Talk:An Exceptionally Simple Theory of Everything/Archive 1

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Initial comments

Considering that the paper was just written and not (yet?) considered an influential paper, I'm not sure this yet deserves a Wikipedia article. Also, the title of the Wikipedia article (though I understand that it is also the title of the paper) will likely attract a lot of pseudoscience people and people claiming that it must be pseudoscience based on the title alone and the people attracted to it. In a few months perhaps, an article should be written depending on how things flesh out, but I'm sure that there should be one with the theory in such a premature state. 128.2.16.121 20:18, 15 November 2007 (UTC)

I think this deserves to stay. It is a proper scientific theory, has been widely reported on in the media, and has already garnered initial praise if not optimistic scepticism from the scientific community. I do agree however that as this theory gains steam, and is eventually tested, it will likely be renamed, and as such this page could or should be moved. For the time being though, I think it should stay as is. This will be a good repository for links, references and data as it develops. Oldsoul 20:33, 15 November 2007 (UTC)

I created this article and the article on Lisi in the hopes that physicists would add qualitative information on the theory. This paper has already grabbed the attention of many laypeople like myself, and many of us will look to Wikipedia to find answers to our questions. I agree the page will likely move, but the current title is what people will search for until the theory gains an "official" name. gnocchi [22:20, 15 November 2007 (UTC)]

Section "Overview"

I don't have the expertise to say if this deserves to stay or not. However, the entire "overview" section is copied directly from the paper, and thus should not be in Wikipedia. If someone who is more familiar with the subject could write a summary instead, that would work much better. Crito2161 22:27, 15 November 2007 (UTC)

I don't expect it to. I simply pasted it in order for someone to draw on when writing the summary you've mentioned. Oldsoul 22:29, 15 November 2007 (UTC)

It should at least be in quotes and cited for the time being, so it is clear that it is an excerpt. I am not, however, qualified enough in physics to write a meaningful summary of the topic. 24.19.238.74 00:54, 16 November 2007 (UTC)

That is an absolutely terrible overview; I wouldn't even want to use his text. He's being overly grandiose and talking about how a TOE should have this and a TOE should have that, but he's not really saying anything about his theory. Someone please replace the current overview with something meaningful, preferably about the topic this wiki page is supposed to be on. — Eric Herboso 01:49, 16 November 2007 (UTC)

Eric, I agree. I simply put it there as a temp. place holder that others could draw from when writing a new one. Again, I'm not an expert, and will defer this to you if you wish. Oldsoul 02:19, 16 November 2007 (UTC)

It's a copyright violation to copy that much text from the paper, so I've removed it. Somebody familiar with the subject should write an overview in their own words. - Merzbow 03:07, 16 November 2007 (UTC)

I've written the summary. I am a physicist, but definitely not a particle physicist, so someone more expert than I should probably check it over. Dragons flight 08:42, 16 November 2007 (UTC)

As a non-physicist, it's an excellent summary. It seems amazing to me that since Lie groups were already being used in conjunction with the Standard Model, why didn't anyone before think of applying E8 to the whole shebang before Lisi. - Merzbow 10:11, 16 November 2007 (UTC)

Well, embedding simply for its own sake isn't really productive. It merely obscures the underlying structure. The key is that the embedding should give rise to new conclusions not available in the previous mathematical system. Lisi's certainly has the potential to do that, but for the most part he hasn't yet done so. Dragons flight 15:30, 16 November 2007 (UTC)

Yes, thank you for adding this. It gives us weekend physics geeks a good start on understanding the theory. --Gnocchi 16:22, 16 November 2007 (UTC)

Apologies for the copyright violation. Thanks a lot for improving this section. It's fantastic now! -- Oldsoul (talk) 17:43, 16 November 2007 (UTC)

Lisi's theory does not provide "a solution to the problem of quantum gravity". His paper essentially describes a classical E8 field theory, components of which are identified with Standard Model and gravitational fields. Quantization isn't even mentioned until the second last paragraph, at which point he appeals to the existing procedures of QFT and LQG.

Also, I think eventually his theory will acquire a more descriptive name, like "Lisi E8 field theory" - ESToE is just the name of his paper - but we will have to wait for the down-to-earth designation to emerge from the ongoing discussions. Mporter (talk) 07:01, 17 November 2007 (UTC)

• I considered changing "...within the mathematical framework of E8, which is the largest of the simple Lie groups" to "....which is the most complex of the finite-dimensional exceptional simple Lie groups" but yuck. I guess anyone who needs the distinction would dig deeper? But I'm uncomfortable with using "largest" to refer not to the cardinality of the group's set. Pete St.John (talk) 21:04, 20 November 2007 (UTC)

Agree re largest, is A9 a larger group? --Salix alba (talk) 00:25, 21 November 2007 (UTC)

It is the largest exceptional Lie group so I changed it to that. The A, B, C, D series groups do get arbitrarily large, but they're not exceptionals precisely because they are infinite in number. Mporter (talk) 00:45, 21 November 2007 (UTC)

A9 has a larger Cartan subgroup, but has only dimension 80, compared with E8's 248. There are infinitely many simple groups of higher dimension than E8 (e.g. A16 has dimension 255). Geometry guy 00:51, 21 November 2007 (UTC)

Yeah just using the word "exceptional" is great, I like the new wording; thanks, Mporter. Pete St.John (talk) 19:16, 21 November 2007 (UTC)

