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.
Hello Peter,
This is a well thought out post, as usual. I did consider our short emails — and the very existence of you and this blog — encouraging enough to include you in the acknowledgments. Your concerns are all valid, and are some of the same concerns I discuss in the paper. Though I do think the way I’ve combined the gravitational frame-Higgs and used the MacDowell-Mansouri description of gravity is new. You are correct that I don’t have a good reason or mechanism for what breaks the E8 symmetry, and this is needed. What I’ve done is break the symmetry by hand, including the few terms necessary to recover the action of the standard model and gravity. I am biased towards E8 because of its beauty, and similarly towards the general idea of unification. The success of electroweak symmetry breaking in the standard model is compelling evidence that symmetry breaking of this sort plays a very important role in nature, and I’m surprised you dislike the idea of applying this on a larger scale. Surely you acknowledge that successful predictions from electroweak symmetry breaking indicate it did more than just add new structure to the problem? In any case, I am very much looking forward to reading your work on BRST, as it’s a very complicated and fascinating subject, and it plays an important role in this E8 theory that I’d like to understand better.
There is a good chance that Garrett is on a watchlist. I have it on good authority that I’m on the hep-th watchlist, even without having tried to post anything there for years.
Hi Garrett,
By “adding new structure” to the problem I meant to imply something not negative, but potentially positive. The new structure may be usable to constrain things and thus allow non-trivial predictions. If you are using a scalar field to do the breaking, then the question becomes how constrained this set-up is. In the electroweak theory, the Higgs sector on the one hand fits in well with the symmetries of the theory and has a limited number of free parameters, but it still has quite a few, and is the main source of the problems of the Standard model. Because of this situation, I’ve always been most interested in ideas about unification that tell you more about the Higgs, not so much in ideas that don’t do that, but add other Higgs sectors.
That’s my prejudice, but, sure, starting from other reasonable prejudices, like the desire for a single simple group to act on everything, may lead one somewhere. Maybe you’ll have better luck than the GUT program, which hasn’t been successful so far.
OK, this makes sense. You must be looking forward to the LHC results even more than most, since it will provide some experimental insights into the Higgs sector.
Meanwhile, I’m sitting here with a bunch of old men, waiting for a proton to decay. đ But I’m not holding my breath.
These are interesting times.
This is kind of way over my head so I’m a bit afraid to comment, but what the heck.
In terms of just the pure math here– the one thing I’m at least superficially in a place to comment on– what Garrett’s doing, with breaking down E_8 into the various gauge groups we’d need to describe reality, seems to make sense. Where I get lost is in trying to understand how you use this model to tell us something about the physical world (maybe Garrett’s view of E_8 would be obviously useful or obviously unsuitable for this to someone with a good understanding of what the gauge group “does” in a gauge theory, but that person is not me). Can you help me understand what the physical significance of some of this stuff is or might be, assuming some understanding of what the groups themselves are doing?
I mean, so you’ve shown, it looks like, that E_8 can be decomposed into SU(3)xSU(2)xU(1)xSO(3,1)xHiggsxFermion. The mere fact that this is possible does seem suggestive of something. What do we gain, however, from describing all of these fields as the one big E_8 group– you know, rather than just leaving all those component groups separate with their own yang-mills theories and such (or perhaps just awkwardly x-ing them together like we do to hook up SU(3) to everything else in the Standard Model)? How does the unification of all these groups change things?
I’m meanwhile somewhat confused as to the physical significance we are meant to take from the various features of E_8’s structure. I’m particularly baffled by what to make of the big root diagram which is shown in the video Bee links and in various ways in the paper. What does it mean for two roots in this diagram to have an edge between them? If I’m not mistaken (er, am I?) then from a mathematical perspective an edge between two roots in the E_8 root system polytope corresponds to the lie bracket between those two roots. But what does this mean physically, when we use E_8 as Garrett has here?
Also, what is the meaning of the “rotations” of the root system shown in the paper and the youtube video? Do these rotations correspond to anything physically meaningful, or are the rotations just showing the root system diagram in different ways to make the different groups the system breaks down into visually clear?
Meanwhile, if elementary particle fields correspond to roots in Garrett’s gigantor gauge group, then what do products of those roots physically correspond to? The paper says “The interactions between all standard model and gravitational fields correspond to the Lie brackets between elements of the E8 Lie algebra, and thus to the addition of E8 roots.” Hm, okay, so additions of E8 roots produce interactions between? What are those “interactions”? Or is this specified by the yang-mills action or something?
