On Beauty and String Theory

One of the arguments often given for string theory is that it is somehow exceptionally “beautiful”. This has always mystified me, since that’s certainly not the way I would describe it. Over the years I’ve paid close attention whenever I see someone trying to explain exactly what it is about string theory that is so beautiful. Lubos Motl has just posted his own detailed answer to this question, something I read with interest.

As usual, Lubos is not exactly concise, so I won’t quote him extensively, but let me try and summarize his arguments for calling string theory beautiful, together with some of my own comments.

1. Symmetries are beautiful and just about every symmetry you can imagine gets used somewhere, somehow in string theory.

Even Lubos is not so sure of this argument, since he says ” I don’t really thing that we view symmetries as the most important reason why string theory is beautiful”. What is beautiful about symmetries is the way they constrain things. If your theory is based upon a simple symmetry principle (take for example gauge theory and the gauge symmetry principle), a huge amount of structure follows from a single, simple principle. String theory is not based on a simple symmetry principle, rather it is a complicated framework, into which you can fit all sorts of different symmetry principles. But because they are not fundamental, these symmetries don’t constrain the theory much if at all. This is very different than the standard model, where at a fundamental level the theory is built around a single symmetry principle, one that governs a large part of the structure of the theory and its physical predictions.

2. The way in which “miraculous” cancellations occur in string theory, constraining the theory by only allowing it to make sense for certain specific choices.

The most well known example of this is the way in which anomaly cancellation picks out 10 dimensions and SO(32) or E_8 times E_8 for the superstring. This was the main reason people got so excited back in 1984, when they thought that the anomaly cancellation principle would give them a nearly unique theory that could be used to make predictions. If the anomaly cancellation principle had picked out four dimensions and SU(3)xSU(2)xU(1), that certainly would have been a beautiful explanation of why the standard model is the way it is. In the standard model itself, anomaly cancellation for the chiral gauge symmetry does work in an impressive way. If you take just the leptons or just the quarks, you have an anomalous theory, but the anomalies of the one cancel those of the other.

In string theory, all anomaly cancellation does is pick out a much too large dimension of space-time and a much too large gauge group. You can certainly embed the standard model in this structure, but you could also embed just about anything you want in it because there is so much room. In the end you are stuck with some version of the “Landscape”, essentially an infinite number of different possibilities with no way to choose amongst them. The anomaly cancellation ends up providing very little constraint on what the structure of low energy physics looks like.

3. String theory is a unique theory that can predict everything about the physical world.

Lubos likes to go on about how unique and predictive string theory is. While I understand this is the dream of every string theorist, the reality of what they actually have is a long ways from what they hope is true. The vision of what they would like to be true may be beautiful, but the reality is something else. The reality is that there is no “unique” string theory that can reproduce the real world, just a dream that such a theory exists. And as for predictions of string theory, there are none. When Lubos says that “string theory predicts” things, what he really means is that if every thing he would like to be true actually were, then in principle you could predict things from string theory.

4. String theory manages to extend quantum field theory in a consistent way, something which is very non-trivial and the way this happens can be described as beautiful.

This seems to be Witten’s main argument these days for promoting the continued study of string theory and I have a certain amount of sympathy for it. There certainly is something of interest going on behind the complicated framework that people are studying under the name “string theory” and maybe it will someday lead to insight into something about physics, most likely the strong coupling behavior of gauge theories. But the fact that there is interesting structure you don’t understand doesn’t mean that this structure has anything to do with a fundamental unification principle for physics.

5. There are beautiful connections to new pure mathematical structures.

The relation of string theory to mathematics is a huge topic, and I’ll comment on it at length at some other time. In brief though, while I think string theory has been an utter disaster for theoretical physics during the past 20 years, it has lead to many interesting things in mathematics. However, most of these interesting things really come from 2d conformal QFT, and I would argue that it is QFT which is having a huge impact on mathematics, much more so than string theory. Witten’s Fields medal was for his work on the relation of QFT to math, not for anything he has done using string theory.

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39 Responses to On Beauty and String Theory

  1. D R Lunsford says:

    Chris W – re those Smilga papers:

    Alright, I read these papers. I was disappointed.

    1) His main idea seems to be – 3d ang. momentum to SU(2) spin nets is the same as spacetime angular *and* linear momentum to SO(3,2) spin nets. This isn’t true generally, so he spends most of his effort patching up the problems by contracting SO(3,2) to Poincare. This is a mistake – the idea itself is good, but the realization is not (see below).

    2) His transition from 2-spinors to 4-spinors is hand-waving nonsense. As we know, this amounts to going from the restricted Lorentz group to the full one including spacetime parity. The physical net gain is antimatter, which he never mentions.

    3) His identification of s_m4 with y_m is itself not correct, so he gets the Clifford algebra wrong. For the purpose of his application this is harmless, but for the purpose of the correct approach it’s fatal.

    What’s the correct approach? You need to do it for SO(3,3) – then one has real translations without the need for approximation, like this…

    The Lie algebra has terms that look like (indices go 1-4)

    [ Jm5, Jn6 ] = i gmn J56 = i gmn M (mass!)

    [ Jmn, Jp5 ] = -i (gmp Jn5 – gnp Jm5)

    [ Jmn, Jp6 ] = -i (gmp Jn6 – gnp Jm6)

    etc.

