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Garrett Lisi: An exceptionally simple theory of everything

The most entertaining paper that managed to creep into hep-th today is called

An exceptionally simple theory of everything (PDF).

Update I: the preprint was re-classified from the professional hep-th archive to gen-ph, general physics, an archive mostly dedicated to laymen's fantasies. Thanks God. Comment for general readers: this preprint is of course not peer-reviewed and probably won't get published anywhere.

Update II: Roger Highfield whom we know from his article attacking the scientific method and claiming that Einstein may have started the rot has returned. In a new, equally breathtakingly silly article, he suggests that A. Garrett Lisi is a new Einstein. Two months ago, I wrote about bad physicists and populism. You may see that virtually all of the myths I described are realized in this story. Mr Highfield has written at least one more stupidity of the same magnitude - namely that the cosmologists are bringing the Universe closer to the doom by observing it. Sensations are much more important for him than rational thinking or the truth.

Update III: Thousands of blogs and news outlets have copied the utter nonsense from Mr. Highfield and at least tens of thousands of people are Google searching for this "new Einstein". It's called mass hysteria. Isn't it cool if a poor surfer dude (see a snowboarding video) finds a theory of everything? It is surely cool but "cool" is not the same thing as "true". ;-) ArsTechnica, a server dedicated to PC professionals, seems to be one of a limited number of remaining sane sources.

Update IV: Lisi's paper has four citations. The most famous authors referring to him are Ferrara and Bianchi who call Lisi's construction a "(hopeless) attempt to unify" on page 16 of their paper.

Update V: Jacques Distler and Skip Garibaldi wrote a paper for mathematicians, explaining that there can't be any "theory of everything" that embeds gravity and other forces into any form of E8.

Its author, A. Garrett Lisi, claims to have found nothing less than a theory of everything. An exceptionally simple one, for that matter. It may sound as a bold statement but from a genius of A. Garrett Lisi's caliber, it shouldn't be surprising. :-)

This extraordinary surfer dude managed to collect five citations in the last thirteen years which is only 4 orders of magnitude below leading physicists. Because the work is based on the E8 group that I love, you bet that I have opened the paper.

Reading the paper

Needless to say, the visually intriguing and colorful paper is a huge joke. The first place where I exploded in laughter was the equation (1.1). It says, using words, the following:
My connection of everything = connection for gravity + weak force + strong force + electromagnetism + electron + neutrino + up-quark + down-quark + other-generations
That's pretty cute! :-) The author is not constrained by any old "conventions" and simply adds Grassmann fields together with ordinary numbers i.e. bosons with fermions, one-forms with spinors and scalars, neglecting any traces of dimensional analysis, too. He is just so skillful that he can add up not only apples and oranges but also fields of all kinds you could ever think of. Every high school senior excited about physics should be able to see that the paper is just a long sequence of childish misunderstandings. I understood these things when I was 14.

Confirming my essay about crackpots' common errors, Garrett Lisi is unable to falsify a wrong hypothesis even in the simplest cases.

Concerning the title, I present it as a joke but I agree with Freedom of Science that if the title is viewed seriously by some important readers and if the author allows it, it is a case of scientific fraud.

There is not a glimpse of physics in that paper. You won't find anything like a "Lagrangian", "amplitudes", "masses", "cross section", "quantum corrections", "anomalies", "energy", "force", "Hamiltonian", "entropy", "phase transition", "path integral", "renormalization", "temperature", or other words that you expect in a particle physics paper. When he talks about actions, they're always wrong actions from some previous obscure papers that have clearly nothing to do with observable physics either. Of course, the author also seems to have no clue about quantum aspects of gravity - a unification of gravity with quantum mechanics is not even attempted because the author clearly doesn't know what it means. On the other hand, you find a lot of random assignments of particles to vertices of polytopes - something that you know from papers about the octopi.

It is the same kind of "unification" as if you put stickers with elementary particles on a chessboard and argue that chess is the ultimate theory of everything. Some stickers don't fit so you call them your predictions. Kindergarten stuff, indeed. Or let me give you a better analogy.

A. Garrett Lisi and his 222 close personal friends. He needs 18 more to reproduce the roots of E8 and make his theory complete. Click the picture for more details.

The role of the E8 group in his picture is therefore completely unphysical. Because different components of the E8 multiplet are assumed to be particles with completely different properties, the E8 symmetry is broken at stage zero. There is no E8 symmetry - and there can't be any E8 symmetry - that would actually relate these different particles.