Also a little confused: so counting up all the fields we expect to see in nature we find they fit with 222 of the roots in your E_8 root system, leaving 18 “extra” roots whose properties as fields are described on page 22 of the paper. The paper seems to be saying that these 18 new fields each act kinda like the Higgs, and each one is identified with a specific one of three generations and a specific color or anti-color. If this reading is correct, what do these generation/color identifications refer to? Does this have to do with the color or anti-color of quark that the field is able to interact with, or is the idea that the field carries color charge, or…?
One more general, possibly dumb question, is there any potential form of correspondence which one could draw between how E_8 is used here, and string theories which use E_8 (or products of E_8) as a symmetry group? Or is the usage of a “symmetry group” simply too different in these different contexts?
Trying to understand, thanks!
As long as Coin is asking questions, I didn’t understand (1) why this doesn’t violate the Coleman-Mandula theorem, and, (2) what about the nonrenormalizability of GR?
MQ, Garrett does seem to offer an argument concerning your (1) in a reply to Moshe in the comments section of the Backreaction post:
Several more posts over the course of that thread drill down on this point further…
more questions:
(1) The first person I know of to point out this loophole in Coleman-Mandula was Thomas Love (a visitor here) in his 1987 dissertation. There is also a discussion of this loophole in this recent paper by F. Nesti and R. Percacci: Graviweak Unification. Or you can go to the source and look at Coleman and Mandula’s paper, in which their first condition for the theorem is “G contains a subgroup locally isomorphic to the Poincare group.” The G = E8 I am using does not contain a subgroup locally isomorphic to the Poincare group, it contains the subgroup SO(4,1) — the symmetry group of de Sitter spacetime.
(2) I’m banking on the LQG community to crack this one. So multiply the odds of this E8 Theory being right times the odds of LQG finding the right answers for quantizing the theory… and I’m first to admit it’s a long shot. But I think it’s got a chance, which is why I work on it.
Hi Coin,
Peter teaches classes in representation theory, so he can answer most of these questions better than I can, but I can at least help out with what’s in this paper. You have a correct understanding of what’s going on, so I’ll just answer your specific questions.
“What do we gain, however, from describing all of these fields as the one big E_8 groupâ you know, rather than just leaving all those component groups separate with their own yang-mills theories and such (or perhaps just awkwardly x-ing them together like we do to hook up SU(3) to everything else in the Standard Model)? How does the unification of all these groups change things?”
Because all these fields are parts of E8, we can assemble an E8 principal bundle connection (technically a superconnection) which consists of 1-forms and Grassmann fields valued in this E8 Lie algebra, and use the curvature of this big connection to get the dynamics. The curvature, in the action, determines how E8 interacts with itself. And since everything is part of E8, this corresponds with how all the fields of the standard model and gravity interact with each other. This action is built by hand to match the standard model, which is an inadequacy of the theory, but it’s very concise. And I think it’s bloody amazing that this works at all.
“Iâm meanwhile somewhat confused as to the physical significance we are meant to take from the various features of E_8âs structure.”
Physically, as this theory develops it should make definite predictions for the coupling constants, predict a handful of new particles and some non-standard interactions, and (if things go astoundingly well) have something to say about the particle masses. These predictions may end up being wrong, killing the theory, but so far things are looking good.
“Iâm particularly baffled by what to make of the big root diagram”
The root diagrams correspond to the structure of the Lie algebra. If two E8 roots add to give a third (in eight dimensional Euclidean root space) then the Lie bracket of the corresponding two Lie algebra basis elements give the third. In the paper, I describe which roots correspond to which elementary particles. Also, since the projection used to plot the eight dimensional root system is linear, you can determine particle interactions by adding these roots together as two dimensional vectors, extending from the origin — it’s fun, try it. This is standard representation theory, and it’s very pretty. In my opinion, Peter doesn’t push his own subject hard enough — I wish I had learned about this stuff earlier than I did, it’s wonderful.
“are the rotations just showing the root system diagram in different ways to make the different groups the system breaks down into visually clear?”
Yes, precisely.
“Hm, okay, so additions of E8 roots produce interactions between? What are those âinteractionsâ? Or is this specified by the yang-mills action or something?”
Yes, the addition of the roots corresponds to the Lie brackets between fields, which is in the curvature, which is in the action, and this gives the interactions between particles, appearing as Feynman vertices in QFT calculations.
