It’s been unusually long since my last posting, with the main reasons being that
Garrett Lisi has a new paper on the arXiv, with the rather over-the-top title of An Exceptionally Simple Theory of Everything. Sabine Hossenfelder has a typically excellent posting about the paper, and Garrett has been discussing his work with people in the comment section there. Lubos Motl, has a typically, how shall I say, Lubosian posting on the topic.
I’m the first person thanked in the acknowledgment section of the paper, but at Sabine’s blog Garrett explains that this is just because he is using reverse alphabetical order. I’ve corresponded with him in the past about his research in this area, without being able to provide any real help other than a certain amount of encouragement. Two of the ideas he is pursuing are general ones I’m also very fond of. One is well-known, and many people have also tried this, it’s the idea of bringing together the internal gauge symmetry and the symmetry of local frame rotations. The problems with this are also well-known, and some have been brought up by the commenters at Sabine’s blog. I don’t think Garrett has found the answer to this, or that he claims to. I’m still hopeful that this line of thinking will lead somewhere, but think some dramatically different new idea about this is still needed. The other idea he likes is that of trying to interpret the fermionic degrees of freedom of the BRST method for handling gauge invariance as providing the fermions of the Standard Model. I suspect there is something to this, but to get anywhere with it, a much deeper understanding of BRST will be required. I’ve been spending a lot of time trying to understand some of the mathematics related to BRST in recent years, and am in the middle of writing some of this up. It seems to me that there is a lot that is not understood yet about this topic even in much simpler lower-dimensional contexts, so we’re a long way from being able to really see whether something can be done with this idea in a realistic four-dimensional setting.
One idea Garrett is fond of that has generally left me cold is the idea of unification via a large simple Lie algebra like E8. While there may be some sort of ultimate truth to this, the problem is that, just as for GUTs and for superstring models, all you’re doing when you do this is changing the unification problem into the problem of what breaks the large symmetry. This change in the problem adds some new structure to it, but just doesn’t seem to help very much, with the bottom line being that you get few if any testable predictions out of it (one exception is with the simplest GUTs, where you do get a prediction, proton decay, which turns out to be wrong, falsifying the models).
Anyway, I’m glad to see someone pursuing these ideas, even if they haven’t come up with solutions to the underlying problems. Garrett is a serious and competent researcher who has pursued a non-traditional career path, and was recently awarded a grant to by the FQXI organization. You can read more about him in an article on their web-site.
Unfortunately, some of the reaction to Garrett’s article has been depressing. A commenter who sounds well-informed but hides behind anonymity goes on about “this nonsense” (although Garrett’s polite reaction to him/her did lead to a more sensible discussion). Early on in my experience with blogs I believed that no serious professional in particle physics would attack someone and try and carry on a scientific argument anonymously, so any such comments had to be coming from misguided students, or someone not in the profession. Unfortunately I’ve all too often seen evidence that I was wrong about this. Lubos Motl on his blog denounced the fact that Garrett’s paper appeared in the hep-th section of the arXiv, then later wrote in to Sabine’s blog to crow that it had been removed from hep-th. As always with the arXiv, how moderation occurs there is non-transparent, so I don’t know how or why this happened. My own experience with the arXiv over trackbacks to hep-th has been a highly disturbing one. The current hep-th policy seems to be to allow any sort of nonsense to be posted there if it fits into the current string-theory-based ideology (see for example here), while suppressing any criticism of this. A paranoid person might be tempted to wonder whether hep-th is being moderated by someone so ideological and petty that criticism of string theory or including string theory critics in an acknowledgment section would be cause for having ones article removed from hep-th…
Update: I hear from Garrett that the story of this paper at the arXiv is that it was submitted to gr-qc, not hep-th. Before it was posted, it was re-classified as hep-th, and appeared there. Later on (after the appearance of Lubos’s blog entry denouncing the arXiv for allowing the paper on hep-th I believe), it was re-classified again, this time as general physics (with cross-listing to hep-th).
