Are Fermion Masses Like Planetary Orbits?

A more and more common argument one hears from string theorists these days (for one version see a recent anonymous comment posted here) goes more or less like this:

“A fundamental theory shouldn’t be expected to predict things like fermion masses or the standard model gauge group anymore than it should be able to predict the physical properties of the planets. Anyone who expects this is making the same mistake as Kepler, who tried to relate Platonic solids to planet orbits.”

The idea here is that many or even all of the things we don’t understand about the standard model are not fundamental aspects of the theory we should expect to be able to predict. Perhaps they are determined by the details of the history of how we ended up in this particular time and place, just as the properties of the planets were determined by the detailed history of the formation of the solar system.

As far as we can tell, the properties of the standard model hold uniformly throughout the observable universe, so to adopt this point of view one needs to postulate the existence of an unobservable “multiverse” of which we see only one small part. The so-called “landscape” of an unimaginably large number of possible vacuum solutions for string theory provides one realization of such a multiverse.

What are the problems with this idea? First of all, it is not so easy to dismiss out of hand. One can certainly imagine the possibility of the existence of an M-theory (maybe now the “M” is for “Multiverse”) with a local vacuum state that corresponds to our universe, and some dynamics that allows evolution from one universe to another. Perhaps tomorrow night a preprint will appear on containing a simple equation expressing a dynamics such that the possibility of a universe exactly like ours does arise as some part of a solution. Should we believe in such a new theory, whatever it is?

There seem to me to be two possible cases in which such a theory would be compelling. The first would be if the theory made experimentally testable predictions. Perhaps it would have only one solution that agreed completely with current experimental observations. Then the properties of this solution could be used to predict the results of experiments not yet done. If these predictions were accurate, the theory would have strong evidence in its favor.

Even if the theory had so many solutions that one couldn’t readily use it to make predictions, one still might find it compelling due to its “beauty” or “elegance”. If it were based on a very simple equation or idea, the fact that the relatively complex structure of the standard model could be made to fall out of a much simpler equation would again be strong evidence for such a theory. Just how compelling this would be would depend on how much simpler it was than the standard model. If the new equation was more or less as complicated as the equations which determine the standard model, it wouldn’t be compelling at all.

The current state of affairs in particle theory is that many people believe that they are on the road to finding such a compelling theory, but all the evidence is that this is nothing but wishful thinking on their part. There is no viable proposal for an M-theory based on a simple set of equations with a solution corresponding to the real world. This simply does not exist. An easy way to embarass a string theorist who is going on about the beauty of the theory is to ask them to write down a simple set of equations that characterize this beautiful theory. They can’t do it now and I don’t see any reason to believe they ever will be able to in the future.

What string theorists have now is not a single, consistent theory, but a set of several inconsistent fragmentary theories that they hope can be turned into a consistent whole. This circle of ideas is significantly more complicated than the standard model that it is trying to explain.

Even this complex of ideas might be compelling if it could be used to explain one or more not yet understood aspects of the standard model, or if it made new experimental predictions that could be checked. All the evidence of recent years is that this is impossible. If the whole framework makes any sense at all, it appears to predict nothing and explain nothing about the standard model. Not a single one of the parameters of the standard model can be calculated, not a single experimental prediction, at any energy scale, can be made. It is becoming increasingly clear that the circle of ideas known as “M-theory” is completely vacuous.

Strong evidence that this is the case comes from the fact that string theorists have no idea what, if anything, M-theory is supposed to be able to predict. Polchinski and others feel they have demonstrated that M-theory can’t predict the cosmological constant, but can’t come up with anything else it can predict and, increasingly, seem happy to live with the idea of promoting a theory that can’t predict anything. This wholesale abandonment of the scientific method upsets some physicists such as David Gross quite a bit, but more and more people seem to have no problem with this. Frankly I find this all bizarre, disturbing, and becoming ever more so all the time.

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13 Responses to Are Fermion Masses Like Planetary Orbits?

  1. Anonymous says:

    Er… empirical Bode’s law fits the planetery orbits, isn’t it. And I have heard some good attacks to try to derive the orbits from chaotical dynamics, particularly at the moment of condensation of the planets.

  2. Peter says:

    I’m afraid I’m really the wrong person to ask the questions you’re asking, since these aren’t the kinds of alternative ideas I’ve ever tried to pursue. They are close enough to string/M-theory that you are more likely to get good answers from a string/M-theorist.