Criticism

This page has a rather scathing criticism of the paper. Unfortunately I'm not familiar enough with either the high-level mathematics or the physics to interpret his criticisms with any confidence. Perhaps someone else can add this to the article :-) fraggle 11:47, 16 November 2007 (UTC)

Lubos Motl may be right. He is certainly a lot closer to the field than I am (my primary background is geophysics). On the other hand, he is also a bit of an eccentric at times himself, so it is hard to tell. Dragons flight 15:25, 16 November 2007 (UTC)

Lubos' criticism has been met with a little distaste and disdain by other bloggers in the field:

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 think we should de-emphasize the criticism by Lubos and emphasize the more balanced criticism of Hossenfelder. -- Oldsoul (talk) 17:41, 16 November 2007 (UTC)

Problem was a stray ref tag... I fixed it. - -- Merzbow (talk) 18:34, 16 November 2007 (UTC)

Thanks Merzbow. (blush) -- Oldsoul (talk) 18:37, 16 November 2007 (UTC)

Disappearing Act?

Why is the criticism section disappearing? I didn't remove it, I simply added another paragraph to it, and now, although it appears in the edit code appropriately it doesn't show up in the saved article page. (wtf)-- Oldsoul (talk) 18:07, 16 November 2007 (UTC)

I did "edit", and then "save" with no changes--and it came back. I have no idea why.---- Todd (talk) 18:46, 16 November 2007 (UTC)

The server was down for a few minutes within the last 15 minutes. Try again? -- Oldsoul (talk) 18:48, 16 November 2007 (UTC)

New Particles

If I'm not mistaken, the citation that is needed for the LHC and previous statements can be attributed to the paper itself [1]?? -- Oldsoul (talk) 17:47, 16 November 2007 (UTC)

I've added two citations. -- Oldsoul (talk) 18:50, 16 November 2007 (UTC)

Stub Status?

I'm thinking we can remove the stub tags, as there doesn't seem to be a whole lot more core information we can add. Obviously this will evolve as the paper is peer-reviewed, the theory is tested, and Lisi calculates the masses of those 20 new particles. Anyone else agree? -- Oldsoul (talk) 18:50, 16 November 2007 (UTC)

Agreed. There is certainly a lot more than could be added, but the article is definitely looking non-stubby at this point.---- Gnocchi (talk) 20:20, 16 November 2007 (UTC)

E8 vs e8

Shouldn't this be uppercased everywhere? It seems to be uppercased in other Wikipedia articles, in the paper, on aimath.org, essentially everywhere but here as far as I can tell. - Merzbow (talk) 08:31, 17 November 2007 (UTC)

Upper case is the group, lower case is the algebra. See Lie algebras#Examples, example 4. Mporter (talk) 14:00, 17 November 2007 (UTC)

Or see E8 (mathematics)#Constructions. Mporter (talk) 14:04, 17 November 2007 (UTC)

Lisi's claim of unification is not verified

I think the summary needs to be clear that the claims of unification made by the author are not verified. It is wrong to say that this paper unifies standard model and gravity. So I changed it to: His theory makes the so far unverified claim to unify all fields of the standard model with gravity using a 248 point lattice of e₈ geometry. —Preceding unsigned comment added by Zeyn1 (talk • contribs) 14:33, 17 November 2007 (UTC)

I'm not sure you need to go so far as saying that it is unverified. I think it's good that we say that it is a 'claim', and then follow up in the overview that the theory has not yet been peer-reviewed or tested. Oldsoul (talk) 21:38, 17 November 2007 (UTC)

What is the criteria for unification? He has unified gravity and the Standard model, which is undoubtedly unified since he is using the triality decomposition of the e8 lie algebra...or is there some additional criteria that you want other than this? It's got everything you need, the standard model + gravity contained neatly in one nice group...or algebra to be precise... Pqnelson (talk) 21:15, 23 June 2008 (UTC)

Structure of article

I think we need to remove the reaction and criticism from the opening section and form a new, Academic reaction section with both criticism and support paragraphs. Right now we've got a whole bunch recently added to the opening paragraph which, in my estimation, should simply state that the paper has garnered both critical and positive responses from the academic community. Thoughts?Oldsoul (talk) 21:41, 17 November 2007 (UTC)

Overview revisited (in laymen's terms)

This section reads like original research... I'm not saying it's inaccurate, but can we find a reliable source that says these things, and maybe cleanup the language to be more neutral? - Merzbow (talk) 06:42, 18 November 2007 (UTC)

The second section seems (appropriately, IMO) to try to informally explain the issue of Lisi combining both 1-forms and Grassman numbers in his connection (or super-connection):

However, in order to get these numbers to come out just right, Lisi's theory has to make calculations using numbers where, although it makes perfect sense geometry-wise, it makes little to no sense physics-wise. For example, at multiple points in his paper, he adds the spin value of fermions and bosons together. According to everything we know previous to this paper, you should not be able to do that. But when Lisi does, he gets the dramatic result that predicts the standard model. While detractors fault him for using techniques that strictly deviate from normal computational physics procedure, one cannot help but wonder if it is the rule, and not Lisi, that is at fault, since the theory's prediction of the standard model is too dramatic to just idly dismiss as chance.