Update: Latest news about this is that the paper has now been reclassified again, to the perfectly appropriate hep-th, cross-listed as gr-qc, although no one seems to know why this happened. Another continuing mystery is the trackback situation: there are four trackbacks to the paper, to postings by Lubos, Bee, and to Physics Forums, as well as to an old TWF from John Baez that doesn’t even link to the paper. My postings still seem to be non-trackback worthy on hep-th, not that I can argue with this particular case, since the discussion elsewhere has been more substantive (except for Lubos’s, which is valuable for the way it accurately represents the hysterical reaction to speculation that is not string theory speculation all too common in certain quarters).
Update: Garrett is making the news here. Whether this is a good thing is yet another question for debate on the next thread, I guess. A lot of the attraction for the media seems to be his personal story. Maybe it’s a good thing for physics for people to see that one can be a theoretical physicist while surfing in Hawaii…
Update: Lisi-mania spreads. See stories in New Scientist, the Ottawa Citizen, Slashdot, and probably lots of other places I haven’t noticed.
Update: Steinn Sigurdsson has an excellent posting summarizing the situation. As usual, blogs are the place to get the highest quality information about scientific issues…
Update: I’ve given up on keeping track of the media stories on this. For some discussion of the representation theory involved, see this posting by Jacques Distler, and comments from Garrett.
Update: The Angry Physicist examines the Distler critique in some detail.
Eric:”Just curious why noone has brought up the work of Jacob Bourjaily with geometric engineering three-family GUTs from E8? It seems to me to be somewhat higher quality work than that of Lisi.”
Lubos blogged about it but the press did not pick up on that. Maybe that’s because Jake is still a grad student and not a surfer with a Ph. D. :).
He does get exactly three families from a single E8 and his paper is much easier to read.
Curiously, he automatically gets three generations of Higgs doublets which is an interesting prediction. The symmetry breaking is geometric, described pretty explicitely by five complex parameters.
There is a very nice table on page 6 of his paper where the explicit spectrum is given. The title of Bourjaily’s paper is more humble as he does not claim to have a “theory of everything”, so maybe that’s another reason why Bee and others decided not to blog about his work 🙂
Thanks for the long and thoughtful response.
I read Lisi’s response to Distler. I don’t think Lisi is lying (and I said nothing about his being a fame whore). He has been very straightforward in his responses to Distler. I think the problem is more one of inexperience and a lack of critical judgement. It is not considered good form to make dramatic claims at the beginning of a paper (i.e. that all standard model particles fit into E8) and then only on page 22 point out that this is not really correct. You say Lisi “anticipated” this problem. I would say he was aware of it, and tried to solve it, but his solution (involving triality) didn’t work. If you want to know why, please read Distler’s blog.
It’s probably time to drop this topic. No use beating a dead horse. Unless of course Lee decides to write in and tell us all why he thought this theory was so “fabulous.” That would be entertaining, to say the least.
Watching the hostility and contempt heaped upon Garrett Lisi by the physics establishment has been an ugly spectacle, but hardly a shocking one. And he is right that his idea is a beautiful; I wish him every success in winning converts from among all the bright people futilely beavering away at string theory. But while his idea is beautiful he himself is also to be admired–an Overman of sorts. His battle with the string theorists–a herd of Last Men–reminds me of Nietzsche’s Zarathustra:
Give us this Last Man, O Zarathustra,” — they called out — “make us into these Last Men! Then will we make you a gift of the Overman!” And all the people exulted and smacked their lips. Zarathustra, however, turned sad, and said to his heart:
They do not understand me: I am not the mouth for these ears.
Perhaps I have lived too long in the mountains; I have hearkened too much to the brooks and trees: now I speak to them as to the goatherds.
My soul is calm and clear, like the mountains in the morning. But they think I am cold, and a mocker with terrible jests.
Now they look at me and laugh: and while they laugh they hate me too. There is ice in their laughter.
* * *
Long slept Zarathustra; and not only the rosy dawn passed over his head, but also the morning. At last, however, his eyes opened, and amazedly he gazed into the forest and the stillness, amazedly he gazed into himself. Then he arose quickly, like a seafarer who all at once sees the land; and he shouted for joy: for he saw a new truth. And he spoke thus to his heart:
A light has dawned upon me: I need companions — living ones; not dead companions and corpses, which I carry with me wherever I go.