Of course, the comments that this theory may be tested by future experiments are nothing else than journalists' confusions or a politically correct lie (because it is always OK to say an untrue thing about an "anti-establishment" outsider who is moreover a broke). The theory can't reproduce even basic aspects of the observations that have been made decades or centuries ago which is why any talk about even more ambitious tests is rationally unjustifiable.

E8 group and decompositions

The main mathematical content in these 30+ pages is the decomposition of the fundamental representation of E8 under its F4 x G2 subgroup. It is an elementary fact that e.g. freshmen in Prague who follow my textbook written with Miloš Zahradník know as equation (12.95). For A. Garrett Lisi, this single line reflecting a simple calculation that has been done a century ago and that a fraction of freshmen learns is a topic for a 30-page paper and an impressive albeit two-dimensional movie.

Unfortunately, Garrett Lisi, painting himself as an E8 expert, already doesn't know that E8 has a SU(5) x SU(5) subgroup. It's kind of amazing to be ignorant about these elementary facts for a person who is pictured as an expert.

Nude Socialist has already created a 2-minute commercial for this nonsense. Don't be intimidated by the animation. It is just a collection of points given by 8 coordinates (being 0, +-1/2, or +-1) projected to a 2-dimensional plane whose direction - i.e. the relevant coefficients - are changing with time. The visual effect has nothing to do with physics. And mathematicians routinely create more sophisticated animations, see e.g. turning sphere inside out.

Some people might be impressed by some of these formulae about the E8 group - some of which are correct - and/or the pictures. But I assure you that the E8 group is a pretty standard material that students learn in courses of group theory. And there are millions of pictures like that. For example, the picture of the E8 Gossett polytope below is from Wikipedia's article about E8; see also string theorist Clifford Johnson's blog from March 2007. E8 is the biggest exceptional animal in the exciting ADE classification and a large portion of string theorists work with it every day.

This stuff has been known for a century or so. For example, the E8 group itself was discovered by Wilhelm Killing (click the picture) in 1887. New insights were added by Élie Joseph Cartan (click the picture below) in 1894.

The basic facts about the E8 group have nothing to do with problems that physics has been solving in the last 50 years: they are just a part of the mathematical background that high-energy physicists are supposed to know. Garrett Lisi remembered something from math classes he was taking 15-20 years ago but he has forgotten virtually all of his physics classes. Be sure that every physicist who knows basics of his field agrees with me that everything that is nice about the paper has been known for a long time. For example, Le Monde quotes Thibault Damour and Jean Iliopoulos saying exactly the same thing.

The way how Antony Garrett Lisi combines his spotty knowledge with ambitious claims mimicks the approach of thousands of other "amateur Einsteins". He was just luckier because a journalist has endorsed him.

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, namely E8(24). 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.

Of course, the SO(3,1) group mentioned a minute ago plays a different role (in the vielbein formulation of general relativity) than the Yang-Mills groups and the fact that these two kinds of a group cannot be merged is the content of the Coleman-Mandula theorem to be discussed at the end of my text. Moreover, the fermions clearly can't arise from the connection because they have a different spin and statistics and they don't transform in the adjoint representation. For people like A. Garrett Lisi, it is not hard to unify everything with everything else because they don't know any difference between different concepts in physics.

Let me repeat the same idea differently. A unification of different forces and matter in physics is difficult because different force and matter particles have different properties, especially spin and statistics (and other features that follow from them, e.g. non-renormalizability of gravity). Garrett Lisi attacks the problem of unification by completely ignoring all these features that actually contain the whole problem. That's why his work is physically vacuous and meaningless.
If you want a lecture of a well-known physicist about the Coleman-Mandula theorem, look at MOVIE 13 by Edward Witten at the Sidneyfest.
The technical statements that the decomposition etc. can give the right spectrum, e.g. the number of generations, is also wrong. See, for example, Jacques Distler's post. Jacques' group theory looks impressive but his complaints are analogous to telling cargo cult scientists that they should change the shape of their wooden headphones, as Richard Feynman would say.

Additionally, you might think that the E8 starting point is analogous to heterotic GUTs - models such as the heterotic MSSM by Bouchard et al. Except that it is completely crucial for physics that E8 in heterotic string theory is compact. Non-compact gauge groups would lead to ghosts and negative probabilities. Moreover, the whole Standard Model is embedded into the same subgroup of the heterotic E8 once it's broken, e.g. to SO(10). Also, everyone knows that the fermions arise as chiral multiplets and not vector multiplets: they are simply not and cannot be a part of the gauge bundle. Most importantly, no sane person has ever claimed that the E8 portion of the heterotic theory already contains gravity. That would be really silly.