I'm not sure that calling this "add[ing] the spin value of fermions and bosons together", as if to get some single composite spin number is quite right though. Instead, as I understand it, a better analogy would be the combining a real number and an imaginary number into a single complex number, which is neither real nor imaginary, but sometimes quite useful for describing rotations -- and something we are all quite used to, without having to ask "but how the hell can I add a scalar to a bivector?" (except sometimes maybe to make a pedagogical point [1])

Of course, as Aaron Bergman writes (Backreaction blog, 12:16pm, 16 Nov), "you can formally add whatever you want -- that's what "formal" means. The question is whether what you get is meaningful".

In QFT, normally such Grassman number fields can only appear as "ghosts" -- they can't have external lines in Feynman diagrams, so can't be identified as 'real' particles.

However, Lisi contends that "If we're working with one of the exceptional Lie groups as our gauge group, and we build a certain action, some of the ghost parts ARE, algebraically, spinor field multiplets with respect to some subgroups of the exceptional group. This means, mathematically, they are fermions" (Lisi, 11:43pm, Nov 15). In fact, asked by an anon "would this explain "why" fermions exist at all, assuming the pure gauge theory exists?" (11:31 am, Nov 16), he responds "Yes" (12:09 pm, Nov 16).

But Lisi's critics remain to be convinced. It seems Lisi's approach only works because Lisi puts in, by hand, a particular term for the action, that does not transform cleanly under the symmetries of the system (i.e. it is in itself symmetry breaking / gauge fixing). The question arises, does this make it unphysical? Or, if only this gauge produces recognisable fermions, does that signpost this choice of gauge as uniquely the only gauge that is physical? Jheald (talk) 14:32, 18 November 2007 (UTC)

Please see section below about adding back a section like this to the entry. — Eric Herboso 10:45, 20 November 2007 (UTC)

Technical description and criticism

I think the following two paragraphs from Motl's and Hossenfelder's blogs are useful raw material.

Motl: "If you care how the forces and particles are supposed to be embedded into his group, it's like this. You start with a non-compact real form of E8. You embed a G2 into it. Its centralizer is a non-compact version of F4. Now, you embed the strong SU(3) into the G2 while the non-compact F4 acts as the source of a "graviweak" SO(7,1) group that contains SO(3,1), a "gauge group" that is now fashionable in the circles of amateur physicists to "describe" gravity, and SO(4), their source of cargo cult electroweak symmetry."

Hossenfelder: "Given today's status, Garrett's model does *not* naturally lead to a unification of the SM interactions with gravity (he has to chose the action by hand that contains both), it does *not* allow us to understand quantum gravity (since there's nothing said about quantization), it does *not* explain the parameters in the SM (since there isn't yet a mechanism for symmetry breaking), it does *not* explain the cosmological constant or its value (as said above, to claim there has to be one, it would be necessary to show there's no way to do it without one), it does *not* explain the hierarchy problem (and I see no way to do so), it does *not* explain why we live in a spacetime with 3 spatial and 1 timelike dimensions, it does *not* in my very humble opinion yet qualify being called a Theory of Everything."

The graviweak unification which Motl describes with scorn is here[2], and the "amateur" rewrite of gravity is Macdowell-Mansouri theory[3]. The "non-compact real form of E8" is E IX (Lisi, p.29). Hossenfelder's first criticism refers to the second two terms in equation 3.7 in Lisi's paper, which break the full E8 symmetry. Mporter (talk) 07:21, 18 November 2007 (UTC)

Hossenfelder quote added. The rest I leave to someone else. Jheald (talk) 10:40, 18 November 2007 (UTC)

Understand quantum gravity

A point from the article:

• it does not allow us to understand quantum gravity (since there's nothing said about quantization),

I'm not sure what to make of that point. As far as I understood, theory describes relations and interactions (through the "action") between GR SO(3,1)and strictly quantum mechanical SU(3) and S(2)xU(1) (i.e. former two groups describe world in terms of evolution of quantum wave function). I'd think that such theory does allow to understand quantum gravity.

What is this question of "quantization" about? Does still people hope to find "quantum-particle-like" description of QM? (even knowing the Bell's theorem?) SalvNaut (talk) 17:54, 18 November 2007 (UTC)

The point being made is that it isn't really a quantum field theory (as opposed to a classical field theory) until one demonstrates that second quantization can be performed on the field, which he didn't do. Dragons flight (talk) 21:49, 18 November 2007 (UTC)

Thank you for the explanation and the link. Maybe this (i.e. a sentence about second quantization) should get into the article? SalvNaut (talk) 00:11, 19 November 2007 (UTC)

A Layman's Explanation section

Due to the fact that this is all over the blogopshere, I have gotten numerous requests from my non-physics friends to explain just what this theory is all about. This article needs a section that explains, in simple terms, what his paper is getting at. It needs to explain why it is important, and why it creates a divide with physicists, where some say he's definitely wrong and others think he's gotten onto something.

A few days ago, I added a section that dealt with just that. It was then edited by a few others, and eventually was completely removed here. I understand that my writing may not have been the best, but if not by my hand, someone needs to put up a section that non-scientists can read to understand what is going on. Please don't assumethat just because you're smart enough to get what is on the page right now, that others aren't totally confused. Wikipedia is THE website people go to to try and understand these things, so we cannot let them down by not having anything put up about the theory they can understand.