But I need living companions, who will follow me because they want to follow themselves — and to the place where I will. A light has dawned upon me. Zarathustra is not to speak to the people, but to companions! Zarathustra will not be shepherd and hound of the herd!
To steal many from the herd — for that purpose I have come. The people and the herd will be angry with me: the shepherds shall call Zarathustra a robber.
Shepherds, I say, but they call themselves the good and just. Shepherds, I say, but they call themselves the believers in the orthodox faith.
Behold the good and just! Whom do they hate most? The man who breaks their tablets of values, the breaker, the lawbreaker: — yet he is the creator.
Behold the believers of all faiths! Whom do they hate most? The man who breaks up their tablets of values, the breaker, the law-breaker — yet he is the creator.
The creator seeks companions, not corpses — and not herds or believers either. The creator seeks fellow-creators — those who grave new values on new law-tablets.
The creator seeks companions and fellow-reapers: for everything is ripe for the harvest with him. But he lacks the hundred sickles: so he plucks the ears of corn and is vexed.
The creator seeks companions, and such as know how to whet their sickles. They will be called destroyers, and despisers of good and evil. But they are the reapers and rejoicers.
Zarathustra seeks fellow-creators, fellow-reapers and fellow-rejoicers: what are herds and shepherds and corpses to him! …
I will sing my song to the lonesome and to the twosome; and to whoever who still has ears for the unheard, I will make his heart heavy with my happiness.
I make for my goal, I follow my course; over the loitering and tardy I will leap. Thus let my on-going be their down-going!
Eliza, the initial criticisms have been borne out. You are not doing the guy any favors with your cut-and-paste.
“Better to know nothing than to half-know many things! Better to be a fool on your own account than a wise man in someone else’s eyes!”
Mitchell, I don’t think it’s appropriate at this point to dismiss Lisi out of hand. Clearly his theory is in its infancy; there is a great deal of work to do; and as long as he is working toward falsifiability, sensible people should reserve judgment.
And my primary object is not to do favors for Garrett Lisi. What brought the passage to mind was the hysterical vituperation of people like Lubos Motl who have attacked Garrett with the zeal of religious fanatics.
And it’s interesting that you cast yourself in the role of the trodden one. You must have a very narrow window on the world of knowledge, for the man goes on to expand and extend his remarks:
“That, however, of which I am master and knower, is the brain of the leech:- that is my world!
How long have I investigated this one thing, the brain of the leech, so that here the slippery truth might no longer slip from me! Here is my domain!…
For the sake of this did I cast everything else aside, for the sake of this did everything else become indifferent to me; and close beside my knowledge lies my black ignorance.”
Moving on, anyone who thinks that Lisi’s publicity is “bad for physics” is grasping the wrong end of the stick. I think we can all agree that if he is right, Lisi will be a celebrity, and money will be flung at researchers from all directions for many years to come. There’ll be tearing up the county building particle accelerators.
If his theory fails? There will be very little mention of it in the popular press. “Surfer Dude’s Theory of Everything Proven Wrong”: That’s a dog-bites-man story, not big news. But even if it is reported, the public is sophisticated enough to understand that falsified theories are still valuable: they tell us what the answer is not. Even a child can understand that.
Most absurdly, someone has suggested that if Lisi fails to deliver after all the positive press coverage, the public will then lose faith in physics research. Baloney. Decade after decade string theorists give us nothing but fodder for sci-fi novels; and yet, thirty years on, every time they pass around the begging bowl the taxpayers obligingly fill it up. And the beauty of it is that they make no falsifiable predictions that can be tested, so they can carry on the flimflam until someone like Lisi comes along and reminds everybody what the meaning of a genuine scientific theory is. That’s the real threat he poses.
The truth is that people don’t expect a whole lot of progress from the physics community. They don’t even mind the somewhat parasitic nature of the relationship. What they do want for their money is evidence of activity, a sense that scientists are enthusiastically working as hard as they can to move the ball down the field. Whether Lisi’s theory soars or flops, he’s given people a sense that physics deserves to be funded. We should all be grateful for that, even you, master of leeches.