Also, if you have ever heard about "GUT" (Grand Unified Theory), you should realize that unlike E6 and others, E8 cannot be a grand unified group because it only has real representations which is not good enough to create chiral fermions. In string theory, E8 is only relevant because it is broken to a smaller subgroup by intrinsically stringy effects. Needless to say, Garrett Lisi has no idea what a "chiral fermion" or even "fermion" means so he is not worried about any of these "details".

Endorsement system

A few years ago, such a paper would almost surely be filtered out from hep-th. Paul Ginsparg has introduced the endorsement system which was circumvented in this case and is likely to become a complete joke in the future. Why? Well, we have seen that a completely continuous spectrum of people between serious physicists and manifest crackpots has been created and the recent fashionable trend is to accept an ever broader set of passionate amateurs and undereducated, intellectually challenged loons into the physics circles.

This paper by A. Garrett Lisi had to be endorsed by someone. If you read the acknowledgements, it is not hard to see possible answers. Some of those people such as Lee Smolin may endorse any crackpot paper because they are both endorsers and crackpots at the same moment. Moreover, they have a vested interest to increase the proportion of similar papers on the arXiv because this is where they belong. As Lee Smolin recently pointed out, irrationality has been extremely useful for him in the past.

If Ginsparg wants to prevent this possible collapse of his arXiv, he probably has to fine-tune the mechanisms a little bit and make sure that people who are ready to endorse papers like this one are simply not endorsers. Otherwise you can be pretty sure that similar papers will eventually overrun the arXiv.

Tony Smith is among the crackpots thanked to in the acknowledgements. Next time, he may also submit his own paper supported by similar endorsers. And maybe A. Garrett Lisi will become an endorser himself. Really entertaining times will start afterwards: the hep-th era of the UFO abductee Jack Sarfatti, Tony Smith, Peter Woit, and their friends.

Coleman-Mandula theorem

Recently I was stunned that a person who has been a string theorist couldn't understand, despite months or years of working on similar questions and months or years of hearing the right answer, what the Coleman-Mandula theorem actually implies. There seems to be a whole industry of people who are just not getting it.

So let me say a few words about the theorem. They asked what symmetries "G" the scattering matrix of a physical theory can have. They assume that it is a group that contains the Poincaré group as a subgroup. If the Poincaré group is not a symmetry, the theory is dead. If the Poincaré symmetry is broken by small effects, a theory may be partially alive or hoping. But if it is broken by effects of order 100 percent, it is the end of the story.

Garrett Lisi's statement that the Coleman-Mandula theorem no longer holds because the cosmological constant is nonzero while Coleman and Mandula assumed the Poincaré symmetry instead of SO(4,1) is utterly naive. The cosmological constant is a tiny correction to the flat space, comparable to 10^{-120} in natural units, and the laws associated with the flat space must thus hold with the same accuracy. Moreover, full-fledged generalizations of the theorem exist for spaces with a nonzero cosmological constant.

Coleman and Mandula have shown that a theory satisfying the necessary conditions above must contain a spinless excitation and they studied the scattering of several copies of such an excitation. The scattering amplitude is constrained by the Poincaré symmetry and perhaps other symmetries. If you require that there exist Noether conserved charges arising from symmetries that are neither internal (scalar charges) nor the momentum (a vector from the Poincaré symmetry), you can see that it is such a strong constraint that the scattering amplitude is forced to vanish. You can do it with various quantities and prove that a theory with these new kinds of symmetries must be non-interacting, which also means physically unacceptable and uninteresting.

The only exception - found a few years later, in the early 1970s - are spin 1/2 conserved charges associated with supersymmetry. They also constrain the S-matrix dramatically but the interactions can nevertheless remain nonzero. The more general theorem that takes supersymmetry into account and excludes other possible symmetries is called the Haag-Sohnius-Lopuszanski theorem.

How fields of different spins can't be unified

The local Lorentz group in general relativity is sometimes used analogously to other gauge groups - when we write down e.g. anomalies in supergravity-super-Yang-Mills coupled system - but it is essential that physics of gravity is technically different from physics of Yang-Mills forces. Gravitons have spin 2 while gauge bosons have spin 1. It is a technical difference that doesn't spoil certain philosophical analogies between gravity and other forces. Nevertheless, it is a huge technical difference that certainly prevents you from combining the graviton and gauge bosons into the same multiplet (unless you have supersymmetry).

