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.
Dear Lee,
Perhaps it would be best if we retreated, for a moment, to the “euclidean” case, where we are embedding Spin(4), instead of SL(2,C). Then
R = (2,1, r) + (1,2, rbar)
which is still complex, if r is a complex representation of H.
In any case, Lisi’s game (interpreted most broadly) is to embed things in the adjoint representation of some real form of some Lie group. That is always a real representation.
P.S.: If you really want to have a technical discussion, with equations, ‘n such, you might consider moving things to my blog, where the software is suited to the task of facilitating such discussions.
Jacques,
But in the lorentzian case where complex conjugation exchanges the left and right factors,
R_ps = (2,1, r) + (1,2, rbar)
of SU(2)_L+SU(2)_R+H
is equivalent to its complex conjute.
Thanks,
Lee
Hi Moshe,
Yes, I agree, that’s not constructive either. Since it’s going nicely I’ll shut up now and leave the discussion to the experts (I’ve had trouble commenting, so Sean put in my previous comment with some delay. Hope it works now.) Best,
B.
Lee,
That’s the point! A priori, in the Lorentzian case, R is a real (or pseudo real) representation. So you might think that you could get a chiral spectrum (a net number of copies of R). But, for any embedding of SL(2,C) in the noncompact real form, which is related by Wick rotation to an embedding of Spin(4) in the compact real form, this never happens. I have just explained to you why it never happens.
More broadly, there are other embeddings of SL(2,C) in the noncompact real form, not related by Wick rotation to embeddings of Spin(4) in the compact real form, which also necessarily yield a nonchiral spectrum. Specifically, I have looked at embeddings that proceed via SL(4,R) and via SU(2,2).
What I have not done is show that these are the only remaining possibilities. So there’s still a challenge outstanding, to any readers of my blog, to close that gap.
Hi B,
A good example of what I was proposing in the comment you refer to in your #148 is precisely what Lee and Jacques are doing at the moment; ignoring discussions of the form, insults or what not and actually having an interesting and relevant discussion about the physics. So I will also shut up (unless I get something relevant to say to the physics) and follow the discussion. 🙂
I wrote
But let me be very clear that this “potential loophole” is irrelevant to your paper, which concerned the Euclidean case (embedding Spin(4) in the compact real form of some Lie group), and to Lisi’s paper, which concerned an embedding via D_4xD_4.
Neither of these can ever lead to a chiral spectrum (let alone to 3 Standard Model generations).
And, with that said, I will apologize, again, for the interruption. Y’all can return to your previously-scheduled discussion of etiquette and anonymity, which I fear was prematurely squelched by this boring disquisition on group representation theory.
Woit says:
“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.”
Let me put a disclaimer first that I am not a string theorist. I am not qualified to comment on Distler’s although I have learnt quite a few things reading his comments here and at his blog. Peter Woit, for you everything is a game of impressions. You seem to see everything stringy versus anti stringy. Also, just because you wrote a anti stringy rant does not mean that you and Smolin are at the same side. It seems to me that whenever you are not able to comment on anything, you just hide your tails by sounding like voice of Smolin represents you. If attacked, you start manufacturing your disagreements with Smolin.
However, if something technical appears in any discussions, you start your rhetorical statements such as “I dont like …” But the real impression, I have gotten in the last couple of years is I have never seen you comment on ANYTHING non-trivial at ANY depth. The best thing that you do with is assorted links which I find useful. I really suggest that you(who have a voice) in these influential blog support yourself with robust arguments than redundant raving and ranting.
On the other hand, I have learnt a great deal by reading Distler, and to some extent Smolin in this whole TOE saga.
Sean, although it may not be the objective of this blog, I would suggest you to let the technical stuff flow(if that is not too much of a burden to the disk space). I am sure students like me find such discussions more valuable than unsubstantiated likes and dislike which seems to degenerate into really absurd discussions.
Woit,
you write on your blog: “Informed comments relevant to the posting are very welcome and strongly encouraged. Comments that just add noise and/or hostility are not.”
Do you think you are removing noise and/or posting informed comments here? I think you are doing just the opposite.
Ahem, getting back to the food fight after the brief physics interlude..