    Calling Pm = Jm5 + iJm6 and Qm = Jm5 – iJm6 we see that both Pm and Qm represent translations abstractly, but they go off shell into complex spacetime, so one needs *two* of them in succession to get a *real* displacement. Since they are translations, they still commute. Thus one can build up finite translations in spacetime *without contraction*. This should allow one to build a 4-d checkerboard model on the lines of Gersh’s and Feynman’s 2-d model. One should also be able to construct a spin network model of the 6d spacetime. I’ve been meaning to do this but occupied with other things. Note that the Weyl theory on SO(3,3) – SO(3,3) neutrinos – leads to the Dirac theory on spacetime, with the two neutrino helicities correpsonding to positive and negative mass terms. A paper on this subject should appear soon.

    -drl

  2. sol says:

    Thanks DRL for responding.

    I have to walk very slowly in these circumstances, being the layman, I am just learning to walk on these topics.

    Speculation?

    1. Background Independence And The Holomorphic Anomaly

    Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in the subject, and so far has remained out of reach. Moreover, some highly simplified special cases or analogs of the problem, which look like they might be studied for practice, have also resisted understanding.

    I assume a high energy consideration from the early universe.

    G -> H -> … -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)

    Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups – G, H, SU(3), etc. – represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature

    Some might have assumed a false vacuum as existing instead of “nothing”, and from it, a true vacuum to emerge. This would encapsulate, and like bubble eversions, explain what would have been held to the brane, and what is allowed to roam in the bulk? I know this might seemed far fetched as I am trying comprehend the nature of of the abstract world given to defining feymans integral paths as loops, defined in that abstract geoemtrical thinking. This because of it’s background dependancy, had to be modifed in order to to speak from the compactified dimensions, and find themselves revealled in spacetime. You see?

    I apologize to those of you who may find this easy.

  3. D R Lunsford says:

    Sol,

    You don’t have to indulge in any speculation. If a theory has a Lagrangian and variational principle where everything in sight is varied, leading to equations involving all the elements, then that theory is background independent practically by definition. So for example the Einstein-Hilbert action is

    S = integral R sqrt(det(g)) dx..dt

    R is a function of g_mn and its first and second derivatives, and this appears again in the volume element sqrt(det(g)) – so the equations that come out of delta S = 0 are background independent. The Maxwell action

    S = integral Fmn Fab g_ma g_nb sqrt(det(g)) dx..dt

    leads to Maxwell’s equations in vacuo and these are not, because the g_mn are not varied. You might ask what happens if I vary the g_mn in the latter as well as the A_n (F = curl A) – answer: because no derivatives of g_mn appear in the action the Euler equations are simply

    F_am F_mb + 1/4 F_mn F_mn g_ab = T_ab = 0

    F_mn,n = 0

    that is, the energy tensor for the EM field also vanishes, and so there is in fact no field.

    The best you can do with both, in the existing scheme, is to paste together an ad-hoc Lagrangian

    L = R + k W

    where k is an additive (dimensional) constant – one then can get

    R_ab – 1/2 R_mn R_mn g_ab = -k T_ab

    that is, the Einstein-Maxwell equations (Maxwell in curved space with the field energy as a source of curvature). So, Einstein-Maxwell is background free, but *not* unified, because the Lagrangian is not irreducible. To sum up, background-freeness is not a mystical property, it’s simply the statement that all the essential elements can change from place to place.

    -drl

  4. sol says:

    Well let’s see here. Neocons( playing with words very creative:)

    The Problem of Dynamics in Quantum Gravity

    The problem of dynamics in quantum gravity is still a big challenge. We don’t know how to make spacetime a truly dynamical entity with local degrees of freedom while taking quantum theory into account. Neither string theory, nor loop quantum gravity, nor the spin foam and causal dynamical triangulation approaches have yet found a background-free quantum theory with local degrees of freedom propagating causally. We sketch some avenues for making progress in this direction.

    As I was trying to comprehend how gravity was to be inclusive in string theory, it soon became apparent that it was background dependant. Truly as John Baez implies this is not desired, by others as well.

    But if we assume background dependancy, then from what I understood, it became the background and the quantum mechanical discription of the spacetime fabric. Please anyone correct this perception if it is wrong.

    Thus from this perspective, a emergent geometry would have been allowed to surface, where all other geometrical approaches, could not have been allowed?

    Again this is not what is desired of string theory and the background independance is most preferred. I have many links on quantum grvaity that would innuadate your selection DRL.

    I would rather a concensus on whether any geoemtry shall emerge(what shall emerge in the Third Superstring Revolution) and how it shall do that. If we do not consider this context, then we are left to consider, the value of glast determinations and the link Peter offerred.

    Inside Gamma Sphere:

    The device’s 110 gamma-ray detectors point to the center of the spherical array, where a beam of nuclei from a particle accelerator smashes into a thin target. The collisions create unstable nuclei that decay by emitting gamma rays, an extremely high-energy form of light. Gammasphere catches and measures as many of the gamma rays as possible, so that scientists can study what happens to nuclei under extreme physical conditions.

    http://www.symmetrymag.org/cms/?pid=1000017

    Is this a bad thing? No it reaffirms the direction of glast on the cosmological scale and secures QF visionist on the roads to percieving how quantum grvaity makes sense leaving GR alone(Smolin’s position ?).