    I don’t think any of these things have rigorous no-go theorems. The closest may be the higher-spin problems, where I think what happens is if you look at the structure of the poles of the propagator, you can see that there’s a problem with finding a prescription for dealing with them in a way that maintains locality and causality. I’ve never looked at this carefully, but if this is the heart of the problem, there may be a rigorous argument possible.

    For dealing with the conformal factor, a lot of people have worked on this, often in the context of trying to get strings to work in 4d. You really need to find an expert on this, not me.

    Similarly with theories of quantized membranes. A lot of people have tried hard to do this and they are the ones who would know what the fundamental problems are.

  3. gut says:

    For the cases of massless spin > 2 particles in interacting quantum theories, is there a rigorous theorem that says these theories don’t exist? Or is it mostly “circumstantial evidence” of repeated failures in attempts to construct these particular interacting theories? (ie. we don’t know what to do, so we just ignore the problem?)

    Can the same be said about d > 11 brane theories with respect to (conformal) anomaly cancellations?
    (ie. “rigorous theorem” vs. “we don’t know what to do, so we just ignore the problem”?)

    Has anyone ever produced a quantized membrane or p-brane theory that at least has a perturbative Feynman diagram type of expansion (with or without renormalization)?

  4. Peter says:

    Superstring theory is in d=10 because that’s the dimension in which the conformal anomaly cancels. For higher d, you’ll need to figure out some way of dealing with the conformal degree of freedom. M-theory conjecturally handles this in 11d, I don’t think anyone knows what to do for d>11. The dimension of your branes is limited by the space-time dimension.

    Interacting QFTs with spin >2 have problems with unitarity and causality that no one knows how to resolve. This limits the number of supersymmetries you can have.

    Nothing sensible I can say about the other questions.

  5. gut says:

    I have a question.

    Why stop at 11 dimensional M-theory or 10 dimensional superstring theory?

    Why don’t we have interacting quantum theories with massless particles with spin 3, spin 4, spin 66, spin 500, spin 9678900, spin aleph_0, and higher?

    Why don’t we have quantum theories of 30-branes, 32-branes, or for that matter 100-branes, 210-branes, 10024-branes, and higher?

    Why don’t we have field theories with N=43, N=200, N=1000, N=12345 supersymmetries, and higher?

    Why don’t lie algebras with 3-grading, 5-grading, 1001-grading, 665543-grading, and higher show up as a more “general supersymmetry”?

    Why do we only count dimensions by positive integers? Why don’t we have a non-integer number “dimensions”, such as 0.4444 dimensions, log(500) dimensions, pi^300 dimensions, -34 dimensions, -log(35353522) dimensions, etc …?

    Why don’t we have aleph_1, aleph_4, aleph_700, aleph_34588345, etc … being used in the number of dimensions, number of supersymmetries, lie algebra grading, or aleph_34 branes, massless spin aleph_2 particles, etc …?

    Why would a “unified field theory” reject such objects mentioned above?

  6. Peter says:

    Note that I didn’t say this was what string theorists as a whole think, I said it was an argument one hears from string theorists more and more often. For other examples of this, search the last year or so of sci.physics.research to find Robert Helling arguing that expecting string theory to predict standard model parameters is like expecting a fundamental theory to predict the properties of screws. I also recall Urs Schreiber making the analogy with predicting his phone number. Here’s a quote from Lenny Susskind:

    “Physicists always wanted to believe that the answer was unique. Somehow there was something very special about the answer, but the myth of uniqueness is one that I think is a fool’s errand. That is, some believe that there is some very fundamental, powerful, simple theory which, when you understand it and solve its equations, will uniquely determine what the electron mass is, what the proton mass is, and what all the constants of nature are…. On the other hand you could have a theory which permitted many different environments, and a theory which permitted many different environments would be one in which you would expect that it would vary from place to place. What we’ve discovered in the last several years is that string theory has an incredible diversity—a tremendous number of solutions—and allows different kinds of environments. A lot of the practitioners of this kind of mathematical theory have been in a state of denial about it. They didn’t want to recognize it. They want to believe the universe is an elegant universe—and it’s not so elegant. It’s different over here. It’s that over here. It’s a Rube Goldberg machine over here. And this has created a sort of sense of denial about the facts about the theory. The theory is going to win, and physicists who are trying to deny what’s going on are going to lose.”

