Garrett Lisi’s Theory of Everything!

Garrett Lisi has a new paper, “An Exceptionally Simple Theory of Everything.” Many people seem to think that I should have an opinion about it, but I don’t. It’s received a good deal of publicity, in part because of Lisi’s personal story — if you can write an story with lines like “A. Garrett Lisi, a physicist who divides his time between surfing in Maui and teaching snowboarding in Lake Tahoe, has come up with what may be the Grand Unified Theory,” you do it.

The paper seems to involve a novel mix-up between internal symmetries and spacetime symmetries, including adding particles of different spin. This runs against the spirit, if not precisely the letter, of the Coleman-Mandula theorem. Okay, maybe there is a miraculous new way of using loopholes in that theorem to do fun things. But I would be much more likely to invest time trying to understand a paper that was devoted to how we can use such loopholes to mix up bosons and fermions in an unexpected way, and explained clearly why this was possible even though you might initially be skeptical, than in a paper that purports to be a theory of everything and mixes up bosons and fermions so casually.

So I’m sufficiently pessimistic about the prospects for this idea that I’m going to spend my time reading other papers. I could certainly be guessing wrong. But you can’t read every paper, and my own judgment is all I have to go on. Someone who understands this stuff much better than I do will dig into it and report back, and it will all shake out in the end. Science! It works, bitches.

For a discussion that manages to include some physics content, see Bee’s post and the comments at Backreaction.

241 Comments

241 thoughts on “Garrett Lisi’s Theory of Everything!”

  1. H-I-G-G-S,

    I don’t recall ever seeing you reveal your actual identity in any of your postings, so I don’t know who you are, and I assume the same is true of Lee.

    “I’ll let you be the judge of your own opacity.”

    “you might want to take a look at the chapter on fermions in any modern book on quantum field theory.”

    are among the things you’ve written here that I think could be described as the particle physicist’s equivalent of trash talking. I strongly suspect that if your real name was on the comments you might have decided to, in your words, “Take a deep breath”, and express yourself in a different manner.

  2. Peter,
    All you’re trying to do by complaining about anonymous comments is distract attention from the fact the Lisi’s paper has been shown to be completely wrong and Smolin et. al. have completely embarassed themselves. From where I stand, HIGG’s comments have been very reasonable and on point.

  3. Dear Peter,

    In a world where the internet can quickly provide personal information I think having a pseudoynm is perfectly appropriate. You can disagree, but please stop attacking me on this point. As to whether the
    above was trash talking or appropriate responses to Lee’s unjustified attack on Distler, I’ll let readers make their own judgements.

    Let me make one final point. You often complain about ad hominem attacks
    and about people who attack you based on your publications or record rather than on the content of your posts. Please treat me in the way you wish to be
    treated. You attack me personally for not revealing my true name or for “trash talking”, even after I offered an apology and then provided the details requested about my judgement of Lisi’s work. I’d appreciate it if you would not do this in the future. I of course am more than happy to respond to critical comments about the physics issues I am discussing.

    H

    p.s. as for the “deep breath” comment, I had the definite impression that Lee was responding quickly, without thinking things through, and was thus missing the important fact that psi_R^* is left-handed and that this accounted for the discrepancy with Distler. Taking a deep breath and having a look at a QFT textbook seemed to be precisely what he needed to do.

  4. Dear HIGGS,

    Thanks, what is frustrating for me is that you and others don’t credit progress to address points you raise when it happens. Let’s go through your points (not in your order, for clarity)

    “3) He has nothing new to say about dynamics so I expect the theory to be non-renormalizable, to the degree the theory is even defined.

    5) The E8 symmetry is not a symmetry at all since there is no limit proposed in which it is restored.”