    But as I said, without th econsistancy of a geoemtry to emerge, there is no hope for a perspective to form around quantum geometry as a discritor of quantum gravity?

  5. D R Lunsford says:

    Chris O,

    It’s damned unbelieveable, what?

    Strings depend essentially on KK theory, a failed attempt to extend Riemannian geometry to encompass the A field as part of an ersatz cylindrical metric in 5-d. The simplest contradictory logical loopbacks seem to be beyond the Greenes of the world. They remind me of our neocons.

    Now there really *is* an effort to make quantum geometry, see for example

    http://www.physics.gatech.edu/people/faculty/dfinkelstein.html

    You won’t find any hippocoprolitic stringism there.

    -drl

  6. Doug says:

    drl wrote:

    Furthermore, what sort of disingenuousness is it to say “field theory is ugly”, when string theory would have to reproduce that same ugliness to be taken seriously? (It won’t, but this is rhetoric.) Whatever next step turns out to be the right one, it will have things that look like gauge fields, energy tensors, etc. etc. and people will say “Ah! Now we know why field theory was that way – how beautiful!”

    Great observation! As Hestenes, in his New Foundations for Classical Mechanics, observes: “[Newton] deserves the title of “founder” (of classical mechanics) because he integrated the insights of his predecessors into a comprehensive theory.”

    However, while your statement hits the nail right on the head, it also assumes that a successor will be successful, as was Newton, in moving modern physics forward “by integrating the insights of his predecessors into a comprehensive theory.” This may not happen. As Hestenes points out, Newton did more than integrate these insights into a more encompassing theory, he launched “a well-defined program of research into the structure of the physical world.”

    The two great revolutions in physics of the 20th century, QM and GR, are the great insights to be integrated, but it may take a theory that does more than integrate them to move us forward, it may require a new “program of research into the physical world.” Of course, that’s a tall order, but it’s the “new physics” everyone talks about these days, but in the true sense of the word; that is, in the sense of a new program of research, rather than new phenomenology.

    That such a program would be characterized by the simplicity of geometry and the beauty of fundamental,powerful ideas, unencumbered by the excesses we see today, is certain in my mind. The mathematical indulgences and wild speculations so popular in normal science today remind me of the days when doctors proudly wore blood smeared smocks as testimony of their professional virtuosity. The irony is palpable.

    According to Hesetenes, the central hypothesis of Newton’s program “is that variations in the motion of a particle are completely determined by its interaction with other particles,” and that [Newton's program of research] has been interpreted as a dictum: to focus on forces. He says, “The aim is to classify the kinds of forces and so develop a classification of particles according to the kinds of interactions in which they participate.”

    Perhaps, however, such a focus cannot deliver the goods. I think that Newton understood that force was a property of motion, and that motion was the proper study of physics, not forces, and that a new program of research, focusing on motion, that is, the reciprocal relation of space and time, may be more fruitful now than to continue the present course, as successful as it has been. We have explained the diverse properties of objects in our experience in terms of a few kinds of interactions among a few kinds of particles, but it appears that we have reached the limit of our methodology. Thus the challenge has reverted to the epistemological side of the reciprocal relation between methodology and science as described by Einstein. The old man, it turns out, was right on once again.

  7. Chris Oakley says:

    *Cough* *Splutter* Just a minute … until they’ve proved that they can get “classical” G.R. as a limiting case, String theorists have no right to claim this as part of their theory.

  8. sol says:

    Interesting link CW. It made me think, that the efforts that Einstein went through to quantize grvaity, had the opposite effect as well that they(Dirac, Bohr, Schrodinger) would work to understand GR as well

    The gravitational treatment of point particles thus brings in one further difficulty, in addition to the usual ones in the quantum theory.” This is rather curious coda since the above problems are really as relevant classically, and of course they are very different from the perturbative nonrenormalizability issues that have dominated all subsequent studies. After this pioneering foray, Dirac’s original publications in the field waned, apart from one later paper [17] on conformally invariant extensions of GR.

    Now for me when a picture enters my mind, it is unassociative for a bit, but neuronically connected, and relevant. So to Mona Lisa’s smile and the trampoline.

    DRL,

    Figure 10.1 When standing on the Mona Lisa trampoline, the image becomes most distorted under your weight

    The Heart of Reimannian Geometry

    This example cuts to the heart of Reimann’s mathematical framework for describing warped shapes. Reimann, building on earlier insights of mathematicians Carl Friedrich Gauss, Nikolai Loachevsky, Janos Bolyai, and others showed that a careful analysis of the distances between all locationson or in an object provides a means of qauntifying the extent of its curvature…..

    The Elegant Universe, by Brian Greene, page 232 & 233

    One has to still endure the geometry that is progressive, and has developed along side of the physics. One does not disavow what the world of gauss(the roads leading too hyperdimensional space) is doing in light of Maxwell’s gains. That any toy model is found correlated in relation to QFT, was a monumental effort by Kaku, in his loop calculations?

    You see. So between Smolin who adopts the GR attitude of leave Gr as it is, a Einsteinain way, and strings to adopt, the quantum mechanical discription of the background, neither can reject the ideals of the quantization of gravity, and a geoemtrical perspective.