“these 18 new fields each act kinda like the Higgs, and each one is identified with a specific one of three generations and a specific color or anti-color. If this reading is correct, what do these generation/color identifications refer to? Does this have to do with the color or anti-color of quark that the field is able to interact with, or is the idea that the field carries color charge, orâŠ?”
Yes, exactly so. These new scalar fields have color quantum numbers, and so interact with the quarks and gluons.
In my dreams at night, these new Higgs fields give the CKM matrix, but I don’t know how that works when the sun comes up.
They’re also a potential dark matter candidate, but I don’t say that in my paper because I think that’s a cliche.
“is there any potential form of correspondence which one could draw between how E_8 is used here, and string theories which use E_8 (or products of E_8) as a symmetry group? Or is the usage of a âsymmetry groupâ simply too different in these different contexts?”
They are completely different theories, which happen to use related Lie groups. I could list many specific differences:
non-compact E8 vs compact E8 x E8
gravity in E8 vs gravity via other
four dimensional spacetime vs 11 dimensional spacetime with Kaluza-Klein orbifold compactifications
principal bundle connection vs strings, branes, and who knows what
etc.
“Trying to understand, thanks!”
I consider it a testament to the simplicity of the theory that you seem to have understood most of it after a first reading. I should put that in among the differences list… đ
I consider it a testament to the simplicity of the theory that you seem to have understood most of it after a first reading.
Hm, I think that would be an exaggeration to say I understand most of it. But thanks for the clarifications, this helps đ
The Coleman-Mandula theorem applies to “All Possible Symmetries of the S-Matrix”, the title of their paper. The S-matrix formalism is based on particle democracy, there are no fundamental particles. In “The Geometry of Elementary Particles”, my 1987 dissertation which Garrett mentioned, there are truely elementary particles and the S-matrix formalism is not valid, hence the Coleman-Mandula theorem is not applicable. I use U(3,2) as the symmetry of a complex spacetime by passing the no-go theorems (which relate to the Poincare group).
About Coleman-Mandula, Steven Weinberg said at pages 382-384 of his book The Quantum Theory of Fields, Vol. III (Cambridge 2000):
“… The proof of the Coleman-Mandula theorem … makes it clear that the list of possible bosonic symmetry generators is essentially the same in d greater than 2 spacetime dimensions as in four spacetime dimensions:
… there are only the momentum d-vector Pu, a Lorentz generator Juv = -Jvu ( with u and v here running over the values 1, 2, … , d-1, 0 ), and various Lorentz scalar ‘charges’ …
the fermionic symmetry generators furnish a representation of the homogeneous Lorentz group … or, strictly speaking, of its covering group Spin(d-1,1). …
The anticommutators of the fermionic symmetry generators with each other are bosonic symmetry generators, and therefore must be a linear combination of the Pu, Juv, and various conserved scalars. …
the general fermionic symmetry generator must transform according to the fundamental spinor representations of the Lorentz group … and not in higher spinor representations, such as those obtained by adding vector indices to a spinor. …”.
In short, since E8 is the sum of the adjoint representation and a half-spinor representation of Spin(16),
if Garrett builds his model with respect to Lorentz, spinor, etc representations based on Spin(16) consistently with Weinberg’s work,
then
Garrett’s model could well satisfy Coleman-Mandula.
Tony Smith
Pingback: Physics needs independent thinkers « Theorema Egregium
Garrett: your remark at the end of section 3.2.1. Can this be translated into ‘the theory is background independent’, one of Smolins reasons to reject strings?
Berlin: It implies that, yes.
Berlin: I should clarify that this is not a complete quantum theory of everything, so in that sense it is incomplete. It will need to be successfully partnered with LQG and/or QFT — this is nontrivial, and time will tell whether it works or not. But the pieces are in place.
Hi Peter,
Thanks for the link. Anybody here knows how the arxiv makes decisions like 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-thâŠ
It might simply be insecurity. Whoever makes this decision they will try to make it such as to not upset the majority of users. And I doubt they do actually study the paper in great detail. Best,
B.
Garrett: Your use of Clifford bundles, plus the fact that your theory allows the Standard Model to be extended, suggests a possible tie-in with ELKO spinor-fields, which have been proposed as an extension of the SM (and also – pardon the cliche! – as a dark matter candidate). For a very recent paper on ELKO, in which Clifford bundles are used explicitly, see: http://www.arxiv.org/abs/0711.1103
(Disclaimer: I am not in any way involved in research on ELKO myself.)