    These two points are addressed in my paper, by the giving of an action which is fully E8 gauge invariant and by the proposal of a spin foam quantization based on that E8 invariant action. While we do not yet know if that leads to an ultraviolet finite quantum theory, it is known that related forms of spin foam actions are uv finite, for reasons that may apply here. In particular, spin foam models for just general relativity are ultraviolet finite and well defined. So there is a solid basis to proceed to investigate a quantum theory of an E8 unified theory. (Note that my paper applies to a general class of theories that include Lisi’s E8 proposal.)

    So why do you keep repeating these points when they have already been substantially addressed?

    “4) He starts with all couplings equal but does no RGE analysis to see whether they take reasonable values at low-energies. This seems unlikely since the low-energy couplings do not unify without superpartners or some other new structure at low energies.”

    I agree it would be good to a RG analysis but I also hope that the first paper proposing a new theory does not already have to present a full renormalization group analysis. I am also puzzled by your statement, is it not true that in any spontaneously broken gauge theory, broken at a scale M, the couplings must unify above the scale M? Is it not also true that there must be many ways to fill in the desert so as to explain a unification of couplings at a scale M, the MSSM gives just one way to do this? The MSSM is sufficient, but not necessary to complete grand unified theories to give a unification of gauge couplings.

    “1) It does not contain the standard model fermions in a chiral rep. In fact it contains fermions in real reps, so they will presumably have large masses and one will not get the chiral structure of the SM.”

    This is claimed, but I for one have had trouble following Distler’s argument to the end. Let me ask two questions, related to this issue in the whole class of models I study including E8. Since you imply above that the group theory is trivial, perhaps you know the answer. In these models a semi-simple gauge group G with exact G invariant dynamics is spontaneously broken to a subgroup

    H= local-lorentz x Y,

    where Y is a yang-mills gauge group. The definition of chirality you use involves treating the left and right handed parts of fermion fields differently, so it cannot be applied directly to reps of G. Now do you know the answer to the following question: what property does a representation of G have to have so that it gives rise, after spontaneous symmetry breaking, to spacetime spinors which are chiral in Y? If you know the answer I would be grateful, it would help me understand and generalize Distler’s argument.

    Second, one reason I have trouble understanding Distler’s post is that it seems to involve two distinct claims. First that the particular gauge groups Distler, in an earlier post, claims are subgroups of a parrticular non-compact form of E8, are not. Second that the construction Lisi gives of fermions arising from certain pieces of the adjoint of E8 do not give rise to chiral reps (in the senses that you use it) after the spontaneous symmetry breaking. In my efforts to isolate the precise mathematical claim being made and understanding the precise arguments for them I find the mixing of these two issues confusing. In particular, if Distler is making the first claim, why is it at all necessary to bring up the issue of chiral fermion reps?

    Perhaps this is just my ignorance, but as I indicated above I am very open to communicating with anyone who does understand the details of the claim.

    2) It mixes bosons and fermions with some talk about BRST but no definite proposal about what the mathematical structure is that lies behind this. For exampe, are the physical states defined by BRST cohomology classes?

    Lisi is definite about the mathematical structure he is referring to, he is using a certain definition of a “BRST extended connection”, but he is not using it the way BRST is often used to construct gauge invariant amplitudes for yan-mills theory. In any case, as I indicated in my paper, in case Lisi’s approach fails there is another way fermions could arise in such a theory. This does not in particular, limit them to coming from generators in the adjoint of E8. This is one reason why I am interested in the more general question I raised above.

    Dear Eric,

    I find this situation disappointing for the following reason. From behind a veil of anonymity you make the claim that “Lisi’s paper has been shown to be completely wrong” and I have embarrassed myself. Using my real name, I attempt to engage in a constructive dialogue to understand the precise argument Distler is making and I do it in an open-minded professional spirit, asking questions when I am confused and easily admitting when I am wrong and what I get for it is just further insults from people who do not have the decency to use their real names when insulting and criticizing others.

