sort in recent times have arisen in the context of string theory. I don’t think that wholly inappropriate, given the general content of this blog.

You propose that “general relativity would have taken many more decades to come to fruition” if the appropriate mathematics weren’t already developed. Yet you seem remarkably impatient with string theory not being in final form thirty years on from its inception as a candidate for a fundamental theory, given that there is no ready-made theory of quantum geometry for us to read up on. (BTW, I would rather have said we are forty years on from the work of Scherk-Schwarz/Yoneya showing that string theory is a quantum theory of gravity.)

As for contact with experiment, indeed that may be hard to come by given the large disparity between the electroweak scale and the Planck scale. If the scale of extra dimensions and the string tension scale are close to the Planck scale, then string theory looks remarkably like a 4d theory of quantum gravity coupled to matter — ordinary particle physics up to near the Planck scale, a handful of odd resonances that we’ll never see, and then a spectrum of black hole states. But absence of evidence is not evidence of absence. String theory could easily be correct and not testable by humans — in fact that could well be true of any theory of quantum gravity given the remoteness of the Planck scale.

In such a situation, internal consistency is one of the few routes to progress. Einstein was initially motivated to resolve the apparent inconsistency between Newtonian gravity and special relativity. Today, we have the apparent inconsistency between locality, causality, and quantum unitarity manifested in the black hole information paradox. String theory has made undeniable progress in this direction, but not a complete resolution.

As for particle physics unification, while it would be nice for there to be some rigid structure and a limited possibility to arrive at anything other than the Standard Model at low energies, it has so far not emerged, and looks increasingly unlikely. And the number of clues we are likely to get from experiment seems increasingly limited. The situation is unfortunate, but again nothing here says string theory is wrong (rather than simply not useful in this particular context).

Which brings us back to the issue of multiverse speculation. It seems to me a legitimate scientific question whether the structure and parameters of the standard model of particle physics and cosmology are (1) predetermined, or (2) properties of the part of the state we have access to, and therefore environmental. I suppose (1) splits into subcases of being (a) calculable in principle, or (b) fixed metadata. Maybe we will know enough someday to say definitively one way or the other. What questions are worth pursuing differ depending on the answer. Again, this is an issue for any theory of quantum gravity, not just string theory.

At the moment, I think we are in no position to answer, and trumpeting one particular possibility in the media is not particularly helpful, and tarnishes the subject with a patina of unseriousness. We simply don’t know enough to say one way or the other. I cringe when I hear statements to the effect that a multiverse is a “prediction” of string theory. At best, it’s a possibility.

Such speculations are putting the cart way before the horse. Let’s get a quantum theory of gravity first, and learn how to calculate with it; only then might we hope to address such questions. I suppose it’s human nature to want to jump to the final answer, and fill in the details later. But what if the nature of the final answer depends crucially on the details?

I suppose you’ll dismiss this as some dodge that it’s premature to judge string theory (again the scare quotes). Your mind was made up long ago and I’m sure I won’t change it. I will simply conclude by stating that I still think the subject is making interesting progress on important questions; they’re just not the questions we were initially asking 30 (or 40) years ago about unification of particles and forces, and instead have more to do with the nature of quantum gravity.

Emil,

So, it seems that your position is that string theory is unlikely to ever be testable by humans, but that showing it is an internally consistent untestable theory is the future of the subject. Since you don’t have an actual theory (what is M-theory again? everyone seems to have given up on even trying to answer that), what you’re actually talking about is just showing that a “circle of ideas” is consistent, while being completely empty of content. This is really nothing but a set of excuses for giving up on doing science. It’s not surprising that people doing this don’t clearly explain to the public the state of their subject, but instead produce such huge amounts of promotional hype.

My how you love to twist people’s words! I said that for ANY theory of quantum gravity that, because of the remoteness of the Planck scale, experimental or observational tests will be hard to come by, and it is a distinct possibility that such tests will be beyond our reach. Does that mean we should give up trying to reconcile the fundamental incompatibility of quantum theory and general relativity, two theories that we have abundant evidence for? Some (you, apparently) might say yes, others (me, for sure) continue to be intrigued. Having at least one example of a consistent theory that combines the two is still a useful exercise IMO. At the moment we don’t have any.