It might be a tempting idea to combine fields of a different spin but in field theory, it simply can't work. That's why all of the hundreds (?) of papers that tried to do such a thing have failed and hundreds (?) of similar papers will fail in the future.

Some people - see e.g. the recent paper by Nesti and Percacci - think that if they present the vielbein as a Higgs boson that breaks the local Lorentz symmetry (which is of course possible), they achieve a unification of gravity with gauge forces. That's of course a complete nonsense. If we use the vielbein approach to general relativity, the local Lorentz symmetry is an additional symmetry that is needed to make the new unphysical degrees of freedom in the vielbein decouple. Besides this symmetry, there is still the old diffeomorphism symmetry of general relativity that hasn't been moved closer to unification, not even by a millimeter. Diffeomorphisms and Yang-Mills symmetries (and, correspondingly, graviton and gauge bosons) can only be unified if the fundamental "coordinates" in the theory carry a nonzero spin.

In string theory, it is true that the string field or the first-quantized wave function combines fields of different spins. But the spin is only generated because the fundamental object, namely the string, is extended: extended objects such as strings simply can spin around their "axes". The expansion in the stringy oscillators - the Fourier modes of the coordinates and fermions over the string - generates internal angular momentum. Alternatively, Kaluza-Klein scenarios also unify these things because the higher-dimensional metric tensor is decomposed into fields of different spins in four dimensions, including a gauge field. See also Why string theory contains gravity. Additionally, gravity may be deduced from spin-two gauge invariance but not spin-one gauge invariance.

If you analyze local, four-dimensional field theories which are equivalent to point-like particles, they can't spin. The only way how to add spin to components of a field is to have spacetime coordinates that carry spin themselves. Again, spacetime and superspaces of various kinds (and the space of internal string excitations may be included in this category) are the only known spaces of this kind. Under various assumptions, we can prove that other solutions can't exist.

Of course that one has to work a little bit to see that one can't create too many new things analogous to the superspace that would be compatible with observations - or at least with basic consistency and qualitative features of physical theories - but different from the well-known superspaces in an essential way. But Jesus Christ, once you have a pretty well-defined candidate, it is a straightforward homework exercise to show that it can't work.

Stephon Alexander and Fabrizio Nesti, just sit down and try to derive the free particles and their leading interactions from whatever bizarre theories with mixed internally external symmeties and with frame-Higgses you consider conceivable. I guarantee that you will fail and mature physicists know why you will fail. Or analyze what global symmetries remain unbroken and try to follow the Coleman-Mandula procedure. What you're doing is just a completely childish and trivial sequence of mistakes and meaningless mathematical masturbation that puts you into the same category as Tony Smith or Garrett Lisi.

And that's the memo. (By Luboš Davros-Motl.)

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reader Unknown said...

Here is what Garrett replies to your post:

Lubos' post is a hoot!

First he makes two statements that are blatantly wrong, and uses these to justify saying there's no physics in the paper. Then he attacks the physics in the paper. Heh.

His only rational attack is based on the Coleman-Mandula theorem, the abstract of which he kindly provides a link to, but evidently didn't read, since the first assumption of the C-M theorem is stated there in the abstract, and doesn't apply in the case at hand, as stated in the paper. The only other arguments he employs are ad hominem, based on my association with other non-string researchers who I am proud to call colleagues.

I couldn't have asked Lubos to write a more helpful critique, as it fails in its goal of tearing down the paper, while confirming just how different this E8 theory is from string theory.

reader Luboš Motl said...

Dear fringan and others, too bad that Mr Garrett Lisi thinks that pointing out that a paper is adding bosons with fermions, fields of different spin and dimension, is not a legitimate criticism.

The issues about the assumptions of the Coleman-Mandula theorem are discussed in the fast comments. Of course that one can't circumvent the Coleman-Mandula theorem just by saying the sentence about SO(4,1) that Garrett Lisi did.

Realistic theories must still be Poincare-invariant with a high accuracy. For example, the cosmological constant deforming the Poincare group to the de Sitter group is a tiny perturbation of order 10^{-120}. Such a tiny correction can only cause comparably tiny corrections to the conclusions of the Coleman-Mandula theorem. Garrett Lisi violates the conclusions by a quantity of order 100%. He violates its very essence which is of course incompatible with the theorem.