    Now, let me make this completely explicit: I do not have a big stake in how the issue turns out with Lisi’s fermions because I have a different proposal for how fermions can arise in the kind of gravity-gauge theory unifications his proposal fits into. This proposal does not limit them to arising from certain generators in the adjoint, as Lisi’s does. A cynical person would even say I have a stake in Lisi’s failing, so that mine would be paid more attention to. But in fact, I am happy either way, I just want to understand what is true.

    You cannot say, X has been shown, by an argument posted a few days ago that is highly technical and not easy to follow, and then insult someone trying to understand it. The use of the form “X has been shown” applies to cases where the argument has been understood and digested by experts and agreement has been reached. There are subtle issues involved-as I indicated above this is a different kind of unification than the usual GUTS because its incorporation of the local spacetime symmetry group makes the usual definition of chirality difficult to apply – and it is easy to make mistakes when one uses old arguments in new contexts. These kinds of issues often take some time to be digested and understood. We are far from agreement here. I have no doubt that eventually all will be clear, and we will have agreement, but simply insulting people who take more than a few hours to reach agreement over a highly technical point is not helpful. And I find it simply incomprehensible that anyone who had respect for others in the scientific community and pride in their own reputation would attack other scientists from behind a veil of anonymity.

    Thanks,

    Lee

  5. H-I-G-G-S,

    I’m not about to change my mind on the anonymity issue, or to stop bringing it up when appropriate, and the anonymous defense of bullying and trash-talking by “Haelfix” made it a highly appropriate issue to raise here. I still think you should reconsider your views on this, but if you don’t, you should take extreme care in the future to stick to physics and avoid personal comments.

  6. From a completely journalistic point of view of what has transpired here, it is Distler and H-I-G-G-S who have embarrassed themselves with an attitude that exposes insecurity. Of course we don’t know who H-I-G-G-S actually is, so I suppose he’s not really embarrassed.

    For those of us watching what is transpiring it is somewhat disappointing to see people acting this way if for no other reason than to think we won’t privy to this type of debate in the future.

    Whether this theory is right or wrong, you people who count this field as your career could do yourselves all a big favor and embrace the attention this story has received. This type of attention doesn’t come often, so you should at least conduct yourselves in a way that will help people like you and the science you represent.

    Can you imagine seeing transcripts of your heros acting like this? Would they be your heros if they had?

  7. I’m not a physicist, but do I follow physics research on the arXiv and whatnot. I have been following the fate, or progress, or whatever, of Garrett Lisi’s paper from its appearance on the arXiv. I’m not qualified to comment on its technicalities.

    But I AM qualified to comment on the way its discussion has proceeded, partly because I am a scholar myself in the field of computer music. I have published in peer-reviewed journals, presented papers at conferences, and so on although I am not a teacher. I also have taken part in numerous extended technical discussions of this kind, online, in my own field. Some of those discussions were even more rancorous than this one… sigh….

    I don’t think it’s anonymity that tempts people to misbehave, but simply being online typing in a room instead of being face to face with one’s interlocutors.

    The way the Lisi discussion has proceeded disturbs me. I cannot see how a dismissive tone, name-calling, implications or accusations of ignorance and incompetence, and the like can possibly advance the cause of science. In my experience, this kind of discussion just makes people mad, and when they get mad, they stop thinking, and they have trouble hearing what the person who is making them mad is saying. And in my experience, there IS a very real risk that talented people can be driven away from a field in which they had been doing valuable work — just to be clear, I’m not talking about myself here, I am quite active.

    I do not know who in this discussion is getting money from me, i.e. receiving public funds in the form of a salary at a public university or research grants from the federal government or the military, but I find the idea that perhaps people I am paying to think about very important things are calling each other names like this disturbing in the extreme.

    As for the specific issue of anonymity, as we all know, one critical foundation for the success of science is open discussion and the freedom of information. Take the anonymous critics here. How I am to know how their credentials compare with Lisi’s or Smolin’s? To the extent that I am a peer in the field, of course, I can simply review the arguments, but to the extent that I need to rely on an expert’s judgment, suddenly I am in the dark here. This is not scientific. Mr. X can’t just say “I’m an expert,” that means nothing whatsoever.