    As for consistency and beauty, all the things you mention either are completely inconsistent with reality (four large dimensions and the standard model)

    N=1 supergravity in 11 dimensions, known facts about matrix theory, N=2 and N=4 supersymmetric vacua

    or completely ill-defined

    M-theory, conjectural matrix theories with better properties

    N=1 supergravity in 11d may or may not be beautiful, but it doesn’t look at all like the real world.

    I never said that there aren’t people who think that “low-energy N=1 supersymmetry might be a prediction of string theory”. But even though many if not most string theorists wish this were a prediction of string theory, it isn’t. It’s a nonsensical abuse of language to say that something “might” be a prediction. To make a prediction is to claim that something “will” be true, not that it “might” be true.

    String theory has failed utterly as a unification idea. It has no consistent version that can give 4d and the standard model and it makes absolutely no predictions whatsoever. If most of the energy of the particle theory community hadn’t gone into string theory for the past 20 years, we might have some good alternatives now.

  7. Thomas Dent says:

    An anonymous comment is good evidence for what string theorists as a whole think? At least, try to find someone speaking ‘on the record’. Otherwise we will be at the level of letters that begin “As a lifelong Democrat…”.

    Please tell us how string theory (or theories) is or are “inconsistent” as you claim. On the contrary, it is believed that many perturbative N=4 and N=2 supersymmetric vacua are theoretically perfectly consistent. I don’t think you have any counterargument to this. Perhaps you mean that more recent developments are inconsistent. But in what way?

    Some people (in Santa Cruz, Michigan and other places) think that low-energy N=1 supersymmetry might be a prediction of string theory. You could at least acknowledge that such people exist.

    Do you not think that N=1 supergravity in 11 dimensions is a beautiful theory? And this is what M-theory is in some limit. There are lots of other beautiful things about, for example matrix theory. Of course, they take a little time to explain.

    What is the alternative to string theory? Because nothing else could possibly “predict” the Standard Model parameters either, in the strong sense that you want.

    In QFT we have GUT’s and other symmetric constructions, that build on our prejudice for simplicity and unification, but strictly, field theory has no predictions, since there might be a field theory that is not unified but has values of the SM parameters very close to GUT values: there is a continuous infinity of equally consistent QFT’s in flat space.

    But, of course, no field theory is completely consistent as a description of the world. If we are not to do string theory, what can we do to make QFT work with gravity? After all, people didn’t go into string theory for no reason at all.

  8. gut says:

    A few very telling lines on page 87 of the postscript version, or on the web version

    Another confession of Pauli’s went to Paul Ehrenfest:

    “By the way, I now no longer believe in one syllable of teleparallelism; Einstein seems to have been abandoned by the dear Lord.” 195 (Pauli to Ehrenfest 29 September 1929; [250], p. 524)

    Pauli’s remark shows the importance of ideology in this field: As long as no empirical basis exists, beliefs, hopes, expectations, and rationally guided guesses abound.

  9. D R Lunsford says:

    gut (?) –

    Seems like a very fine review, and the list of references is comprehensive, but oddly misses the main point for modern work, namely:

    The unification of Kaluza is non-dynamical. This is most easily seen by dimensional analysis. Mathematically, the “leftovers” in bottom corner of the extended metric must be constrained in an artificial, purely formal way that forces the n5.. components in the metric to mimic the required behavior. The vacuum problem of string theory is the price paid. That this is the death blow to Kaluza’s ansatz was already known by Pauli ages ago. I can’t see how anything has changed since then. The “cylinder condition” is never really lifted, only explained as projective differential geometry in a particular representation. The lack of a cogent variational principle without essential arbitrariness is further evidence for the ad-hoc nature of the ideas.

    Given the leading role of string theory, I find it strange that so little is said about the basic nature of the Kaluza ansatz. It would be interesting to understand how Kaluza’s theory became popular again after having so completely failed as physics and for so simple a reason. I have no idea how this happened. One should emphasise the marked contrast to Weyl’s ansatz, which is dynamical from the outset, because of the fundamental role of Am in the geometry. The persistent hints that masses are associated with conformal scaling should inspire more interest in this idea, but in spite of all efforts this seems unlikely to happen.

    In the newsgroup the issue of a theory of trivectors (three-forms) came up. I’ve actually worked this out and, as an illustration of the non-essential nature of the Kaluza ansatz, can exhibit it in “unified” form with the 4-d metric. The potential is a bivector and one need only form symmetric objects from it – these are easy to find (think of the energy tensor for electrodynamics). There is a gauge invariance that gets mimicked under the cylinder condition in exactly the same way the gauge invariance of the vector potential does in the original. Is it a UFT? Of course not. The metric is what it is, and the gauge potentials are what they are. The “twain may meet”, but only in a more comprehensive geometry than Riemann’s. Attempting to make the gauge potentials part of the metric itself is physical folly.