    What geometry shall emerge?

    But now, almost a century after Einstein’s tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of general relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry.

    The Elegant Universe, by Brian Greene, pg 231 and Pg 232

    Enjoy:)

  9. Chris W. says:

    Dirac’s 1935 (!) paper is discussed in this short review by Stanley Deser.

  10. D R Lunsford says:

    Chris W – the work by Smilga seems to pick up on an idea of (who else?) Dirac, “The Electron Wave Equation in deSitter Space”, and “On a Remarkable Representation of the 3+2 deSitter Group” (I think those are more or less the correct titles). The former appeared, I think, in either the Royal Society Proceedings or some Russian journal – the latter appeared in JMathPhys sometime in the early 60s I think. Dirac clearly was thinking about (anti)deSitter space in some detail, over a number of years.

    I read these papers years ago in school, and filed them in the “very interesting” drawer.

    Also interesting here is the dropping of the name Wyler and his work on the fine structure constant.

    Again, nice papers, very nice.

    -drl

  11. D R Lunsford says:

    Chris W – those are intriguing, related to what I’m working on now! Thanks for that.

  12. Chris W. says:

    The quote attributed below to Einstein (“any intelligent fool ..”) actually seems to be due to E. F. Schumacher.

  13. Anonymous says:

    DRL,

    You can’t do “new physics at the Planck scale”, or anywhere, until there is new physics. The stringers have one thing right – this needs a new idea about matter. I have a model that should be explored, and probably will be eventually. Like the things that preceeded it, it is evolutionary, not revolutionary.

    Doesn’t all this radical talk ever get on your nerves? What I find most strange about the stringers is how they can be so satisfied with nothing but a lot of radical talk, triumphal hand-waving, and weird imagery.

    Would I be wrong to say that quantum mechanics started off theoretically, and that in having developed, brought the science along?

    For me, I am quite young in terms of my academic career but older in age, that if I did not find some consistancy in the way the geometry evolved, then yes, these abstract spaces that topological genus figures would never make sense. But, this is one end of the geometry that is revealled in the hyperdimensional realities, and might have found it’s correlates, in the cosmos?

    Klein`s Ordering of the Geometries

    A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean
    geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry
    .”

    http://www.ensc.sfu.ca/people/grad/brassard/personal/THESIS/node21.html

    So to me this geometrical math developing has to be based on the predessors somehow, and along side, the physics? Would you not consider Reinmann in the value of GR? His Teacher, Gauss?

    Brane World models only carry this unique topology solution a bit further returning in part, though often modified in present format, to
    Klien’s solution to the unification of gravity to electromagnetism through an additional dimensional set. The beauty of this path as we
    should rightly call it is that it is a natural progression of Einstein’s dream of a pure geometric explanation for everything we see
    around us in nature.”

    What do you think of this statement above?

    I also draw your attention to Lubos’s post and note the comments on Robert Lauglin.

    What is the nature of the math that should emerge, if not by string theory?

    Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature. – Hermann Weyl

  14. Chris W. says:

    Speaking of economy of ideas, I urge readers of this weblog to take a thoughtful look at these papers, so far uncited except by the author himself.

    In my humble (and relatively unschooled) opinion they are extraordinarily well conceived and superbly written. The author’s professional career apparently began in the 1960s (in Germany).

  15. Frank says:

    Hmmmm…. Appealing to beauty is not neccesarily out of touch with reality. But it may be that for the time being our concepts and modells of beauty are inadequate, thus we have to resolve to patchworking.

    Some more quotes:

    “I think that there is a moral to this story, namely that it is more important to have beauty in one’s equations that to have them fit experiments. If Schroedinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.”
    – P.A.M Dirac

    What i think is most critically missing in physics today is search for simplicity. Many people are interessted in making bigger badder more complicated theories, a few are interessted in making existing ones more rigorous, but who is actually trying to simplify them?
    Perhaps we are just not ripe yet to move in that direction.

    “Any intelligent fool can make things bigger and more complex… It takes a touch of genius – and a lot of courage to move in the opposite direction.”
    – Albert Einstein

    That to me rings to the core issue with Stringtheory.

  16. Chris Oakley says:

    … the expediency of renormalization seems to be a wart on the face of it

    I’m glad I’m not the only one saying this. Having said that, in the (few) post-doc job interviews I had in 1984/5 I am sure I detected a groan when I said that my ambition was to “crack renormalization”.

    It is unfortunate that something that claims to be as brilliant and beautiful as string theory hopes at best just to reproduce all this garbage.

  17. D R Lunsford says:

    Doug,

    Beauty in some sense = economy of ideas. Field theory is very economical in ideas. That it is phenomenology, is no fault of the thing in itself. And, in the context from which it emerged – utter pessimism about HEP – it was certainly beautiful in the sense that it gave reasonable answers.

    Furthermore, what sort of disingenuousness is it to say “field theory is ugly”, when string theory would have to reproduce that same ugliness to be taken seriously? (It won’t, but this is rhetoric.) Whatever next step turns out to be the right one, it will have things that look like gauge fields, energy tensors, etc. etc. and people will say “Ah! Now we know why field theory was that way – how beautiful!”