    I will continue to follow this discussion and other physics research with interest.

    Best regards,
    Michael Gogins

  8. Can you imagine seeing transcripts of your heros acting like this? Would they be your heros if they had?

    Dude, the remarks on the internet about Lisi’s theory have been kind compared to what famous physicists of the previous few generations would have said.

  9. Quick comment, almost despite myself, in response to Bee and others. When the technical case is so clear cut as the one Jacques presents, it is difficult not to regard complaints about the “tone” and similar issues as simply a rhetorical strategy. It is disheartening to observe time and again how efficient it is.

  10. Scott,

    I fear that some of our heros in physics and mathematics are known to have engaged in less than edifying behavior in discussions, although they’re still our heros. I just finished reading (and writing about on my blog), an excellent book by Peter Freund that tells about some such episodes. But, except for a small number of extreme cases involving borderline mental illness, in the past professional mathematicians and physicists have had enough sense to avoid such behavior in print in public. They were not exposed to the temptation of anonymous comments on internet forums, it’s a bit scary to think about how they might have responded to this challenge…

  11. Moshe,

    I assure you that this is not a rhetorical strategy on my part, since I’m no fan of the idea of trying to fit everything into E8 multiplets.

    But I really think string theorists like yourself should, instead of attacking me and Lee for pointing out a problem, give some thought to how much damage your own partisans (anonymous and not) are doing to your own interests. I think the commenters above reflect accurately the perception of people reading these exchanges who don’t know the technicalities, and, no matter what Lee or I have to say, the impression they take away from observing the behavior of string theory partisans is what it is.

    In this particular case, you should also be aware that the discussion has drawn the attention not just of the public, but of some parts of the math community that are expert in these issues. It’s not just the public that is coming away with the impression that there’s something quite odd about how string theorists choose to engage in scientific discussion.

  12. I must say that I am perplexed by this discussion. If the parity mismatch does not shoot down Garrett’s theory, how can one ever hope to make any kind of progress? Even if arrogance is not something to strive for and can hurt your career (just look at LM), at the end of the day it is more important to be right than to be polite.

    At some point, one must accept the obvious: putting fermions and bosons into the same multiplet of a bosonic algebra is plain wrong, the Helling-Policastro oscillator disproves LQG, the anthropic landscape proves that string theory is unable to say anything definite about our universe, and the non-discovery of SUSY and extra-dimensions at the LHC will (if it happens) disprove the scientific part of string theory.

  13. Wow! The complete triumph of form over substance.

    The postmodernists who were burned by the “Sokal Hoax” would be very pleased by this discussion, where zero interest is evinced in the truth-value of any statements that have been made about Lisi’s theory; it’s all about their provenance and their “tone.”

    Still, standing in the middle of the food-fight, Lee Smolin (#130) had some substantive questions. Let me briefly interject some physics by answering them:

    It’s called thoroughness. Even though the particular real form of D_4xD_4, chosen by Lisi, does not embed in any real form of E_8, there are other real forms of D_4xD_4 which do. So a thorough analysis would study those other real forms as well, to see what one can obtain with them.

    That is what I did (I fact, I looked at what you get for all five cases where G can be embedded as a subgroup, though I only reported the result for the two “Pati-Salam”-like cases.

    [W]hat property does a representation of G have to have so that it gives rise, after spontaneous symmetry breaking, to spacetime spinors which are chiral in Y?

    In a nutshell, if you look at the piece of the adjoint representation that transforms as a “2” (as opposed to a “2bar”) of SL(2,C), then that should be a complex representation of SU(3)xSU(2)xU(1). Ideally, it should contain 3 copies of the (3,2)_{1/6}+(3bar,1)_{1/3}+(3bar,1)_{-2/3} +(1,2)_{-1/2}+(1,1)_1.