This seems a lot like Tony Smith’s work. Mentioning Tony in your acknowledgments is guaranteed to get you watched. Calling him your “friend” gets you banned. There is neither integrity nor honor to be found there.
It’s interesting work in a sense, but it’s still phenomenology and doesn’t improve the SM. The statements about gravity are much more doubtful. This approach has been tried again and again and always meets with the same problems.
-drl
Garrett references John Baez’s Octonion paper and that paper also thanks Tony. Don’t think they will be banning Baez any time soon. Funny, models with a great math basis get frowned on while philosophical ideas like the landscape get cheered. Yet they make it sound like it’s those models with the great math that are too philosophical?
As happens more often than not, to the extent that I understand the issues (not very much here), I concur with DRL. I want something that simplifies. From that point of view E8 – in any context – is a non-starter.
Garrett is giving the seminar talk at the ILQGS tomorrow.
His slides are online here
http://relativity.phys.lsu.edu/ilqgs/lisi111307.pdf
The audio will be available here
http://relativity.phys.lsu.edu/ilqgs
these International LQG Seminar discussions are often lively in part because they are conference calls where everybody has the slides to scroll through]
and you occasionally get questions and comment from Ashtekar, Rovelli, Freidel, unidentified Perimeter, Marseille, Penn State people.
Audio and slides from past seminars are available—same link.
I’ll be interested to see how Garrett Lisi and Carlo Rovelli get along, to the extent that one can communicate usefully in that intercontinent telephone conference call setting.
Peter, currently I DO see 4 trackbacks (none of which refer to your blog, though)
Shantanu,
Yes, the 4 trackbacks that are there now are the ones I was describing, sorry for the confusing way that was written.
The ILQGS talk went very well. Abhay Ashtekar and Lee Smolin each had several questions/comments leading to discussion. An expanded set of slides is available.
slides are here
http://relativity.phys.lsu.edu/ilqgs/lisi111307_2.pdf
audio is here
http://relativity.phys.lsu.edu/ilqgs
Thanks to Jorge Pullin for organizing the seminar and making it available online!
Hi Peter,
Thanks for the update on the arXiv classification issue. Still I’d like to know, could anybody fill me in how decisions like that are made? Best,
B.
Bee,
I don’t know exactly how this works, and it’s my impression that the process is rather non-transparent. The arXiv has a difficult problem on its hands of how to maintain a reasonable level of quality, and not get flooded by junk. There are moderators for each section of the arXiv who supposedly take a quick look at submissions and decide if they are correctly categorized and meet their standards. The places where they describe how this is supposed to work are
http://arxiv.org/help/moderation
and
http://arxiv.org/help/endorsement
I have no idea what happened with Garrett’s paper (and I gather he doesn’t either), but presumably decisions were made by gr-qc and hep-th moderators, and perhaps other people got involved later after questions were raised about the decision to classify as gen-ph.
“Yes, exactly so. These new scalar fields have color quantum numbers, and so interact with the quarks and gluons.
In my dreams at night, these new Higgs fields give the CKM matrix, but I donât know how that works when the sun comes up.
Theyâre also a potential dark matter candidate, but I donât say that in my paper because I think thatâs a cliche.”
If your dark matter candidate has color quantum numbers it should interact strongly with ordinary matter. In MSSM the dark matter candidate is typically a neutralino. In some models it’s a sneutrino.
So, in either case it only couples gravitationally – that is why it is referred to as a dark matter candidate.
So, if some construction predicted, say, a gluino LSP (which is strongly interacting) that would be a disaster.
So if Garret Lisi thinks that a colored particle is a “potential dark matter candidate”… well, I’m, to say the least, puzzled.
I said:”So, in either case it only couples gravitationally – that is why it is referred to as a dark matter candidate.”
Correction: it’s only true for the right-handed sneutrino, the neutralino is also weakly coupled, of course.
Thanks! Btw, I found someone for the conference I mentioned.
The link to the Telegraph article is slightly defective.
Typo Guy,
Thanks, fixed!!
NewScientist just published a review of Garrett Lisi’s approach at http://www.newscientist.com/article/mg19626303.900
I am puzzled by (among others..) the gravitational part of tabel 9. Does the spin 2 graviton (still) exist in the theory?
berlin
In response to “berlin”
Loll recently put the business about gravitons succinctly:
The failure of the perturbative approach to quantum gravity in terms of linear fluctuations around a fixed background metric implies that the fundamental dynamical degrees of freedom of quantum gravity at the Planck scale are definitely not gravitons.