I wouldn’t say that people have given up on the question of what M-theory is, rather the focus has moved beyond the aspects of that question easiest to answer using existing tools such as perturbation theory around simple backgrounds, and effective field theory.

One outstanding issue is what becomes of the equivalence principle in a quantum theory of gravity. Accelerated frames are related to thermal effects in the quantum theory, and related notions of density matrices and quantum entanglement; so these are likely to be some of the ingredients, and they also tie into the information paradox. A conceptual framework that ties all these notions together is currently lacking, but is certainly a major topic of current research. I could give other examples.

The first-principles exact calculation of black hole entropy, absorption/emission amplitudes, and so on, in particular controlled examples in string/M theory, was a tour de force of theoretical physics. The “circle of ideas” (oh those scare quotes again) in which those calculations took place is hardly devoid of content, or unscientific.

Emil,

I don’t think I’m twisting your words to say that you have given up on explaining anything about observable physics, by giving up on unification and any of the open questions of the standard model. Worse than that, string theorists have constructed a scenario with no evidence for it, designed to avoid admitting failure, and are aggressively selling this in the media, to students and colleagues, ensuring that future generations won’t try and attack these problems, since it is “well-known” that they can’t be solved.

It is possible to pursue a question purely by the criterion of internal consistency, with no checks from the real world. Mathematicians do it all the time. But if you’re going to do this, the lesson mathematicians all know is that you need to be quite precise about what you are doing, very clear in your arguments, and very honest with yourself when something doesn’t work. As far as I can tell, the way quantum gravity is being pursued by “string theorists” (I think the scare quotes are important, at this point, any actual theory involving strings seems to have little to do with this) involves none of this discipline at all. It’s pretty clear where this kind of activity ends up, and its not with any reliable understanding of anything.

The current Martinec/Woit discussion is one of the most incisive I have seen on this blog, and is getting to some core issues that previous string theorist commenters have denied or ignored (or evaded). Thanks to Prof Martinec for the candid and to-the-point remarks; I hope he continues the conversation rather than exiting at the crucial point as Distler, Motl, Polchinski et al have done in the past.

Yes, this exchange between Peter and Emil was tremendous, and I would love to read more.

But at the end of the day, I can’t help thinking it can be reduced to Peter saying “Show me the money” and Emil arguing about what is meant by “show” and “money”.

@random reader,

I’m not sure what you mean by “the crucial point”; the major points have largely been made above. If I discontinue, it’s because at this juncture there is not much more to say without repeating myself.

@Peter,

As I have said, I am not a fan of the landscape/anthropics, precisely because it implies that much if not all of the structure/parameters of particle physics/cosmology are environmental and not fundamentally determined and so the calculational power of the most fundamental level of physics would be rather limited.

But just because I don’t like it doesn’t mean it’s not a legitimate scientific issue. IF the theory of quantum gravity plus gauge theory and matter has a sufficiently complicated structure of metastable states and IF transitions among them are allowed and IF one can understand enough about how early universe cosmology works, then the part of the universe we inhabit is the outcome of a variety of quantum processes, and the post-big bang universe we experience is but one of many discrete possibilities. If a quantum theory of gravity and matter can be constructed which has these properties, it is worth taking seriously and trying to understand better.

However, not all the string theory community agrees with all the premises. For a rather thoughtful technical critique of the assumptions (which I largely agree with), see section 4 of Tom Banks’ 2010 TASI lectures (arXiv:1007.4001). The landscape is not currently a settled consequence of string theory.

As for all the “media hype” (my scare quotes this time), at the risk of repeating myself, I think it’s unfortunate, but I don’t think there’s much to be done. It is not my job (or any of my colleagues) to police the field. There’s plenty of bad popularization of science. Maybe journalists should do a better job of researching their stories. Like any science idea, either it will have power and find support when we understand quantum gravity better or it will not.