    See here for an argument that applies quite generally to the “Euclidean” (compact real form) case of any group (not just E_8). It is almost, but not quite a proof for the Minkowskian (noncompact real form) case. There are some potential loopholes there.

  14. H-I-G-G-S, for me it doesn’t a matter who you are, but I am curious to know whether you exist (I am not sure that it is defined as natural in this environment).

    Regards, Dany.

  15. Yikes! That didn’t seem to work. Let me try that again. (#$%@ lack of a “preview”!)

    I find the mixing of these two issues confusing. In particular, if Distler is making the first claim, why is it at all necessary to bring up the issue of chiral fermion reps?

    It’s called thoroughness. Even though the particular real form of D_4xD_4, chosen by Lisi, does not embed in any real form of E_8, there are other real forms of D_4xD_4 which do. So a thorough analysis would study those other real forms as well, to see what one can obtain with them.

    That is what I did (I fact, I looked at what you get for all five cases where G can be embedded as a subgroup, though I only reported the result for the two “Pati-Salam”-like cases.

    [W]hat property does a representation of G have to have so that it gives rise, after spontaneous symmetry breaking, to spacetime spinors which are chiral in Y?

    In a nutshell, if you look at the piece of the adjoint representation that transforms as a “2” (as opposed to a “2bar”) of SL(2,C), then that should be a complex representation of SU(3)xSU(2)xU(1). Ideally, it should contain 3 copies of the (3,2)_{1/6}+(3bar,1)_{1/3}+(3bar,1)_{-2/3} +(1,2)_{-1/2}+(1,1)_1.

  16. Jacques,

    Thanks re the first. Re the second, yes, I knew that, the question is, is there some general property of a rep of G that guarantees that or for which this is never the case? Can it ever be true for a real rep?

    Let me add a third question, is the issue of embedding of Lie algebras-leaving the fermion question aside-clear for the euclidean case? That is does SO(4) + SU(3)+ SU(2) + SU(2) + U(1) embedd in the real form of the lie algebra of E8, using the decomposition suggested by Lisi? Is there any sense in which the lie algebra SL(2,C) + SU(3)+ SU(2) + SU(2) + U(1) fits in a complexification of the lie algebra E8?

    Finally, what is the best reference to understand why there are only these two non-compact forms of E8 and where the results you quote come from? At the level of the lie algebra it would seem there might be more freedom. Is it easy to say why there is not?

    Thanks,

    Lee

  17. is there some general property of a rep of G that guarantees that or for which this is never the case? Can it ever be true for a real rep?

    See here for an argument that applies quite generally to the “Euclidean” (compact real form) case of any group (not just E_8). It is almost, but not quite a proof for the Minkowskian (noncompact real form) case. There are some potential loopholes there. (At least, they seem like potential loopholes to me; someone who knew more about the representation theory involved could probably complete the proof pretty quickly.)

    Finally, what is the best reference to understand why there are only these two non-compact forms of E8 and where the results you quote come from?

    See the article by Marcel Berger that I linked to in my post. To define a noncompact real form, you need an involution of the Lie algebra that acts as +1 on the compact generators, and as -1 on the noncompact generators. Such an involution also defines a symmetric space structure, and Berger classified those.

  18. Actually, to find the noncompact real forms, you need to classify Riemannian symmetric spaces. That classification long predates Berger’s paper.

    See the textbook by Helgason.

  19. Prof. Distler, as an interested observer I assure you that what interest I do have in the “tone” of this discussion is secondary to that I have in seeing the discussion continue to its resolution and the resulting understanding I will gain of the truth values of the various claims that have been made. In that regard, I (and I’m sure all of the other readers here) thank you for helping return the discussion to the technical issue at hand.