If only I was a master of Leech-branes!
I am only self-half-educated in these matters. But after its trial by fire, it seems clear that Lisi’s theory has two big holes, generation structure and quantization, which would have to be fixed before one could ever set about “calculating the masses”. Lubos Motl was right about this and that should be respected.
You do not give me the impression that you have actually done research in theoretical particle physics. If you had, you would know that group theory is the easy bit. If it is a question of fitting all the known particles into representations of groups then it can be done in a much simpler way than Lisi’s. SU(5), the simplest unifying scheme, accommodates all the known particles neatly, the only problems – at least in representation theory terms – being that it predicts extra unobserved gauge particles and does not include gravity. Lisi’s model is not a GUT, but the classification of particles in representations of a gauge group would appear to proceed in much the same way. But this group symmetry can only be approximate – the particles in each group representation have widely different masses in the real world, meaning that the symmetry can only be approximate and it is in the – currently – arbitrary and ugly breaking of the symmetry that most HEP theorists will quail (or, at least, ought to). I would be much more interested in researches that address this more difficult, and yet more important issue.
Eliza: “Moving on, anyone who thinks that Lisi’s publicity is “bad for physics” is grasping the wrong end of the stick. […] Most absurdly, someone has suggested that if Lisi fails to deliver after all the positive press coverage, the public will then lose faith in physics research.”
It wouldn’t have been my choice of words, so it probably wasn’t me who you are referring to, but let me comment on that anyhow. Its not specifically about Lisi, but generally there are three problems with such reporting.
For one, such reports are simply inaccurate and cause confusion that was avoidable. The world is already confusing enough, why do we have to make people believe a giant Mandela explains the elementary particles, or we’ve found another universe, if we can’t be sure of it. And if we are not, can’t we at least expect it to be reported on with an appropriate amount of caution, clarifying the amount of speculation?
Second, as it is, the public opinion about our research matters. One aspect of this is what you dismiss, namely that if this happens more often they will start wondering what kind of science it is that we do anyhow. Is is good for something? Science or Religion? Fact or Fiction? I mean, look, theoretical physicists DO already have a hard time getting funding because it’s not immediately apparent what our work might be good for. Prematurely spreading reports of fabolous successes that then end up in the category ‘what ever happened to’ won’t help. What is maybe worse is that the way Garrett’s story was sold it says hey, the surfer dude can do it, who needs all these overpaid professors? You should have seen the amount of ‘Theories of Everything’ that I got send since that thing hit the headlines.
Third, such reporting influences the discussions and the opinion making process in our community. If you deny that, you are hopelessly naive. It’s the topic of the week, it’s what people talk about on the corridor. How many grad studs are out there, who are now dreaming of pulling off a similar show?
I find these trends very worrisome.
Eliza:” anyone who thinks that Lisi’s publicity is “bad for physics” is grasping the wrong end of the stick”.
AGL et al did a great job; not in the theoretical physics but for the theoretical physics. I think he deserves a prize and I would be pleased to see him laughing all his way to the bank.
>>> BEE: How many grad studs are out there, who are now dreaming of pulling off a similar show?
Ha! I am a PhD candidate (not physics), I don’t know any of us that can be characterized as “studs”. But the story is certainly corridor-worthy, and who doesn’t dream of having some revolutionary insight into the workings of our field? I know 99% of papers are incremental (or no) progress, but I actually think that “hero” stories like this are good for us grad students, no matter if Lisi turns out to be prince or goat. Chances are worth taking and original ideas really can revolutionize a field. My advisor revolutionized his field about 12 years ago. This kind of stuff is inspiring. If I thought my career would be a long series of incremental progress and survey papers, I’d leave for industry tomorrow. And, at the risk of being chastised by HIGGS, doesn’t Lisi at least contribute a clever way of sidestepping Coleman-Mandula?