Every problem has a time when it is ripe to be solved, and often premature attempts to solve it don’t help. It’s always a judgment call where to invest one’s precious time for research; even unsuccessful attempts often bring up new ideas or move the field forward incrementally. But at some point people keep rehashing the same old ideas, and at that point it is prudent to wait until new tools arrive. I think the black hole evaporation problem is a quintessential example. There were suggestions that black hole radiance violates quantum mechanics; that the information is stored in microscopic remnants; that it disappears into a baby universe; and on and on. The problem wasn’t ready to be solved until gauge/gravity duality came along, we understood much better what quantum gravity is about, and we could see that all of these suggestions were on the wrong track (at least in the examples where quantum gravity has a presentation as an ordinary quantum field theory).

I look forward to Dorigo’s book. What do you think of Randall’s book which was favorably reviewed in the NYT today?

Emil,

“IF the theory of quantum gravity plus gauge theory and matter has a sufficiently complicated structure of metastable states and IF transitions among them are allowed and IF one can understand enough about how early universe cosmology works, then the part of the universe we inhabit is the outcome of a variety of quantum processes, and the post-big bang universe we experience is but one of many discrete possibilities.”

All three IF-s that you name are theory-dependent, and experimentally very hard (if not impossible even in principle) to verify. It is one thing to study a theory which has all three properties, but it is quite another to teach students that there is no alternative.

It would only be fair to acknowledge the opposite point as well: IF the theory of quantum gravity plus gauge theory and matter has a sufficiently simple structure of metastable states, or IF transitions among them are not allowed, or IF one can understand early universe cosmology without inflaton fields, then the physics describing our local patch of the universe also describes the totality of it, and the post-big bang universe we experience is pretty much unique. The values of fundamental coupling constants then ask for an explanation, and it is quite legitimate to try to improve the theory by trying to calculate some of them from some first principles, as opposed to claiming that those values are an environmental accident.

And of course, yes, there are theories out there that satisfy either of those IF-s, and even those that actually attempt to reduce the number of fundamental coupling constants (say, the NCSM by Connes, Chamseddine et al. at least tries to improve/reduce the number of SM free parameters).

The actual problem is that landscape/anthropics is an ideology, and the fact that it is represented to younger scientists as the only possibility, with students in most major universities being actively discouraged from thinking about alternatives (no PhD advisors, no funding, etc). I’ve heard the sentence “string theory is the only way to quantize gravity” way too many times, on serious conferences, from leading scientists in the field. Even if we accept landscape/anthropics as a scientific possibility (for the sake of the argument), it is by no means the only one, or even the most plausible one. People involved need to be more honest and more humble about what is speculative and what is done-and-dusted, when communicating science to students and outsiders. This lack of this honesty is where the problem is.

Best, 🙂

Marko

Curious Wavefunction,

I took a quick look at it in the bookstore, which convinced me that its content is pretty much orthogonal to my own knowledge and interests. I’ve never learned much about dinosaurs, the Oort cloud, relevant astrophysics of our galaxy, and for whatever reason, they’re just not high on my list of things I’d like to spend time learning more about. So, for an informed take on that book, you’ll have to look elsewhere.

random reader,

I agree with Emil that such discussions as this tend to end when people feel they have nothing new to say. I’m approaching that point and I’m sure he is too. I doubt either of us will convince the other of much, but the usefulness of this is likely to be that of giving a clear expression of differing points of view on these topics, I hope more informative than the usual caricaturizations. I think the point of view he is explaining is a rather mainstream one among sensible string theorists, many thanks to him for providing it.

Emil,

The common reference to “not liking” the landscape scenario I think completely misses the point. If string theory implied that string vacua almost always came with a low energy SU(3)xSU(2)xU(1) gauge symmetry and three generations of matter particles, but the Yukawas were all different in some exponentially large set of different vacua, then I’d say that it’s a scientific theory that has to be taken very seriously even though I didn’t like the implications. The problem though is that there is zero significant evidence for such a scenario. What’s dangerous here is not that people are pushing an idea that goes against traditional optimism about what we can hope to explain, but that they are pushing as science an idea with no scientific evidence behind it (and with a rather obvious non-scientific motivation of wanting to avoid admitting failure of a cherished idea).