    The problem with “tone” is a real one, in that it 1) worsens the signal/noise ratio and 2) might cause a premature end to the discussion. So, while I think tone does matter, it is a means to an end rather than the end itself.

    It’s true that I have also gathered a great deal of data here about who I would and would not like to have a beer with or take a class from, were I in a position to do either of those things, but that’s completely irrelevant to the matter under discussion.

  20. Tyler,

    In 2000, it was the opinion of an overwhelming majority of people that, of the two Presidential candidates, George W Bush was the one with whom it would be more fun to have a beer.

    Seven years later, it is clear to an overwhelming majority that that was a lousy criterion for choosing a President.

    Speaking personally, I think (and thought) that I’d have a much more enjoyable time chatting over some beers with Al Gore. But I acknowledge that people’s tastes in drinking partners might vary.

  21. Jacques,

    I, like you, disagreed with the majority of Americans about both “liking” GWB and the relevance of such a judgment as a valid selection criterion. Unfortunately, the committee was against me, and our nation as a whole decided to go ahead and perform the experiment. Now the data are in, and the likability-over-competence theory of presidential selection has been ruled out, though sadly at great cost.

    Stripped of polite phrasing, the real meaning of my post was “thank goodness the shouting has died down and the debate has resumed, I was afraid a fascinating thread would drown in noise.” The social construction of language is so obvious as to be beyond learned debate at this point; the social construction of science is a ludicrous, discredited fallacy. So meta-arguments about the form of scientific debate are only valid to the degree that they further or hinder that debate.

    I am simply pleased to see that the discussion has continued, here in this forum where I can observe it, and wanted you to know that at least some (or one) of the non-professional interested observers are not taking their eye off the ball, as it were, since you seemed concerned that the actual point of the thread had been lost.

  22. @Moshe #135 I’d hope any discussion about the “tone” and similar issues
    would just be unnecessary. It certainly wasn’t my intention to distract from
    the technical argumentation with a ‘rhetorical strategy’. My comment #100
    was
    me getting upset about an earlier comment that essentially said if you have
    a technical argument you’re free to insult others because scientists have to
    stand above such human weaknesses. I tried to explain that this kind of
    reasoning drives away many people who happen to be human, and drives others
    into depression – therefore I don’t think one should tolerate this.
    Otherwise we might maybe consider PG-rating comment sections. Or to put it
    differently, this blog has about 10,000 readers a day, many of which are
    grad students who’ll be about to make up their mind some time soon which
    area they want to work in.

    @Michael #133

    “I don’t think it’s anonymity that tempts people to misbehave, but simply
    being online typing in a room instead of being face to face with one’s
    interlocutors.”

    You might be interested in this, and
    this
    .

    Best,

    B.

  23. Dear Jacques,

    Now, please straighten me out on the following: Following your post, the Pati-Salam fermions are in a rep given by

    R_ps = (2,r) +(2-bar, r-bar)

    where these refer to their transformation properties under the sum of the spacetime lorentz algebra so(3,1) and H, where H is the Pati-Salam algebra

    H=su(4)+ su(2)+su(2)

    And r = (4,2,1)+(4-bar,1,2)

    Now we established before that r is not equivalent to its complex conjugate, so R_ps is in the standard terms chiral. It is also the case that parity takes R_ps to itself. Now, R_ps is also pseudo-real, ie it is equivalent to its complex conjugate, as it is the sum of itself and its complex conjugate. So suppose there were a bigger lie algebra G that contained so(,1)+H as a subalgebra. Could not R_ps arise from the decomposition of a pseudo-real representation of G?

    Thanks,

    Lee

  24. Bee, I agree with you on the general issue, but like everything else it all depends on the context. So many of the online discussions degenerate almost immediately to discussions of etiquette, I guess that is one topic everyone feels they can comment on. This of course relies on the assumption that you can make such judgments without basic understanding of the context, based on “tone” alone. Personally I find this assumption completely absurd.

Comments are closed.

Scroll to Top