I will not add anything to the main page, because I want to see if I can get consensus first, but for reference, this is what I wrote, plus additions of four others before it got taken down:

Overview revisited (in laymen's terms)

Lisi's theory is a new way of looking at old data with an old technique. What makes his theory notable is that not only does it predict all the standard model particles we know about, it also gives rise to gravity. This is a requirement for any theory of everything. But what makes it revolutionary is that it goes one step further, by actively requiring properties that we previously understood only as an accident of nature. For example, before Lisi's theory, it was known that there are three classes of fermions, but we didn't know why. Lisi's theory actually requires there to be three classes, and this may mean it is an explanation for this natural fact.

However, in order to get these numbers to come out just right, Lisi's theory has to make calculations using numbers where, although it makes perfect sense geometry-wise, it makes little to no sense physics-wise. For example, at multiple points in his paper, he adds the spin value of fermions and bosons together. According to everything we know previous to this paper, you should not be able to do that. But when Lisi does, he gets the dramatic result that predicts the standard model. While detractors fault him for using techniques that strictly deviate from normal computational physics procedure, one cannot help but wonder if it is the rule, and not Lisi, that is at fault, since the theory's prediction of the standard model is too dramatic to just idly dismiss as chance.

If content like this is not acceptable, can someone please explain how we can put an understandable section into text? Please note that another user on this very talk page, Jheald, put up examples of sourcing we can use for statements very similar to these. But no matter what is decided, some kind of section for laymen needs to be put up, if only so I can stop everyone I know from asking me about it whenever I get online. — Eric Herboso 10:45, 20 November 2007 (UTC)

I think your first sentence was on the right track in emphasizing what's not new about the theory. It's still a quantum field theory, for example - and we can link to the QFT article, if the reader wants to know what that means. Every particle is associated with a quantum field, and the fields and their interactions have symmetries.

Historically, first you had the Standard Model, then you have Grand Unified Theories which unified the forces except for gravity, then you had supersymmetric theories which unified fermions and bosons, and then you had supergravity and superstrings which included gravity in the big symmetry defining the theory. You could say that this is a Grand Unified Theory which unifies the fermions and bosons without supersymmetry, and which includes gravity without being string theory - those are some of the claims. It's a retro theory from a 1970s that never was (the 1970s were the high point for GUTs), because it uses a few mathematical ideas that didn't exist then. As physicists have generally convinced themselves that super-theories are the only way to achieve the later stages of unification, some of the dispute revolves around whether Lisi's theory is even well-defined (that was Motl's criticism) or whether it doesn't really unify (see the latest discussions at Woit's blog, about symmetry-breaking by hand).

As for the theory requiring the existence of three generations... This is probably the next claim to be discussed on the blogs. Lisi exhibits a mathematical structure and says there are the three generations, but he admits in the paper it is unclear, and the only person to comment so far on this part (Aaron Bergman) points out what may be a fatal problem. So this has to be cleared up - if it can be cleared up.

The only sense in which the theory predicts the particle masses is that it doesn't have free parameters. But it remains to be proven that the theory really does contain the three generations of fermions. If they are there, then they will have masses and those masses will come from somewhere. But so long as people don't understand how the basics are supposed to work (and it's not clear that even Lisi does), there won't be any calculations. Really, some of the claims for the theory have more to do with Lisi's optimism about what it will be capable of doing, when developed and understood. This was a common thing in the 1970s and 1980s - people hoping that particle properties would be uniquely determined by dynamics, for example, even though they couldn't perform those calculations just yet. Mporter (talk) 12:01, 20 November 2007 (UTC)

I think Mporter's point about the masses is very important. The key issue about whether or not this theory is testable is not whether or not the Large Hadron Collider is online; but the more fundamental difficulty of whether or not it is possible to predict masses with this theory at all.

The real problem with the article, IMO, is not that the article needs a bolt-on "Layman's explanation". The real problem is that the main explanation is so poor, and is little more than tangential to the main ideas, questions and controversies about the paper. The present introduction doesn't even contain the word Connection (mathematics); nor does it flag Lisi's key "crazy" [4] idea about shaping the theory so that Grassman numbers in the connection can be identified with actual fermionic fields, rather than unobservable "ghosts".

According to Lisi, this is only possible if the Connection includes transformations described by exceptional Lie algebras. Others dispute that it is possible at all. When the e8 Lie algebra is chosen, this algebra of transformations can be built up from generators that Lisi asserts interact with each other in ways that closely match the interactions of particles in the Standard Model [5]. Even if correct, however, these transformations relate to classical fields (or descriptions of them) -- it is not clear (at least not yet to me - but then I'm only a layman) how (and/or why) quantization is supposed to come in. And Lisi is only able to get the dynamics of his particles to match the Standard Model if he puts those dynamics in by hand (although he finds he can do this in a single surprisingly simple formula). These 'handmade' dynamics treat different particles/transformations in different ways - ways which do not reflect an overall E8 symmetry; but this 'by hand' symmetry breaking is essential for the different particles to have their characteristically different properties.

That's my (limited) understanding, anyway. As far as I understand, there is work relating Lie algrabras of transformations of classical fields to quantum particles, but not in as grand a setting as e8; but I don't start to know anything about it, hence my gap in understanding the quantization step above.

I don't think a separate "Layman's explanation" is a good idea; and OR - mine or anybody else's - is not good enough either. This needs to be signable-off by people who know what they are talking about.

What is needed, however, is much more informed analysis in the article of what is new in this paper; some indication of what does and what does not appear to be more solidly founded, or on the other hand more speculative/not accepted/controversial; a discussion of some of the criticisms which have led some people to react so violently against the ideas in the paper; and a gauging too of whether or not those criticisms seem to be solidly founded or well informed, in the light of the responses and rebuttals of the paper's defenders.