For a good example of why anonymity is neither a necessary or sufficient condition to be wonderful pricks to each other see for instance the recent exchange:
http://arxiv.org/abs/0712.2620v1 and preceding notes.
Comic value is high, but then such a thing is somewhat of an aged, acquired taste and requires a thick skin which I would have thought most physicists tend to develop sometime during undergraduate research =)
C’est la vie!
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Dear Lee,
You said “Thanks, what is frustrating for me is that you and others don’t credit progress to address points you raise when it happens.”
To me, the “progress” looks like putting lipstick on a pig. It’s not going to make it fly, nor make me want to embrace it.
H
I suppose one could have predicted that the response to pointing out that anonymous insults on physics blogs are a problem would be… anonymous insults.
I thank Jacques for the recent improvement in tone of the technical discussion with Lee, that’s great to see. Unfortunately there’s still the anonymous H-I-G-G-S, who I continue to believe would behave in a more professional way if his name was attached to his words.
No Peter, I’d make the same quip in person.
Glad I provided you with a way to participate in the discussion.
Dear Jacques,
I am not sure I understand your last point. Let me review. We have been discussing the situation encountered unifying the Pati-Slam gauge symmetry with the local lorentz transformations. This leads us to consider
R_ps = (2,r) +(2-bar, r-bar),
with r = (4,2,1)+(4-bar,1,2)
as described in my 149 above.
We have established 1) that r is chiral, in the sense that it is in a complex rep of the YM gauge symmetry that acts on left handed spinors, 2) that R_ps is parity invariant and 3) that R_ps is equivalent to its complex conjugate.
Thus, if there were a unification of gravity and Yang-Mills in terms of the connection of a larger G which has as a subalgebra local lorentz+H_ps, along the lines of Peldan, myself and others, R_ps could arise from the decomposition of a rep of G which is also equivalent to its complex conjugate.
Do I understand correctly that you agree with this but are arguing that in the particular case of if G=E8, R_ps cannot arise from decomposition of the adjoint of E8 ?
Note: the above is all assuming lorentzian signature. It is true that in my paper I worked with Euclidean signature, but only for simplicity.
Thanks,
Lee
Lee,
Try reading again what I wrote (not just here, but in the blog post I linked to).
If the embedding of SL(2,C) in the noncompact real form of G is related by Wick rotation to an embedding of Spin(4) in the compact real form of G, then R is nonchiral.
This has nothing to do with the specific choice G = E_8.
————————————————————
Since you are a physicist, I did not spell out what the phrase “related by Wick rotation” means. But perhaps I should not have made such presumptions.
So let me step back, and spell out precisely what the above phrase means.
For concision, I will phrase things in terms of embeddings of Lie algebras, instead of groups.
Let g_C be the complex Lie algebra, which has (at least) two real forms: a compact real form, g_e, appropriate to the Euclidean case, and a noncompact real form, g_l, appropriate to the Lorentzian case. Let h be the lie algebra of the SM or Pati-Salam, and h_C the corresponding complex Lie algebra (of which h is the compact real form).
We are interested in embeddings of
so(4) x h ? g_e
and
so(3,1) x h ? g_l
I say “these embeddings are related by Wick rotation” if they stem from the same embedding of complex lie algebras
d_2 x h_C ? g_C
by choosing different real forms.
Dear HIGGS,
huh? You made a list of criticisms which I responded to by explaining how some of them are solved or addressed in subsequent work. Your response is highly unprofessional, it has no content except a statement of your unwillingness to engage in a scientific discussion based on results in papers. So why should anyone take anything else you have to say seriously?
Don’t you understand that to be taken seriously a scientist who wants to criticize other scientist’s work must be professional and precise in their criticisms. The point is to convince other scientists to change their minds and to do this you must show your respect for them and you must reason with them. When you degenerate from reasoning with people to insutling them, you are behaving unprofessionally because you hurt both the processes and the reputation of science. It matters not the context in which you do this.
Thanks,
Lee
Oh boy, here we go again with smokescreen tactic that Woit/Smolin use whenever they’re losing an argument of accusing the other side of being impolite.