Moreover, full-fledged theorems generalizing the theorem to spaces with nonzero cosmological constants exist, too.

Every person with at least elementary physics intuition - even if she knew nothing about the generalized theorems above - would know that a tiny effect such as the observed cosmological constant simply cannot kill the entire conclusion of a theorem, without leaving an infinitesimal trace of it.

But Garrett Lisi has no intuition about current (or even 50 years old) particle and theoretical physics, just like he has no knowledge about it and no innate aptitude to work on it.

reader BurningStar said...

I agree with goetz.

You come off sounding like a pissed off jew, what with your name calling and frivolous arguments.

Yea, all signs definitely point to you being a jew.

reader Script Uncle said...

I did not intend to comment on this thread. I am not very well versed in physics.

I think that the most significant information to be gathered from Iumo's post is not his ancestry (and the one proposed would if anything be a compliment, from my perspective :) but whether he *has a point*

I.e. If he is truly (yet again) trying to set someone straight who has a blatant fault in their reasoning - it can only be a good thing.

if he himself has faults in his rebuttal - go ahead, show us the money.

Trolling, though, feels a little bit 80's (for those of us who were there)


reader GaryB said...

I don't know bosons about physics, except perhaps at the level of levers and other useful stuff, but I'm in the field of machine learning, computer vision and, dare I say it? "AI". So crackpots come with the territory, since so little is actually known about the territory. I think TOE suffers from this too.

Some crackpots are very interesting people at the level of drinking buddies who often have other interesting hobbies (I bet Garret *is* a pretty good surfer/snowboarder because it takes a kind of obsessiveness to be a crackpot).

As for "AI", who knows what the "I" part really is? But one can still make useful progress in robotics, clustering etc

reader Unknown said...

Excellent post, Luboš.

BurningStar, you're obviously an educated and enlightened individual. *cough* But do us all a favor and drop off the face of this planet.

reader Carl Friedrich said...

burningstar - considering that Jews have won about 100 times more physics Nobels than one would expect based on their percent of the world's population, they have every right to be "pissed off". Pissed off because they have to share this Earth with the likes of atavistic pissants like you.

reader Unknown said...

It would be interesting so see Lisi proven right, though.

Because if what you argue is true (sans personal attacks, because these things (like number of citations, for example) are irrelevant to the truth of Lisi's theory anyway), then verification of his theory means that a lot of what we've known about physics and math turn out to be actually wrong.

Now wouldn't that be fun.

reader Luboš Motl said...

That would surely be fun but "fun" is something different than "truth", too. In fact, as seen in this and many other examples, "fun" doesn't even guarantee something to be remotely conceivable.

Unfortunately, many people's wishful thinking is incomparably stronger than their rational reasoning. By many orders of magnitude.

reader Unknown said...

Hi, Lubos. Could you explain with some detail this:

If we use the vielbein approach to general relativity, the local Lorentz symmetry is an additional symmetry that is needed to make the new unphysical degrees of freedom in the vielbein decouple.

Which are the new unphysical degrees and how does the local SO(3,1) deal with them?


reader Luboš Motl said...

Dear patxi,

the (symmetric) metric tensor g_{mn} has 4.5/2.1 = 10 components at each point, assuming four dimensions.

On the other hand, a vierbein e^m_a has 4x4 = 16 components at each point. That's more than the number of components of the metric tensor.

If you do a local Lorentz transformation of the vierbein at a given point, you can obtain other vierbeins that generate the same metric. Because the Lorentz group SO(3,1) is 6-dimensional, there is a 6-dimensional equivalence class attached to each value of the vierbein.

This means that not all 16 degrees of freedom in the vierbein are physical: only 16-6 = 10 of them are, precisely matching the metric tensor.

The local Lorentz transformation that changes the vierbein but not the metric is a gauge transformation, analogous to those in Yang-Mills theory. It must be - otherwise new particle excitations would appear in the spectrum (many of which would have negative norm - negative probabilities - bad). However, the action is different.

But for every gauge symmetry of this kind, you must require that only the states in the Hilbert space that are invariant under these local gauge transformations are physical. This effectively means that the wave functional has the same value for all configurations that differ by local Lorentz transformations acting upon the vierbeins.

But what I want to emphasize is that besides this SO(3,1) local Lorentz group, there is still an additional, diffeomorphism symmetry - 4 parameters (vector) per point. Physical states in a quantum theory also have to be invariant under diffeomorphisms (at least those that become trivial at infinity).