It seems to me that the main explanation section covers pretty well none of this at the moment, and the article is thus sorely in need of an {{expert}}.

-- Jheald (talk) 14:28, 20 November 2007 (UTC)

The symmetry of the Standard Model itself is a Lie group, so yes, the steps from symmetry group -> fields -> quantum fields is well-known, it is almost the definition of model-building outside of string theory. E8 per se is not supposed to explain the quantization step, it's just the input. But what perplexes people is that Lisi has assigned fermions and bosons to elements of E8 in a way which implies the possibility of transmutation, yet his resulting theory doesn't involve supersymmetry (and "super-Lie groups"). The possibility of such an assignment has been noted previously, but dismissed precisely because of the quantization problem. And he gets around it by having the fields interact in a way which actually removes most of the E8 symmetry, leaving only the Standard Model symmetry (but with some extra fields) - leading to protests that it's not really an E8 theory, because the more exotic relationships implied by full E8 play no part in the theory. But there is also the possibility that the symmetry-breaking terms are not fundamental (e.g. that they describe emergent effects). For the pure (unbroken) theory, he appeals to an argument from Nesti & Percacci (authors of the graviweak model, which is part of the theory) that the full symmetry shows up only in a high-temperature topological phase. This has to do with his model of gravity (Macdowell-Mansouri) being based not on a metric, but on a connection, so that under certain conditions, there is no metric. (This way of thinking was introduced by Witten's Fields-Medal-winning work on topological field theories, which are metric-less theories.) I have no idea yet if this alleged topological loophole in the Coleman-Mandula theorem is valid or not. Mporter (talk) 15:34, 20 November 2007 (UTC)

I think that such section can be constructed and/or sourced with this FAQ where Lisi himself responded questions to journalists. The "new factor" in this theory is also well explained by Lisi here, although using himself as the main source is not the best way to go.

We join all of these fields as parts of one superconnection, over a four dimensional base manifold. This general idea should be familiar from grand unified theories, which combine the gauge fields into a single, larger connection. We're proceeding in the same spirit, but going further by using two unusual tricks. First, we're including gravity -- the connection AND the frame -- as parts of this connection. This reproduces general relativity through the MacDowell-Mansouri approach to gravity, discovered in the late seventies, which I first learned about in Smolin, Freidel, and Starodubtsev's quantum gravity papers. The second trick is that we're also including all the fermions in this superconnection, as Lie algebra valued Grassmann numbers. Now, at first look, this second trick shouldn't work. When we calculate the dynamics of this connection by taking its curvature, the interactions between fields will come from their Lie bracket. But we know gravity and the gauge fields interact with the fermions in fundamental representations. The fermions, such as this Dirac spinor column of spin up and spin down left and right chiral fields, live in a fundamental representation space, and these certainly don't appear to be Lie algebra elements. So how can this possibly work? Well, it turns out that for all five exceptional Lie groups, there are Lie brackets that act like the fundamental action. The structure of these algebras is such that some Lie algebra elements ARE fundamental representation space elements. This fact makes it possible to include the fermions in the connection as Lie algebra valued fields.

SalvNaut (talk) 17:09, 20 November 2007 (UTC)

E8 X E8 X E8

I have just a passing acquaintence with sporadic finite simple groups, and none at all with analogous Lie Algebras, and I'm not a physicist, but I skimmed the paper with some real amusement. There seems to be some prior art modelling (some large pat of) quantuum mechanics (string theoretically) with E8 X E8; also, some modelling (some large part of) general relativity with E8. The "Triad" approach in the paper suggests analogy with joining the two extant models within E8 X E8 X E8; which could be both a cool and useful idea, and a mollification of the grandiousity of the result, at the same time. Also the biggest difficulties he expresses in the paper seem to be on the development of the triads themselves, possibly meaning, "the only difficulty with joining together two prior-art theories is the joining part" which last of course would trivialize the paper.

It's a very nice paper, I'd recommend reading/skimming it to anyone who knows what "Lie Group", "string", and "quantuum" are, with a fairly liberal interpretation of "know" :-) and this paper getting peer-reviewed will be a good thing. Pete St.John (talk) 17:02, 20 November 2007 (UTC)

What a coincidence - I happened to mention E8 x E8 x E8 at Peter Woit's just a few hours ago.[6] Only, your version makes no sense: E8 x E8 string theory is not a "model" of quantum mechanics. And when was E8 previously used to "model" general relativity? Mporter (talk) 22:18, 20 November 2007 (UTC)

Just to explain a bit more - E8 x E8 string theory is already a theory of quantum gravity. What I was suggesting is that the supersymmetry of string theory might derive from an implicit third E8. Mporter (talk) 22:30, 20 November 2007 (UTC)

Supersymmetry has been linked to exceptional groups, for example for heterotic string: N=4 to E8, N=2 to E7 and N=1 to E6. So indeed there is in a sense a E8 x E8 x E8 structure in the heterotic string. That is, the representation theory of the En contain information about supermultiplets, to some extent even including auxiliary fields. The crucial feature is the triality properties of D4 when embedded into En. For details see http://www.slac.stanford.edu/spires/find/hep/www?j=PRPLC,177,1 and http://www.slac.stanford.edu/spires/find/hep/www?j=PHLTA,B214,41 —Preceding unsigned comment added by 137.138.15.138 (talk) 12:10, 11 December 2007 (UTC)