    I’ve never been the least bit impressed by Hawking, other than at his phenomenal virtuosity.

    -drl

  18. Doug says:

    drl,
    Personally, I think Hawking has a fairly solid point of view on the matters of modern physics. At least, I wouldn’t criticise his characterization of philosophical motivations for the pursuit of a unified theory seeing that he is sitting in Newton’s chair. After all, the man isn’t exactly an incompetent crank. However, that’s beside the point. In the matter of judging truth and beauty, clearly the standard model suffers from the fact that it is “phenomenology backed by simple, general ideas.” A theory able to calculate the masses of the particles from first principles would certainly be superior in this regard, and one would certainly like to see how those masses emerge in the generations they do. Also, the expediency of renormalization seems to be a wart on the face of it to my mind. However, some believe that “beauty is in the eye of the beholder,” but if this is true, I don’t believe truth could be beauty or beauty truth.

    Regards,

    Doug

  19. D R Lunsford says:

    Sol,

    I hold quite a definite view of things, for which I can fortunately only blame myself. My view involves, not breaking, but encompassing Lorentz symmetry, which I see as an artifact of the separation of spacetime and matter.

    You can’t do “new physics at the Planck scale”, or anywhere, until there is new physics. The stringers have one thing right – this needs a new idea about matter. I have a model that should be explored, and probably will be eventually. Like the things that preceeded it, it is evolutionary, not revolutionary.

    Doesn’t all this radical talk ever get on your nerves? What I find most strange about the stringers is how they can be so satisfied with nothing but a lot of radical talk, triumphal hand-waving, and weird imagery. It’s like living on LSD and Hershey bars washed down with absinthe. I’m still grapping with the Mona Lisa trampoline, a decidedly disturbing hallucination for some reason.

    Back to Lorentz invariance – you will *never* detect Lorentz symmetry breaking with *any* model of matter that posits a “form and substance” ontology, that is, matter of *whatever* shape cruising through spacetime of *whatever* structure, because Lorentz invariance arises *before* any specific form for matter is assumed. The Einstein-Weyl idea of matter and spacetime having a joint origin thus has to be right.

    As far as S and S goes, I could not care less – all these folks are obviously on the completely wrong track and they bore me to tears. Our own Thomas Larsson is far more interesting.

    -drl

  20. sol says:

    DRL,

    I hate to rain on your parade.:)

    If Lorentz symmetry is broken by some mechanism originating at the Planck scale, is there any hope of detecting such an effect? Surprisingly, the answer is yes. Over the past decade Kostelecky and co-workers have been exploring how a violation of Lorentz symmetry might provide evidence for new physics arising at the Planck scale. However, rather than smash particles together at high energies to explore this, researchers are turning to ultrahigh-precision experiments at low energies to search for signs that Lorentz symmetry has been broken. The idea is that such low-energy effects are caused by corrections involving inverse powers of the Planck scale.

    Possible violations of Lorentz invariance are an ideal signal of new physics because nothing in the Standard Model of particle physics permits the violation of special relativity. Therefore, no conventional process could ever mimic or cover up a genuine signal of Lorentz violation.

    Since a viable theory of physics at the Planck scale remains elusive, it is difficult to make precise predictions for the small corrections that could occur due to Lorentz violation. However, we can obtain a rough estimate. The rest-mass energy of the proton, for example, is about 1 GeV, and the ratio of this energy to the Planck scale is about 1 part in 1019. If an experiment with protons is sensitive to effects at or below this level, then it is effectively probing the Planck scale.

    http://physicsweb.org/articles/world/17/3/7/1#pwfea1_03-04

    One tends to accept that being in the unique position of holding no substantial view in regards to the evolution of thinking here, that you tend to look for the essence of things that might of been driving research and mathematics?

    Lucky guesses?

    Recognizing Smolin’s positon, and then Susskind’s would it hurt to include both in the analysis, and find yourself a onely sol, who wanders searching for how these abstract spaces answers the question of whether they are back ground dependant or not?

  21. D R Lunsford says:

    Hi Doug,

    Let’s deconstruct this statement:

    “The real reason we are seeking a complete theory, is that we want to understand the universe, and feel we are not just the victims of dark and mysterious forces.”

    This sounds suspiciously like an apology for witch-burning. I never recall Dirac or Einstein stating the “real reason” they were so occupied. The “real reason” for their efforts was never in doubt.

    “If we understand the universe, then we control it, in a sense.”

    That’s very strange – I never knew physics was about control. I always thought it was about curiosity.

    “The particles are grouped in an apparently arbitrary way..”

    That is an interesting statement. I did not know until this very moment that the relevant gauge groups were arbitrary! That is fascinating!

    “..and the standard model depends on 24 numbers, whose values can not be deduced from first principles, but which have to be chosen to fit the observations. What understanding is there in that?”

    That’s the nature (ha ha) of a phenomenological theory. One gets the feeling that Hawking was just tossing word salad to come up with a justification for his Faustian ambition.

    Now, for comparison we must cite the supposedly non-arbitrary “shuttlecock” model of Hawking, wherein the actual hyperbolic structure of the world is, “without any arbitrariness whatsoever”, converted to an elliptic one “just for the sheer rollicking hell of it”. Right.