That is (from http://arxiv.org/abs/0711.0273 ) if a theory is fundamental, it should not have gravitons.
One should be able to set up certain fixed situations in which a graviton can be derived as an approximation. But the graviton should not exist in the theory as a fundamental descriptor. If it does exist, then the theory would not be fundamental–according to what Renate Loll says.
I would therefore be surprised if it turned out that the E8 theory being developed by Garrett Lisi (and possibly others lately) should turn out harbor the graviton as a fundamental component.
Actually, there isn’t much to Lisi’s work. It’s mostly just hocus pocus and part of the Smolin et. al. public relations initiative to sell ‘alternative’ approaches to physics. Just read his book and you can see the blueprint, the romantic image of a lone maverick making breakthroughs in physics in between surfing and snowboarding. It’s just marketing.
Given my rather boring lifestyle I think about becoming a ghost writer, and hire someone to market my papers with a better story! Anybody could please point me towards a 30something, white, male, single, good-looking US citizen, who has an interest in extreme sports of whatever kind, grew up under difficult circumstances (but doesn’t suffer from an embarrassing accent), good socializing skills, likes to speak in front of people, does well on TV, preferably works in a patent office or likewise, speaks Spanish and French fluently, and, well, has maybe taken some physics classes in high school?
Wow, apparently I’m an imaginary construct dreamed up by Lee Smolin!
Actually, this would explain quite a lot.
Hi Sabine,
Actually your place in the Smoliniverse is as the young, beautiful woman who happens to be a brilliant and creative physicist. It’s very sly of Lee to choose you as part of his public relations campaign. đ
Pingback: New Scientist reports: Theory of Everything - Page 3 - Bad Astronomy and Universe Today Forum
Pingback: Todo es parte de Todo | Tech Detour
Is the title of the paper so much “over the top” as it is descriptive and a terrible maths pun, being that M8 is both an exceptional group and a simple group?
One should be able to set up certain fixed situations in which a graviton can be derived as an approximation. But the graviton should not exist in the theory as a fundamental descriptor. If it does exist, then the theory would not be fundamentalâaccording to what Renate Loll says.
Hm, while I can see attractive aspects to that approach, that kind of sounds like a dramatic step to take. Do there already exist any other theories of quantum gravity, besides Loll’s, which eschew the graviton or take the “graviton as approximation” approach you describe?*
Meanwhile I find Loll’s argument in the paper you link against the graviton somewhat unconclusive. “Well, we’ve been trying to get useful answers out of this construct for decades and haven’t succeeded, so it’s a good bet we’re doing something wrong” sounds like good strategy to me, but he doesn’t seem to actually be putting forth an argument about reality there, only an argument about “how to proceed”. I don’t see any reason that just because we can’t describe the graviton perturbatively, that would mean it doesn’t exist– since, as far as I understand, perturbation theory is supposed to just be an approximation anyway. (And this is of course assuming that perturbatively modeling the graviton is impossible and not just too hard for anyone to manage right now). Am I missing something about Loll’s argument?
* Does LQG, for example, have a graviton? Looking I am finding references to a “graviton propagator” in LQG but it is not immediately obvious whether that’s the same thing.
Please, Garrett’s paper is a flimsy excuse for turning this into a quantum gravity discussion forum, which is something I don’t want to run. Enough about this unless it directly has some relevance to the paper.
All right, sorry about that. I’ll go harass Marcus on physicsforums đ
J. Barrett
Exactly!
Why do you seem to be the only person to get that? The funniest part was hearing the solemn preaching: “I think it would be better if you were not so over-the-top etc etc…”
I’ve been waiting for someone to point that out here at NEW. You have my gratitude and respect, J Barrett, whoever you are.
What sort of a minimum background would be needed to actually grok this paper?
Believe me, nobody missed the pun.
Coin, Renate Loll is a she (her name should be a clue). And assuming that “graviton” means what it’s normally taken to mean, a perturbative free state propagating on some background a la DeWitt, then to say that gravity can not be described perturbatively is to say that gravitons do not exist.
P. Woit: âOne 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 youâre 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 doesnât 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).â
I admit that I didnât read the paper. However, in my view, all that PR tararam have very positive outcome: it again attract the attention to the Cayley numerical system which seems to be the natural candidate for QG and unification of all fundamental interactions. Since the connection with the GR and relativistic QM is the necessary constraint, one should define the real octonion valued self adjoint operators. My own experience with them is that it is exceptionally not simple problem (indeed, even the solution will be far from being theory of everything).
Regards, Dany.