And more - in E8 x E8 string theory, gravity doesn't come from the E8s, it comes from the closed state of the string (when it forms a loop rather than a line segment). And it's not a model of quantum mechanics because quantum mechanics is one of the inputs, one of the assumptions that goes into string theory, not something that comes out of it. Mporter (talk) 00:38, 21 November 2007 (UTC)

I thought Strings explain quanta? So that models of strings could predict new quanta or quantum properties? Anyway fair question about the E8 (one copy) modelling Gen Rel, I should have jotted that down, but I was not trying to prove anything, just note an impression from what I had skimmed. I am absolutely no kind of authority on this subject. Pete St.John (talk) 19:07, 23 November 2007 (UTC)

A string model will predict the existence of particles with certain quantum properties, yes, but it doesn't explain quantum mechanics itself. It doesn't explain the uncertainty principle, for example. Most quantum theories have a classical counterpart which you can get by applying the uncertainty principle to it (that's "quantization"). So you can start out with a classical theory of a vibrating string, in which its states are completely exact and deterministic; and then you can introduce the uncertainty principle (or any other logically equivalent starting point) as a postulate, and you get a "quantum string" with quantum properties like energy levels. So you could say that strings explain the particular quanta we have, but not why there are quanta at all. Mporter (talk) 01:54, 24 November 2007 (UTC)

Masses

I have added this to the article lead,

as it stands, the paper contains no calculations for particle masses; and it is not clear that such calculations could be done even in principle.

which I hope is a fair understanding of Mporter's comments several sections above, and various blogs.

I'm only a layman, so I hope somebody with more knowledge will confirm whether I have got that right. Is there anything in the theory to suggest even why the different fermion generations should have different masses from each other? Jheald (talk) 12:22, 22 November 2007 (UTC)

Not that I can see, but all the fermion stuff is obscure to me. The masses are to come from a Higgs field, so in theory it's just a matter of finding its ground state. But I don't understand what he's doing with the three generations (section 2.4.2).

By the way, in his critique Distler uses a different group for gravity than Lisi actually uses. The group Distler uses is the one that Macdowell and Mansouri originally used, but the one Lisi uses is commonplace in LQG. Mporter (talk) 14:53, 22 November 2007 (UTC)

Correct me if I'm wrong, but in physics mass (allegedly) results from interactions with Higgs (field/particles) and in Lisi's theory this means that mass will result from a commutator between appropriate E8 Lie algebra elements. Exact values (hence different masses) of this interaction, depend on the curvature of E8 principal bundle over time-space manifold. Curvature results from/can be described with connection. This has to be chosen so that it agrees with reality (so the question stands: can it be chosen this way?). I don't understand this well but Garrett writes that this agreeing of terms is usually done through writing equations for "action" of E8 bundle over our space-time. Garrett has proposed some action formula by hand ("satisfying desire for minimalism" as he writes) but he's not sure if this is the right one and he didn't do any computations that would result with constant values (to compare with reality). So whether this, or other correctly definable, action will result with constants that agree with reality (like different masses of fermion generations) - we don't yet know.

Replying to your question more directly: Is there anything in the theory to suggest... - I suppose that yes, each generation of fermions commutes differently with Lie algebra elements representing Higgs field, so there is hope that properly defined curvature will assign them real-world masses. Sorry for the long post, but writing this down helps me to understand this better. SalvNaut (talk) 18:53, 22 November 2007 (UTC)

The masses don't come directly from the group algebra, they come from the Higgs having a nonzero expectation value, which is dynamics. But there is a problem with the three fermion generations in this theory:[7] under the original assignment of particles to E₈, only the first generation gets the right quantum numbers. You actually have to change the assignment (by a "triality transformation") for the second generation to work out, and then you have to apply it again for the third generation to work out, and then if you apply it the third time it works for the first generation again. But each time the other generations get scrambled. This is switching between representations, and it really means there are three related E₈ theories here, each of which describes one fermion generation correctly (and only with respect to properties other than mass) and the other two incorrectly. I don't see how you could hope to turn that into one successful theory, because even if they could be shown to be different aspects of the same theory under a change of variables (think of how the various string theories were unified), it would still be wrong wherever you went in the configuration space of the unified theory. So either something has to be changed, or we'll have to go back to string theory. :-) Mporter (talk) 00:00, 23 November 2007 (UTC)

Thanks for correction and the good link. the triality rotated G - Garret suggests in his paper that physical fermions may be a linear combination of each of triality partners (p.13) (shouldn't "wrong" quantum number assignments show up some in experiments, then?). He already treats fermion in an unique way. If triality rotation has no explanation, does this leave us with this fit being only a matter of (bad:) luck? SalvNaut (talk) 00:57, 23 November 2007 (UTC)

First let me explain what I meant by saying there are three theories, not one: see p.22. That matrix T is the triality transformation I was referring to. As you can see, it permutes the assignment of Standard Model particles to elements of E₈, and in any given assignment, only one generation gets the right quantum numbers. So if we consider the theory as being defined (in part) by the assignment of particles to E₈, then there are three theories and they are all wrong. The idea of a superposition of triality partners only makes sense if triality is a relationship between particles within the one theory, but Garrett doesn't explain how to do that.