Sure, we all dream of having revolutionary insights. That’s not the point I was trying to make. The question is what is more relevant: having revolutionary insights. Or making everybody believe you have revolutionary insights? Sorry about the ‘studs’, I must have picked it up somewhere, I didn’t mean it in a dismissive way.
The comment section on this blog is becoming something I mostly don’t want to read anymore, and I’m assuming that may also be the case for many other people. Please stop submitting off-topic, irrelevant, mis-informed, poorly thought-out, etc. comments. This is not a place to write in with whatever comes into your head. From now on I’ll be deleting many more comments that aren’t substantive and informative.
I won’t chastise you, but the answer to your question about whether Lisi has contributed a clever way of side-stepping Coleman-Mandula is “no.”
Lisi himself does not make this claim. On his web site
http://deferentialgeometry.org/ you will find a set of slides from talks he has given. At the bottom are extra slides including one labelled Coleman-Mandula. On that slide he says
“E8 Theory does not allow a subgroup locally isomorphic to the Poincaré group. The S matrix exists as an approximation, in which the theorem is satisfied.” What this means in plain english, and in terms of physics, is actually explained quite clearly on Lubos Motl’s post on this if you can ignore the ranting. Briefly, in a theory with a cosmological constant there is no S-matrix. Coleman-Mandula is a theorem about symmetries of the S-matrix. So, no S-matrix, no theorem. But this fact is only relevant if you are doing scattering experiments on scales the size of the universe. At Fermilab, or the LHC or in any conceivable experiment you can treat space as flat to an extremely good precision. There is then an S-matrix that experimentalists measure. It obeys the Coleman-Mandula theorem. Lisi does not provide an exception.
The above is on topic, but this comment is slightly off topic. I hope that pissed you off because your last “update” on this topic pissed me off. The link provides a “sociological” critique of Distler’s analysis, not a mathematical or physical one. You might mention that, you know, just for clarity and fairness and to show you are such a mensch. Distler can be condescending and bristly, but he got the math and the physics right. You didn’t, and neither did Lisi. And anyway, compared to Pauli, the author of the quote that provides the title of your blog, Distler is a pussycat. Maybe you should start criticizing Pauli for being such a jerk. Or maybe you see that criticizing Distler for being difficult while wanting to model your skepticism after that of Pauli’s is exhibiting just a wee bit of hypocrisy.
First of all, I don’t model myself in any way after Wolfgang Pauli. I’m just borrowing his phrase.
I linked to Distler’s posting because, yes, he did have a worthwhile discussion of some of the group theory involved. The fact that Garrett responded to this intelligently and politely led to an exchange that was valuable for anyone to read who wanted to understand what is going on in Garrett’s paper.
I also think though that the “sociological” discussion is highly relevant. There is absolutely no reason for Distler to behave in the juvenile way that he does. He’s an adult, middle-aged man and should behave like a grown-up and like a professional. If he doesn’t understand this, others need to point this out to him.
If you don’t think this is a problem, that his behavior is acceptable, and mine is what you want to criticize from behind anonymity, that’s your choice. I have no idea who you are: for all I know you’re a high school student too young to understand what mature behavior is. If you’re actually an adult professional though, and you are in the field of string theory/particle theory, you might want to consider what effect he and Lubos are having on the perception of people in that field by outsiders. Smolin got a lot of criticism for some of the comments in his book about the behavioral characteristics of some theorists (I avoided this topic in mine), but Jacques and Lubos make it look as if he was far too kind.
Go back and read carefully the posting I linked to. The person who wrote it I think does a good job of describing what this looks like to outsiders. They can’t understand the group theory, but they can understand the significance of this kind of juvenile behavior.
People who have scientific arguments talk about science.
People who don’t have scientific arguments talk about good manners.
You decide who between Distler and Woit/AngryPhys falls in which category.
..I still have to correct my above remark concerning the ‘non-product’ structure of the embedding discussed, this of course applies only to the ‘triality’-part of the embedding. From my point of view, at least by inspecting the triality-part of F4 and its specific Lie-Algebra-structure (see Baez’ week 90) a given connection on E8 should reduce to any of the obvious ‘subgroups’ R in the triality part, given the E8-bundle reduces to them, but this should depend on the base manifold, imposing a condition (allowing sections in a E8/R-bundle). My hypothesis, of course, is that these facts are at least necessary to get ‘predictions’.