    I was pleased to see the work of V.A. Fock acknowledged – he was the first person to take seriously the role of the Dirac gammas as geometrical objects (frame basis). I once owned a galley proof of the paper “L’Equation d’Onde de Dirac et la Geometrie de Riemann” autographed by Born, from his own personal effects (a friend at Maryland had found it on rummaging through some discards of the Physics dept.) It got lost in a move and could not be recovered 🙁 IMO this work is still interesting in the context of Weyl’s ideas because gamma_5 suddenly acquires an essentially dynamical role.

  10. gut says:

    Are you referring to this article:

    “On the History of Unified Field Theories”
    by Hubert F.M. Goenner


  11. D R Lunsford says:

    Peter –

    The situation is very reminiscent of the deluge of “unified field theories” from 1930-50 from Einstein, Schroedinger, and Eddington. Unlike Weyl’s theory which has a simple, cogent principle at base (“pure infinitesimal geometry”), none of these others – “fernparallismus”, asymmetric metric, asymmetric connection, “lambda” invariance – had anything other than a purely formal standing and they are all reducible (no unique vacuum). Because the times were ripe for experimentalists, these theories were rightly forgotten or held up as examples of what not to do.

    Included among these theoretical husks was of course the Kaluza theory, including Klein’s modifications – because like the others, it was based on a purely formal principle without any direct connection to physics.

    That an already rejected, dead theory would be taken so seriously is a sign of either theoretical desperation, or a semi-conscious effort to prop up a publication and funding bonanza.

  12. Peter says:

    I’m actually agnostic on the “univac” vs. “multivac” issue, since my best guess is that the whole set-up in which this discussion is taking place isn’t such that one can get well-defined answers to questions like this.

    What I was writing about was something different. I’d always assumed that all serious theorists would agree that if the “multivac” scenario is correct and there really are so many vacua that you can’t use string/M theory to predict any of the parameters of the standard model, then you would have to abandon the theory as being useless and not explaining anything. David Gross clearly recognizes what a disaster for string theory the “multivac” scenario is, and I assumed his was the majority view these days. I seem to have annoyed Jacques Distler by thinking he was in Gross’s camp. Now I have no idea whether he is “univac” or “multivac” and don’t want to get in trouble by speculating about this.

    It has amazed me recently to see how many string theorists are willing to argue the case that even if the theory can’t explain anything about the standard model, this is not a disaster. They seem to intend to continue believing in string/M-theory unification, even when convinced that there is no way to use it to make predictions or explain any known aspects of the universe. As far as I can tell they are willing to abandon the scientific method in order to keep defending string theory.

    Perhaps I’m misrepresenting people’s views, but my evidence for this includes the following:

    1. The anonymous string theorist here who argued that the standard model parameters and gauge groups are no more likely to be predictable from fundamental theory than planetary orbits. You can find the same argument made in many places these days by many people.

    2. Srednicki’s claim here that even if string theory could not explain anything about the standard model, if it were consistent it would be a “striking success”.

    3. Polchinski, Kachru and others uniformly refuse to answer a question I keep trying to put to them: in the “multivac” scenario, name something that you expect to be able to predict. The fact that they don’t answer this question seems to me strong evidence that the answer is that they retain the wishful thinking that something, someday may be predictable, but have no idea what it may be.

  13. serenus zeitblom says:

    Peter, you should look at
    It’s clear that the claim that string
    theory can produce “anything” just isn’t
    true. In particular, it is very far from
    clear that it can produce a deSitter
    background. The KKLT proposal essentially
    suggested that you could get dS out of string
    theory if you were willing to tolerate extremely
    contrived models involving known gadgets such
    as fluxes. Now it seems likely that even
    this is not true. NOTE that I am not saying
    that it can’t be done — nobody knows this
    yet. What we do know now is that getting dS
    out of string theory is going to be very hard.
    In view of this, it seems rather odd that people
    are worrying about a vast landscape when, as
    Vijay B reminds us, we do not have even *one* credible dS background for string theory! Perhaps *this*
    is *what* Jacques *Distler* was *going* to
    *explain*, no *doubt* with a *superfluity* of
    *italics*, in his *blog*, which *unfortunately*
    is *mainly* about *itself* these *days*……

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