So we have a theory (or a set of three theories) defined classically, but not containing the Standard Model; and we have no proposal for how to turn their classical spinor/tensor E₈ symmetries into a nonsupersymmetric quantum symmetry of fermions and bosons. (Doing it supersymmetrically would probably just lead back to string theory in some form, e.g. with Garrett's particles being zero-length approximations to the strings.) You ask what this partial fit might mean if it really is a big red herring in the quest for a unified theory... It's hard to say. String theory is famous for having zillions of ground states, most of which are nothing like the Standard Model, some of which resemble it, and some of which behave exactly like it. Spaces of mathematical structures are full of repetitive and almost-repetitive patterns. There might be field theories somehow resembling the one in this paper which really do contain the Standard Model (that would be Garrett's hope right now), or the nearest such theory might be several qualitative changes away, so far away that it no longer counts as an instance of the original idea. Mporter (talk) 10:09, 25 November 2007 (UTC)

I said: String theory is famous for having zillions of ground states, most of which are nothing like the Standard Model, some of which resemble it, and some of which behave exactly like it. This may or may not be true, but right now it seems that there is no known string vacuum which behaves exactly like the Standard Model, there are just classes of vacua which are in the right ballpark (some listed here[8]). Also see swampland. Mporter (talk) 00:25, 30 December 2007 (UTC)

as it stands, the paper contains no calculations for particle masses; and it is not clear that such calculations could be done even in principle. We can only add this statement if supported by a published source. See WP:V#Sources ≈ jossi ≈ (talk) 01:00, 23 November 2007 (UTC)

Well, the first half is directly supported by the paper. I think the calculations do-ability at all has been questioned, but it's too late at night for me to find an appropriate source. What is true, regardless, is that it has not been shown that such calculations could be done even in principle. Jheald (talk) 01:56, 23 November 2007 (UTC)

The sentence is still OR - according to who is it "not clear that such calculations could be done even in principle"? I've fact-tagged it for now, if a source can't be found soon that says exactly that the sentence needs to be rewritten or removed. - Merzbow (talk) 01:05, 25 November 2007 (UTC)

I stand be the edit summary I made: This is a real issue. It's a real test to create a theory that doesn't blow up and give infinities everywhere.

As Sabine Hossenfelder wrote, in her opening assessment for her blog [9]:

"He neither can say anything about the quantization of gravity, renormalizability, nor about the hierarchy problem" (my emphasis).

No renormalizability => no calculations.

And here was Stein Sigurdsson's concluding summary, in his blog post: [10]

If the rather dubious bits he pulls off tighten into something half-rigorous, and if there is another loophole in Coleman-Mandula, and if the theory is calculable (like masses of the new scalar fields, or actual expectation value for cosmological constant) then it may be very interesting. (my emphasis)

That is a lot of ifs.

It's a big deal to have a model that produces well-defined numbers without blowing up. Lisi hasn't produced anything in his paper to establish that assertion. Jheald (talk) 15:36, 25 November 2007 (UTC)

I make no judgment if it's a big deal or not, heck knows I can't do the math. But you need a source to say that, you can't add your own opinions to the article. - Merzbow (talk) 19:22, 25 November 2007 (UTC)

Another blogger

Stein Sigurdsson, an astrophysicist at Penn State, has put up some interesting threads running, and various people from the discussion at B's blog, including B herself, have chipped in.

• Overly Simple Theory of Something ("Lisi does not actually have a theory yet, he doesn't really have a model even. [But] he has a couple of insights that may go somewhere...")
• Red Boson, Blue Fermion (On adding bosons and fermions)
• Almost Massless World (Suppose non-trivial couplings between gravity and particles were indeed only possible in non-Poincaré space time? Is this necessarily a problem? Could the size of the cosmological constant and the smallness of particle masses be in some way tied together?)

Not sure whether or not the threads represent anything yet sufficiently authoritative for a link from the article main page; but I thought they were maybe worth flagging here to watch, in case things develop. Jheald (talk) 15:19, 23 November 2007 (UTC)

Edit war?

The recent line, reverted and then unreverted,

• It also now seems that the paper does not after all precisely match the symmetry structures observed in particle physics...

implies that the paper purports to "precisely match..." which seems unreasonable, to me; as it admits of pending difficulites, and is described (more explicitly elsewhere, perhaps) as "a work in progress" not a complete theory. I have no objection to citing the blogs, but this line is something of a strawman by overstating the claims it rebuts. So I support deleting or replacing the line but am reluctant to myself. Pete St.John (talk) 17:39, 24 November 2007 (UTC) (E8^3 == E512? :-)

The paper has been hugely hyped as 'containing the standard model plus gravity'. That's been the basis for the instant celebrity quotes like the one from David Finkelstein, "I think that this must be more than coincidence", etc.

Well, it doesn't match the standard model, and there's no easy way to make it match the standard model. The symmetries required simply aren't there in E8. This ought to be set out right at the top of the article. It's essential, if people are to have realistic expectations of what Lisi has or has not achieved. Jheald (talk) 17:47, 24 November 2007 (UTC)

Sure, there is no easy way to make it fit the standard model and maybe it never will be. I just want to distinguish the claims of the paper (which I admit are expansively posed) from the hype (which is only partly Lisi's fault :-). So I would prefer to say something like:

• Contrary to many impressions, the paper does not present a complete working model for Unification. It is a description of an ongoing investigation which has garnered extraordinary attention.