It is nice to see that physics has joined politics and religion as things people can’t talk about without emotion. I am put off by “spiky” and disrespectful because it takes some of the pleasure out of the conversation for me. But, we have to acknowledge that some enjoy it more that way. So, is it just a style? Even jerks become lovable if you know them long enough – they become “our” jerks. But, it is hard not to think that their spikiness comes from being egotistical, married to their positions, and jealous of other’s successes.
Lee–
What is frustrating to the rest of us is that you always declare that you are making progress without anything technically correct and concrete to back it up. Just because you say it or write a paper about it doesn’t mean any progress has been made. No one is convinced by your paper–relying on your previous mechanism for getting fermions that in turn made absolutely no sense doesn’t make anything any better. Unfortunately physics needs equations and ideas and not just pretty pictures and wishful thinking.
I think you have a lot of nerve to assume that people should take you seriously when you have demonstrated above that you don’t understand the most basic things about field theory–what the PS model is, what parity means, what chirality means, that you can’t get a chiral from spontaneous breakdown of a vector theory and so on. Maybe to journalists or anyone that doesn’t know technical details of physics, your discussion with Jacques looks like “healthy dialog”. But to those in the know it is a complete embarrasment. Jacques had to teach you things I’m sure he has taught for years in his beginning field theory courses. This has nothing to do with the esoteric details of E8, but with basic, elementary QFT.
And why isn’t Peter Woit, prophet of the importance of representation theory in physics, chiming in on the group-theoretical issues with Lisi’s proposal? Still too busy complaining about manners? All of you alternative physics people can never put your money where your mouth is when it comes to physics discussion. Impartial external observers should take away the obvious lesson from this…
Eric,
In this instance, I would quibble with your use of the present continuous tense.
Right now, all I see is foot-dragging.
Lee,
If the above argument isn’t clear to you, I invite you to try to construct a counter-example. I believe you will find the exercise revelatory.
If you have anything substantive to say, I invite you to comment on my blog.
Here, producing anything resembling equations is a pain-in-the-rear, and I fail to see the point of attempting to repeat stuff that is better-explained in my two blog posts.
This goose is cooked. Time to move on.
“What is frustrating to the rest of us (…)”
“No one is convinced (…)”
“I think you have a lot of nerve to assume that people should take you seriously”
Ah. So now an anonymous commenter thinks that he or she is entitled to represent the opinion of the “rest of us”.
“Impartial external observers should take away the obvious lesson from this…”
There is a lot to be learned, yes. I know what I am learning, thank you. But whatever your impressions, I hope this spectacle finds an end soon, so that the technical discussions can continue.
Geez Says,
“And why isn’t Peter Woit, prophet of the importance of representation theory in physics, chiming in on the group-theoretical issues with Lisi’s proposal? Still too busy complaining about manners?”
This is an excellent point. I think like Jacques says the goose is cooked and it is indeed time to move on.
Lee Smolin:” The point is to convince other scientists to change their minds and to do this you must show your respect for them and you must reason with them”.
Eventually you and Jacques Distler both not talking to us, your colleagues, but to the outsider journalists which don’t bother even to differentiate the physical theory from the hypothetical mathematical construct. There is no difference in the approach used by both “collectives” (it is quite new that the theoretical physics community is similar to kibbutz).
You choose, without motivation, some large “unification” group and through the sequence of hypothetical symmetry breakings go to the experimentally defined target U(2) which is the only existing minimal extension of the Maxwell’s U(1).
There is no need to insult each other. You are both wrong in your approach. “There is no royal road to geometry”, but these are not roads at all.
Regards, Dany.
P.S. And you both continue to confuse kids what and how to study the theoretical physics. The detailed knowledge of the huge classical as well as the exceptional group reps is irrelevant for the math-ph.
I’m sad to see that the noise has drowned out the signal.
Some people just don’t know when to stop talking about irrelevant things.
tyler,
I sympathise with your frustration, but speaking from the perspective of someone who earns his living doing theoretical physics I don’t think the signal was all that interesting anyway. (I’m not much of a group theory enthusiast.) It is only because of the “special circumstances” that this is being discussed here at all. Jacques himself wrote on his blog “I *really* wasn’t going to post about the Lisi paper…”, and there are certainly more interesting topics to discuss than this one.
On the other hand, the sociological aspects of all this are quite fascinating…