    -drl

  22. Doug says:

    drl,

    The exact Hawking quote:
    “The real reason we are seeking a complete theory, is that we want to understand the universe, and feel we are not just the victims of dark and mysterious forces. If we understand the universe, then we control it, in a sense. The standard model is clearly unsatisfactory in this respect. First of all, it is ugly and ad hoc. The particles are grouped in an apparently arbitrary way, and the standard model depends on 24 numbers, whose values can not be deduced from first principles, but which have to be chosen to fit the observations. What understanding is there in that?”

    The link to the Hawking talk is here:

    http://www.damtp.cam.ac.uk/strtst/dirac/hawking/

  23. D R Lunsford says:

    Arun,

    I would not say that beauty in *anything* is ineffable – precisely the opposite, beauty is compelling and, usually, obvious. This does require some sort of aesthetic judgment, and the latter may be missing.

    In the case of Kepler, I think you also have it backwards – he had a specific problem to work on, not an axe to grind. His polyhedric orbs were no different in principle than the Lorentzian deformable electron, and no longer lived. It was *because* of his orbs that he eventually made progress, not *in spite* of them.

  24. DMS says:

    “I wrote another article on motls.blogspot.com that clarifies some ridiculous statements made by Peter Woit about Witten’s reasoning being “unrelated” to string theory.”

    I am sorry but I remain unpersuaded. By this logic, theta functions is really a part of string theory because theta functions arise in string theory! And so is algebraic geometry and so on.

    People knew about a lot of stuff before string theory came along, and quite likely most of the neat mathematical stuff would have been discovered (like results that have made Witten justly famous) whether or not string theory was studied.

  25. D R Lunsford says:

    I have to admit the torrent of verbiage that issues from Bon-Motl is a source of continual wonderment and awe. So you see, string theory is not without interest.

    -drl

  26. Lubos Motl says:

    I wrote another article on motls.blogspot.com that clarifies some ridiculous statements made by Peter Woit about Witten’s reasoning being “unrelated” to string theory.

  27. Arun says:

    Beauty in physical theory is an ineffable thing.

    Its been a long time since I read about Kepler, but I think among things that he tried, and was excited about, was the possibility of relating planetary orbits in some way to the regular polyhedra, one inscribed into the next. Thus, the ratios of planetary distances from the Sun would be explained. But the culmination of his research was the laws governing planetary orbits in general, and not why the particular planetary orbits of the solar system had particular radii.

    We do not think science has been held up or Kepler’s laws are ugly because we can’t explain the ratio of the distances from the Sun of Earth and Jupiter. We also see that Kepler did try to imagine a solution, a solution that we would find to be beautiful, if it was true!

    String theory may appear to be beautiful too, once we find out what is proper for it to explain.

  28. Peter says:

    Hi DMS,

    The result about infinitely many smooth structures on R^4 is just one aspect of Donaldson’s results, and it’s a hard one to visualize or say much about. You can think of R^4 as just a topological manifold, but you need to add some extra structure then to be able to differentiate functions (to even say which functions are differentiable and which aren’t). You can think of this extra structure as a choice of coordinates, defined by choosing local coordinate patches. If you choose one global coordinate patch using the standard coordinates on R^4, that gives you one smooth structure, but it turns out there are other ways of putting coordinate patches on R^4 that give an inequivalent notion of which functions are differentiable. I don’t know that anyone has explicitly constructed such things, Donaldson just proves that they exist.

    More relevant are Donaldson’s results about compact 4-manifolds. Here he produces a set of polynomials that are invariants of the smooth structure on the 4-manifold, and these can be used to solve problems in 4-d topology. The correlators in the N=2 twisted SUSY model are exactly the Donaldson polynomials. In general these can be hard to compute and prove things about. The big breakthrough of Seiberg-Witten was to relate the non-abelian N=2 twisted SUSY model to another dual one, where the gauge symmetry is Abelian, but there are monopoles. In this new “Seiberg-Witten” model, computations and proofs are easy.

  29. DMS says:

    Peter,

    I very much enjoy your posts, especially this one and the previous one. I saw a lot of ‘hype’ when in grad school over string theory and SUSY and that proof was just ‘around the corner’, if not already there; I am still waiting. Nothing wrong in trying to see if a certain idea works, but please be honest about it. The gauge coupling unification bit is an example — choose a ‘nice’ parameter set to make your result really good, and omit mentioning that it does not look as good with a different set.

    Like you I am not bitter. I am doing fun things, gainfully employed outside academia and getting the satisfaction of doing work that is actually tested. I try to follow recent developments (your blog helps!) and I see that I am not missing much.

    Regarding Donaldson invariants, I realize that he proved that there are infinitely many manifolds diffeomorphic to R^4. (I guess the other famous result was Milnor’s proof that there are 28 differentiable structures on S^7.) Could you explain what that means, maybe with a simple example? Somewhere I read, it means there are ‘infinite number of ways to differentiate’—what does that mean?

    Also, regarding Witten’s method of getting them (and more invariants?) using his work on Seiberg-Witten theory, what are the topological correlators in the N=2 twisted SUSY that he is calculating?

    Many thanks in advance!