I don’t think media hype for this or other dubious ideas can be blamed on journalists. In my experience they of course miss subtleties and complexities, but they do a pretty good job of giving an account of the story they’re hearing from well-credentialed physicists. Quite a few prominent and distinguished theorists have decided it’s a good idea to publicly promote the anthropic landscape (sometimes claiming they “don’t like” the idea). That very few of their colleagues are willing to publicly disagree with this is a big part of the problem.

Time will tell whether the latest gauge/gravity inspired approaches to the black hole information paradox lead anywhere. I don’t think any evidence for string/M-theory is going to show up this way, but it’s not implausible such work will lead to more promising ideas about quantum gravity (as a fan of representation theory, the appearance of an interesting group in what Strominger and other have been up to looks to me intriguing), or maybe have significant spinoffs in other very different fields (condensed matter, quantum information). But still, I see a two-fold problem, the usual faddish concentration on one particular idea, together with really bad arguments that others are unlikely to lead anywhere. Way back when, I think the point of view of mainstream theorists on the quantum gravity research community was often that such research wasn’t going anywhere, since it was divorced from the parts of fundamental physics that we had evidence for (with the argument for string theory that it captured both the SM and quantum gravity). It might be a good idea for present day string theorists to recall their previous point of view.

The “crucial” new elements of this discussion compared to others seem to me to include the following contributions from Prof. Martinec.

1. The clear statement that “At the moment we don’t have any [example of a consistent theory that combines quantum theory and general relativity].” This is very different from the usual idea that the formal consistency checks on string theory are overwhelming and have essentially decided the issue, and of course also different from the idea that any consistent unification has to closely resemble string/M theory or be essentially equivalent to it.

2. The comment that “If the scale of extra dimensions and the string tension scale are close to the Planck scale, then string theory looks remarkably like a 4d theory of quantum gravity coupled to matter — ordinary particle physics up to near the Planck scale, a handful of odd resonances that we’ll never see, and then a spectrum of black hole states. “. This is more specific than the usual “Planck scale remote implies quantum gravity hard to observe” and raises a couple of interesting possibilities. One, that there will not be a lot more interaction between string theory and 4d quantum gravity questions beyond the picture of stringy microstates for (some) black holes. Another, that there may be a more general and robust class of theories, perhaps falling short of a full theory of quantum gravity, that generate the Standard Model + “handful of odd resonances” + “spectrum of black hole states”. In that case the stringy calculations are a particular and somewhat elaborate realization of a more general pattern that one might as well find and study on its own.

random reader,

Let me clarify on your point (1), as you seem to be eager to extract a takeaway message somewhat at odds with the point of view I was intending to convey. IMO the formal consistency checks on string theory ARE overwhelming evidence that there is a theory combining quantum mechanics and gravity, whose solutions include the ones we have found through string perturbation theory and effective field theory — at least the ones where additional structure such as supersymmetry guarantees the existence of such vacua. Which is not to say that non-supersymmetric vacua do not exist; we can simply say less about them, because our calculational tools are more limited.

Nevertheless, being convinced of the existence of such a theory and having it in hand are two different things. We are in a rather unprecedented situation that the part of the theory we know consists of a set of methods to construct a collection of examples of solutions, around which we can describe perturbation theory in terms of strings and branes. The perturbative limits, together with a set of duality conjectures for which there is strong evidence, piece together a complete picture of the solution space (again in examples with enough supersymmetry) which is conjectural but in the best sense — having myriad checks, eg involving elaborate mathematical identities that one conjectures based on the duality hypothesis and then verifies by independent means. But we don’t have in hand the organizing principle, an underlying idea such as the equivalence principle from which all these results flow as consequences, and which would enable us to formulate the theory beyond these various limits and especially in non-supersymmetric and time-dependent backgrounds.