Public Radio International’s The World did a story tonight on Garrett Lisi’s work. It includes an interview with Marcus du Sautoy (Oxford).
Hi Garrett, just wondering, was the fact that the E8 structure was just recently solved earlier this year by mathematicians in any way related to the decision to use it as your model here? What I’m asking was if the E8 mathematics hadn’t been solved earlier, would you still be able to come up with this physics theory?
The mathematical result earlier this year about E8 has nothing to do with the way Garrett is using it, they’re two quite different things.
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Hi Peter, thanks for clearing that up for me. I was a little curious, considering how coincidental the two announcements to do with E8 were with each other (i.e. well within a year of each other).
On another note, I was in the middle of reading your book Not Even Wrong, when this story broke. So I stopped reading the book to see what all the E8 hubbub was about. Ironically, when I got back to the bookmarked chapter, I found you were talking about some of the BRST and Coleman-Mandula theorems that are considered controversial about this theory. Just love these ironies and coincidences.
Lee Smolin has a new paper (arxiv:0712.0977) on Lisi-like theories in which he says:
“We close the introduction by noting that the well-known Coleman-Mandula no-go theorem is avoided because that only applies to an S-Matrix whose symmetries include global Poincare invariance. This theory, like general relativity, has no global symmetries, the Poincare symmetry acts only on the ground state not the action, and only in the limit in which the cosmological constant is zero. In fact, there is a nonzero cosmological constant, as it is related to parameters of the theory. By the time the S matrix in Minkowski spacetime could be defined in this theory one will be studying only small perturbations of a ground state in a certain limit and the symmetry will only apply in that limit and approximation. As we shall see below, the symmetry will already be broken by the time that approximation and limit are defined, in such a way that Coleman-Mandula theorem could be satisfied in its domain of applicability.”
It has already been observed in a number of places that the Coleman-Mandula theorem has generalizations, and so one should not expect a slight deviation from Poincare symmetry to make much difference. It also seems to be true that the action actually advanced in Garrett’s paper can be quantized without a problem, because most of the notional E8 symmetry is broken by hand, and the actual, residual symmetry is something far more mundane. This remark by Lee Smolin seems to segue between both of these ‘reasons why Coleman-Mandula doesn’t apply’: we start out with the claim that global features make CM irrelevant, and then we are told that by the time we can actually calculate something, the symmetry will have been broken to harmlessness anyway. Call these the ‘argument from global properties’ and the ‘argument from de facto symmetry breaking’.
My questions –
Is the argument from global properties (that CM is irrelevant to a certain class of theories, that a novel loophole exists) valid or not?
Is there any logical connection between that argument and the argument from de facto symmetry breaking?
I intend to go away and try to answer these questions for myself, but I know there are far more knowledgeable people reading.
It will be interesting to see what Motl and Distler will make out of Smolin’s paper. I bet they will be unimpressed.
Without being up to date about the fine print of the CM theorem, I am very suspicious of the idea that a bosonic operator can change a fermionic state into a bosonic one or vice versa. This seems to be the case with Lisi’s paper, if he puts bosons and fermions into the same multiplet of a bosonic Lie group.
Can a theory of everything be “exceptionally simple”?
The paper’s title is a pun on the mathematical nomenclature; E8 is an “exceptional” “simple” group, simple meaning that it lacks a certain type of internal structure, and exceptional meaning that it’s one of a handful of simple groups which fall outside the infinite families to which all the others belong. I suppose it’s also a reference to the unified theories of recent decades; Lisi wants to do without unverified innovations like supersymmetry and extra dimensions.
A theory of everything can be simple, so long as its implications are sufficiently complex. Since most things that exist are regarded as already explained by existing physics, for most physicists the attempt to explain “everything” reduces to explaining, or at least completing, the existing fundamental theories. Everything else is just applied science and historical contingency.
Thank you Mitchell for your answer! It’s a very clear explanation.