    DMS

  30. D R Lunsford says:

    Peter said:
    Sure there’s a personal reason behind my criticisms (and no, it’s not that I’m resentful failure. Academia has ended up treating me far better than I ever expected. Lots of people go through life resentful that they’ve never had their talents properly recognized. I’m not one of them.) The reason is simple: I think what has been going on in string theory recently is an intellectual and moral disgrace, and it defiles something extremely important to me, the whole idea of trying to better understand how the universe works in an honest way.

    This is a wonderful summation of how many of us *feel*. This is not just a matter of thinking – the intellectual fraud that is string theory stabs at the heart of science, in the sense that those who do science need at some point the judgment that derives from being *emotionally involved* with finding things out, and not just occupying an academic position.

    -drl

  31. D R Lunsford says:

    The SM is not “ugly” and it’s certainly not “ad hoc” – if Hawking said this it confirms my opinion that, as a physicist, he’s a superior mathematician. The SM is phenomenology backed by simple, general ideas.

    In contrast, string theory could not *possibly* be more postmodernly ad-hoc, and sets a new bar of loathsome ugliness, both in itself and in the culture it engendered. It is a ridiculous, poisonous, viral fiction.

    -drl

  32. Peter says:

    Hi Francois,

    I was referring to Witten’s TQFT for Donaldson theory, which is a twisted version of N=2 supersymmetric Yang-Mills. This is a 4d Yang-Mills theory with fermions, the fermion charges are just somewhat different than in the standard model. Mathematically this theory has a beautiful interpretation as computing the euler class of a certain bundle.

  33. raj says:

    >I think the state of modern physics, now in the throes of two, incompatible, 20th century revolutions, is looking more and more pathetic from an outsider’s point of view.

    I tend to agree, to some extent. Physicists who rave over a theory merely because it is “beautiful” (a/k/a, full of jargon) instead of having something to do with reality (a/k/a, that it has some experimental justification) strike me as being, well, divorced from reality. One of the reasons that I found physics so interesting, when I was studying it in University in the late 1960s and early 1970s, was that it appeared to be grounded in reality. It is somewhat sad to see the discipline devolve as it apparently has.

  34. Thomas Larsson says:

    The circle is undoubtedly the most beautiful geometrical shape. Hence we conclude that planets must move in circles, or in circles around circles.

    It is interesting that people like Motl, while promoting symmetry principles as an argument in favor of string theory, are vehemently opposed to the investigation of symmetries which are not restricted to one complex dimension. Perhaps this limitation to one-dimensional symmetries is a sign of a one-dimensional mind.

  35. Francois says:

    Hallo Peter, you just wrote

    “The QFT whose observables are the fundamental 4-manifold topological invariants is mathematically very close to the QFT of the standard model. I find it hard to believe this is a coincidence. There’s very deep mathematics, somehow related to supersymmetry, going on here, mathematics whose proper understanding might lead to new ways of thinking about the standard model.”

    Could you explain what you mean by the “closeness” in more detail? Apart from being enlightening in its on right, the answer would clarify the discussion on the beauty/ugliness of string theory.

    Francois

  36. Peter says:

    Hi Z,

    An interesting response, here’s what I think about some of the issues you raise (although I really can’t do justice to the whole issue of string theory and math, it’s a long and complicated story).

    I don’t think 11d supergravity has had any appreciable impact on mathematics yet, or that it ever will (other than in perhaps indirect ways. People have and will continue to get involved in really interesting math sometimes because of questions that came up when they were looking at 11d supergravity).

    About D-branes and CFT: depends what aspects of D-branes you mean. In some sense D-branes are just boundary conditions on CFTs on worldsheets with boundary. A CFT on a worldsheet with a boundary is still just a QFT of a certain kind. The only things that seem to me to definitely be non-QFT results are those involving summing over all genus worldsheets.

    I think CFTs are of great importance not because they can be used to construct string theories, but because our understanding of QFT in general is very crude. By studying CFTs we can get a lot of insight into QFT in general, and hope to apply this to 4d QFT.

    I don’t think I dismiss all of string theory at every possible opportunity. My view of work that has come out of string theory ranges from very positive (CFT, mirror symmetry) to neutral (adS/CFT may solve QCD, may not, seems worth trying, but may not work) to very negative (the Landscape).

    Sure there’s a personal reason behind my criticisms (and no, it’s not that I’m resentful failure. Academia has ended up treating me far better than I ever expected. Lots of people go through life resentful that they’ve never had their talents properly recognized. I’m not one of them.) The reason is simple: I think what has been going on in string theory recently is an intellectual and moral disgrace, and it defiles something extremely important to me, the whole idea of trying to better understand how the universe works in an honest way.

    Of course I’m trying to “destroy the hype”, and make no bones about it. I call things scientifically as I see them, but my point of view is a very specific one, that is not one you are used to hearing. With the most promising aspects of string theory, things like AdS/CFT, there are hordes of people willing to look at them from a very optimistic point of view, and emphasize the possibilities that they might lead to. I don’t think it’s my job to be as optimistic as possible about these things, there’s plenty of that already.

    Actually I’ve often written in a skeptical way about SUSY QFTs, especially about whether the MSSM or SUSY GUTs have anything to do with reality. On the other hand, at least in the form of twisted supersymmetry, there is amazing mathematics going on in certain SUSY QFTs, even though I don’t think anyone knows how to properly relate the mathematics of these theories to physical reality. The QFT whose observables are the fundamental 4-manifold topological invariants is mathematically very close to the QFT of the standard model. I find it hard to believe this is a coincidence. There’s very deep mathematics, somehow related to supersymmetry, going on here, mathematics whose proper understanding might lead to new ways of thinking about the standard model.