As to whether this edifice is unique and inevitable, I am an optimist that time will tell, and that the answer is yes. For now let me mention the example of N=8 supergravity in 3+1 dimensions, whose perturbation theory was the subject of a recent discussion thread. There is no limit of string theory that decouples all the “extra stuff” of string theory — the branes and extra dimensions — and leaves only the 3+1 dimensional quantum field theory of N=8 supergravity. So that’s great, you might say, maybe there’s a theory without all this extra baggage, that doesn’t involve strings and is perfectly consistent on its own. Here is where one needs to think carefully about the spectrum. N=8 supergravity has 28 gauge fields. There are black hole solutions in supergravity carrying electric and/or magnetic charges sourcing these gauge fields. The extremal limits of these solutions are in fact the objects we tried to throw away — the strings, branes, and Kaluza-Klein modes — moving within or wrapped around the extra dimensions; or bound states thereof. We discover this by considering the spectrum as a function of the 70 moduli of N=8 supergravity; in asymptotic limits of that moduli space, the black holes become perturbative objects in string theory. So if there is a consistent theory with only N=8 supergravity in 3+1d without all the extra structure of string theory, it has to come with a reason why ALL the charged black hole solutions, which seem perfectly benign and not all that different from the uncharged black hole solutions, in fact are excluded from the spectrum of the theory. If they are not, then we are led back to the full structure of string theory compactified on a torus. One could go further and think about why these objects indeed cannot be excluded, because they will be pair created in external fields with some small but finite probability, etc, but anyway perhaps enough said.

As for your point (2), indeed the stringy structure in the sort of situation I described naively seems confined to understanding the black hole spectrum, but that is by no means assured. It’s the regime that’s hardest to analyze, because there are no small dimensionless parameters in which to do perturbation theory. Because black holes teach us that local field theory breaks down at some level, there may be subtle nonlocal effects that influence low-energy physics in ways we do not currently understand and should be on the lookout for (but that’s a hope, not an expectation).

I share the sentiment that current string technology is a bit of a Rube Goldberg device when it comes to explaining black hole structure, each example having different particulars but always yielding the same Bekenstein-Hawking area law in the end. This is precisely why people are searching for a more universal explanation. That doesn’t mean strings and branes and extra dimensions will disappear from the final formulation, see the discussion of N=8 supergravity above. They will still be present in the spectrum of excitations in solutions that do have sufficiently large extra dimensions, or weak string coupling, etc. Peter is often complaining that people seem to have stopped doing string theory. I don’t think it’s true, rather I would say people are trying to absorb and abstract the lessons that string theory has taught us in the known examples, into some basic organizing principles from which the rest follows.

“Peter is often complaining that people seem to have stopped doing string theory. ”

I often note that string theorists have stopped doing string theory, but that’s an observation not a complaint (I’m glad to see that they’re doing something more promising). To the extent there’s a complaint, it’s that such people are often still insisting on centrality of the original speculation about strings that they started with, long after it has become clear that didn’t work out well, with other ideas now the center of attention. Explicitly or not, there’s often an argument being made that “string theory is the source of all good ideas”, discouraging work on ideas that don’t fit into the line of thinking that led from string theory to currently fashionable topics.

Thanks again to Prof Martinec for the long replies, which are clarifying and refreshingly detailed compared to most previous online discussions of these matters.

Regarding (1), the strength of consistency checks (versus actual construction of the nonperturbative theory) as evidence for a well-defined theory: the evidence actually looks, from this outsider (mathematician’s) perspective, to be mixed, both in its strength and in where that evidence is pointing.

It is already the experience of the past 3 decades that stringy subjects that are mathematized, or have strong overlap with things that can be constructed as mathematics — things like mirror symmetry, geometric Langlands, CFT/TQFT, loop groups, integrable systems, matrix models, Kac-Moody algebras, deformation quantization (etc) — do have a lot of interrelations, and may well be moving toward a unification. Maybe a topological M-theory, or a “mathematicians’ fragment of string theory”. But this seems very far from string theory as physics relatable, in principle, to observation. Rather, there may be a unification all the mathematical discoveries and coincidences from string theory, but it is likely to be in a generic framework that does not have unique relation to weird critical dimensions like 10 or 26, or big supersymmetry algebras.