Part of the "extraordinary attention" is because of Lisi's boldness, part because of jouralism's tropism for excitement, and part because the paper is very engagingly presented, a definite positive. I just don't think we need to blame Lisi for presenting an erroneous proof, although I think there are actual errors, e.g. whether something is embedded in one subgroup or a larger one, something along those lines he admits to already. I just want to distinguish between the (false) impression made by the hype, and the (brazen) optimism (vs, false claims) in the paper itself. Both may be addressed, but they shouldn't be blurred together (they already are, we want to clear it up, good job for a real-time Encyclopedia).

Incidentally, this is somewhat similar, to me, to the Wolfram (2,3)Turing Machine recent controversy. In my view, Wolfram Research (a business) overstated the result (for publicity), and it was important to distinguish mathematical flaws in Smith's paper, from public relations rhetoric flaws. The issues aren't all resolved but currently most everyone involved is civil and calm; it was dicey for awhile. Pete St.John (talk) 18:07, 24 November 2007 (UTC)

I don't think that sentence was phrased neutrally. I've rewritten it and remove some other original research from the lead. When opinions are stated in the text, we need to attribute them to the source by name, in the text, and be wary of cherry-picking. - Merzbow (talk) 20:04, 24 November 2007 (UTC)

I like the above sentence proposed by Pete, and I think it should be implemented. Problems with E8 theory (like fermions triality, ad-hoc action,...) are already indicated in Lisi's paper, and they're discussed further down in the article. It can't stand in first paragraph, as it stands now, that his paper is wrong, this being cited with only a blog. (Besides, Garrett's last comment on this blog looks to me like a minor thing - isn't that he simply misnamed the group he was working with? EIX instead of E8(8)?) salVNaut (talk) 20:05, 24 November 2007 (UTC)

Fermions and bosons again

Someone added the following passage (which has been touched up a bit):

A somehow exceptional is Lisi's approach to describe fermions. He includes all the fermions in E8 superconnection, as Lie algebra valued Grassmann numbers. Soon after the paper gained attention, there were voices from certain physicists that Lisi had made a mistake by "adding bosons to fermions". However, this seems to be a feature of Lisi's paper. In his own words:

The second trick is that we're also including all the fermions in this superconnection, as Lie algebra valued Grassmann numbers. Now, at first look, this second trick shouldn't work. When we calculate the dynamics of this connection by taking its curvature, the interactions between fields will come from their Lie bracket. But we know gravity and the gauge fields interact with the fermions in fundamental representations. The fermions, such as this Dirac spinor column of spin up and spin down left and right chiral fields, live in a fundamental representation space, and these certainly don't appear to be Lie algebra elements. So how can this possibly work? Well, it turns out that for all five exceptional Lie groups, there are Lie brackets that act like the fundamental action. The structure of these algebras is such that some Lie algebra elements ARE fundamental representation space elements. This fact makes it possible to include the fermions in the connection as Lie algebra valued fields.

I've moved it here because I consider it misleading and it shouldn't be in the article until we can sort this out.

The problem with the bosons and fermions arises when you quantize the theory. Classically, a field is a field and there is no concept of boson or fermion. But when quantized, spinor-valued fields give rise to fermions, and tensor-valued fields (including scalars and vectors) give rise to bosons. The E-series exceptional Lie groups have representations where there are symmetries mixing classical spinor and tensor fields. But if you want to turn that into a symmetry of quantum fields, you run into the Coleman-Mandula theorem. The passage quoted from Lisi's talk does not address this - he's talking about another aspect of E₈.

I think the reference to E₈-valued "Grassmann numbers" is just another way of saying "these will be fermions in the quantum theory", without saying how that could be so. So far I think three separate reasons have been advanced as to why Coleman-Mandula doesn't apply (not working in Minkowski space; full symmetry only applies in a high-temperature topological phase; symmetry is already broken in the action). The first reason isn't valid because the local geometry is close enough to Minkowski for a generalization of CM to apply; I haven't looked into the technical problems with the second reason but they are clearly referenced in the last paragraph of Lubos Motl's original post; and the third reason would mean that this wasn't really an E₈ unification at all. Mporter (talk) 05:05, 30 November 2007 (UTC)

I'm not adverse to citing references to various sides in an ongoing debate, and it doesn't seem misleading to me because of the tentative "...seems to be a feature..." and even in the (presumably pro-Lisi) quote, "...makes possible" (instead of "models"). But the lead sentence:

• A somehow exceptional is Lisi's approach to describe fermions.

isn't. Pete St.John 17:12, 30 November 2007 (UTC)

Whatever the final resolution of this topic, I think that this dispute should find it's place in the article, and I fully agree that it should be phrased carefully.

As for "Grassmann numbers", it is NOT just another way of saying "these will be fermions in the quantum theory". It is like saying, fermions can be seen as Grassmann numbers because in E8 simple exceptional algebra those behave exactly the same as (i.e. can be identified with) elements from fundamental representation. If this works, you can apply quantization to Grassmann numbers (in fact applying it to corresponding spinor-valued elements) and you're cool. As far as I understand, Coleman-Mandula does not apply for different reasons - framework for gravity is De Sitter universe (Lisi talks about it at the end of his seminar and Smolin agrees with him).

The more serious is the problem with triality. If this cannot be fit in SM (with another quantum number?, other unification of 3 generations?) then E8 theory dies. salVNaut 10:38, 1 December 2007 (UTC)