  37. Anonymous says:

    I am definitely *far* from being an expert about the impact of string theory to mathematics, but I couldn’t resist this. It would be great if some real experts gave definite examples, but here goes:

    “However, most of these interesting things really come from 2d conformal QFT, and I would argue that it is QFT which is having a huge impact on mathematics, much more so than string theory. Witten’s Fields medal was for his work on the relation of QFT to math, not for anything he has done using string theory.”

    I am not sure if this is just a statement about what has happened up to now, or meant to be a prediction about the future impact of string theory to mathematics. If it is the latter, it would be clearer if you made it more explicit. Do you, for example, predict that the 11-dimensinal aspects of string theory will not stimulate mathematics in any appreciable way?

    More to the point: Well, the perturbative expansion of string theory happens to be given by 2D CFT. To say that these results really come from 2D CFT, not string theory, seems to me like saying these results actually come from calculus, not QFT. Do you think that the things that came “really from 2d conformal QFT”, like mirror symmetry, would have come our way if we weren’t looking at the 2D CFT from the point of view of strings propagating in background spaces?

    Furthermore, I am not sure *what* you would consider something as coming from string theory, “not just 2D CFT”. Would you, for example, consider mathematical developements related to D-branes to be coming from 2D CFT, not string theory, because D-branes were discovered by a CFT calculation?

    On another note: Even though I would not consider myself an advocate of string theory, and am definitely against the fanatic approach some string theorists seem to be taking, it seems to me that many of the strong criticisms you make of the subject have some personal reasons in the background, which hinder your ability to be objective. It is obvious that string theory hasn’t been able to live up to its premise yet, but stating this as an objective fact and debating about the it (and speculating on the future) is one thing, dismissing the field at every possible opportunity is another thing.

    I can understand the arrogance of some string theorists pissing one off, but string theory is not bullshit, even if it turns out that it doesn’t describe the universe at the most fundamental level.

    You don’t seem to attack the zillions of people writing papers about various SUSY field theories and exploring their properties, even though it is obvious that many of those theories do not contain the standard model. These people are trying to understand the dynamics of SUSY QFTs with the hope that this will eventually help us understand something about the universe. Well, helping understand dynamics of SUSY field theories is one of areas where string theory has achieved a lot. If you think this is rubbish, tell the same to SUSY field theorists!

    Once again, even if string theory turns out not to describe the universe at the most fundamental level, I think even just AdS/CFT proves that string theory is a valuable subject that gives us fascinating insights about the structure of the theories we have been using as building blocks.

    I don’t think there is anything wrong about debating on the eventual success of string theory as a fundamental theory. However, it seems clear to me that what you are trying to do is not just that, but it is to “destroy the hype”.

    I don’t have problems with the latter aim, either, per se, but I don’t think the methods you use for that purpose are scientifically honest.

    z

  38. Doug says:

    While I find your crusade against the indulgences of string theorists enlightening, I’m also reminded of Stephen Hawking’s observation concerning the standard model: “It’s ugly and ad hoc,” he said. So the case you make may be a case of the kettle calling the pot black. I think the state of modern physics, now in the throes of two, incompatible, 20th century revolutions, is looking more and more pathetic from an outsider’s point of view.

    Einstein said that “the reciprocal relationship of epistemology and science is of noteworthy kind. They are dependent upon each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is — insofar as it is thinkable at all — primitive and muddled.” Actually, I think we are seeing the wisdom of this observation more and more clearly today. To my mind, Keat’s ode is still the most compelling, and relevant, dictum of all. Not just because it rings so true, but also because it is so concise.

  39. sol says:

    As I read Lubos’s comments about the beauty, of simplicity, something came to mind of what was linked by Chris W. in regards to the number theory, and a related article about Mona Lisa and Math. It triggered the relation, to the following

    On page 65 of Hyperspace by Michio Kaku, he writes, “Picasso’s paintings are a splendid example, showing a clear rejection of the perspective, with woman’s faces viewed from several angles. Instead of a single point of view, Picasso’s paintings show multiple perspectives, as though they were painted by someone from the fourth dimension, able to see all perspectives simultaneous

    Now I know there are a lot of good intellectual minds here. We cannot ignore I feel what could have existed in the realization of the compactified dimensions(how did you get there ?) as we view the four spacetime.

    As you look through the historical, recognize the Euclide’s fifth postulate, and recognize a geometry that was being lead through, or as Linda Henderson writes,”the fourth dimension and non euclidean geometry emerge as among the most important thgemes unifying much of modern art and Theory.”

    This might seem insignificant to many of you, but without it there is no possbility of entertaining the subjects of Cubist art perspectives and Monte Carlo effects of quantum gravity, as a perception that hopes to explain the geometry of a world that we are having diifficulty explaining.

    I hope this idea of perception and the ideas of this simplicity is more or less asking that we look around the picture of Picasso, and see that the views of Mona Lisa smile, ask that we not look at her mouth directly.:)

    Is this where the landscape issue originated?:)

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