Quantization is an example that looks stringy perturbatively (deformation quantization a la Kontsevich) but does not show stringy characteristics non-perturbatively, as far as anyone knows. Mirror symmetry looked amazing, and continues to lead to amazing things, but the physicists’ curve counts were wrong starting around genus 10.

None of these situations where the mathematical framework can be constructed, shows any sign of the very special features of the 10, 26 or 11 dimensional string/M (or SUSY) theories. It looks like the critical string theories are a non-generic singular point in “theory space” where several submanifolds intersect, with the multiple overconstrained descriptions leading to the extra relations (dualities). In such a picture, the fact that (at least perturbatively) there is an intersection at all is miraculous and needs to be explained, but it may also be that a generic part of the picture is enough for describing nature, and strings are too special, but we cannot see this until enough math is developed.

The appearance of string- or brane-like structures in N=8 SUGRA or other theories does not seem all that surprising. The scarcity of accessible methods (by the standards of earlier unifications) to unify GR and QFT suggests that the new ingredients in different theories that even come close to success are going to be strongly related to each other, otherwise there would have been more freedom to find the new stuff in the first place. This is true of strings and noncommutative geometry, and I have read claims that loop/Ashtekar quantum gravity models (of which I know nothing) also embed into string theory. At any rate, string theory seems to be the most universal known model, so it is expected that all the present contenders will look as though large parts of them can be built from strings, contain stringy structures, or both. But it can also be that once an idea comes along that explains how to get a mathematically rigorous unification (or whatever unification-like thing is the ultimate output), strings will appear as only a universal solution of a specific constraint not tied to what is needed for unification — a special/sporadic/symmetric point in a much larger universe of consistent usable theories that do not all reduce to strings. Sure, if structures such as extremal black holes have a stringy description then whatever else describes them will also have a strong overlap with the string description. But if the “only game in town” argument is really only the “currently most universal object in the category of unification candidate-theories” argument, then finding a principle describing what the theory is about may also be exactly the thing that eventually renders the theory superfluous.

Of course, strings can be unique and consistent because of some universality phenomenon where some large class of underlying models looks like strings as some parameters or number of degrees of freedom get large. But in that case one could model quantum gravity by those underlying degrees of freedom, too.

In all, the quasi-mathematical “consistency checks and coincidences are unbelievably compelling” seems very strong, but not so much as an argument for string theory. The same evidence can point just as compellingly in one or more other directions that are surely related, but are not necessarily an indication that string/M theory will be the lesson to emerge from the consistent mathematics as it is developed. It seems to me that the evidence for the lesson being something non-stringy is stronger, since strings are not fitting any known pattern of what consistent (mathematical) theories end up looking like, and strings’ subtheories that are mathematical have not provided any indication that this historical pattern is wrong.

random reader,

Many thanks for your very thoughtful and well-informed take on this subject. This is the sort of discussion I’d love to see a lot more of. Unfortunately this is an extremely complex subject, with most mathematicians involved not knowing much about the issues of how the objects under study connect (or don’t) to a hoped-for unified theory, and most physicists involved not knowing how the objects connect (or don’t) to the rest of mathematics.

One of my original main reasons for skepticism about the proposed 1984 string theory unification proposal was that the direction one needed to go to connect string theory to the real world was kind of orthogonal to the directions in which I could see beautiful and deep connections to the rest of mathematics. In more recent years, this has become a much more complex topic, with different sorts of connections to possible unified theories via connections to 4d qfts coming into play. Looking at this whole subject for clues as to what is fruitful and what isn’t, without trying to fit things into the original speculative framework of 10 dimensions and strings, seems to me a very valuable thing to do, although few are equipped to do so at the moment.