The SO(3,1) group might look analogous to Yang-Mills groups from particle physics but it is only the artificially added part of the gauge symmetry. The diffeomorphism group is not similar to the Yang-Mills group of the Standard Model and it cannot be unified in any naive Lisi-like way, of course.

Best wishes

reader Unknown said...

Crystal clear, thanks for your great explanation. :)

reader Maciek Sykulski said...

"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."

reader Anonymous said...

Hi! I am just a crusty international old-fashioned physicist, now at Princeton. But the strategy sketched in the previous comment shows that it is often a good idea to read the original sources instead of their wrong misinterpretations.

MacDowell and Mansouri do not use bundles with the SO(4,1) structure group but bundles with the symplectic Sp(4) group. And in the case of extensions of gravity with fermions, they need to replace Sp(4) by OSp(1,4) instead. Anyone can check it. Without the symplectic group, the unification hand-waving is impossible. And the symplectic group cannot be embedded in the way envisioned by the Lisi article.

The second mistake above is arguably more serious. One simply cannot include any Grassmann numbers into ordinary connection: only Grassmann-even terms are allowed. Whether some components of the connection look like the fundamental representation is irrelevant. As far as E8 is concerned, the 248-dimensional representation is both fundamental as well as adjoint. But what is needed for the standard model matter are fundamental representations of the standard model group, not the E8 group.

But the distinction between the fundamental and adjoint representations is a completely different distinction than the difference between Grassmann-odd and Grassmann-even numbers. That is a simple reason why Mr. Lisi's words about the fundamental representations cannot possibly have any relevance for his "unusual" statement that one may include Grassmann numbers in an ordinary connection.

reader FrédéricLN said...


This is my first comment on a scientific blog - and see, this wave of interest towards physics may be a good side of the Lisi affair, as boring and time-consuming as it can be for qualified scientists !

As a 15-years-old pupil in 1981-82, I was wondering about some properties of circular permutations sets ; just recently, I discovered that my wonders had geometrical implications (I blogged this, not to lose it, on, and thanks to you and Lisi (and my friend Roland Besnaïnou, also a non-specialist, who told me about the affair), I have now seen a connection between that pupil thoughts, symmetry groups, and physics.

Whooh ! Had I known this before, I might have went on into a PhD (I stopped after a 5-years degree and went into social sciences). Cause I guess I could have liked that kind of Weltanschauung (yours as well as Lisi's). But I was a zero in analysis (integration and such) and even fell short to understand properly what a renormalization group is.

Well, you in the field, go on, and thank you for discussing your points as openly and frankly as you do !

reader Professor R said...

hi Lubos, enjoy your blog.

Note on history of physics.

Re Lisi controversy, I note all of you refer frequently to the Coleman-Mandula theorem, as is standard practice.
Did you know that the first proof of the impossiblity of combining the internal symmetry of Gellmann with the Poincare symmetry of space-time was furnished by the Irish physicist Lochlainn O' Raifeartaigh?(my late father). The 'O'Raifeartaigh no-go theorem' was a hugely controversial result at the time, as mentioned in Dyson's book 'Symmetry Groups'. My understanding is that the debate was finally closed when Coleman and Mandula published a generalization of the theorem. Given the original controversy, it seems a pity that the original theorem is never referred to now (although it is liberally cited in the Coleman-Mandula paper) other words dad got all the flak but is now forgotten. That said, I don't really understand the details, being a humble experimentalist..

reader Luboš Motl said...

Dear Prof R, that's very nice. Lochlainn O'Raifeartaigh (I hope that the link is not too insulting for your surname!) :-) is the first person from the history textbooks who comes to mind - and papers - these days when supersymmetry breaking is discussed so at least there's some credit besides his partly forgotten contributions concerning combined symmetries. Enjoy your experiments, Lubos

reader French said...

the Coleman-Mandula theorem assumes a background spacetime with Poincare symmetry, but Lisi's theory doesn't have this background spacetime - with a cosmological constant, the vacuum spacetime is deSitter. So this theory avoids one of the necessary assumptions of the theorem, and is able to unify gravity with the other gauge fields. On small scales though, Poincare symmetry is a good approximation, and on those scales gravity and the other gauge feels are separate, in accordance with the theorem.

reader French said...

I almost forgot this but using bosons and fermions in the exact same structure is not in direct violation of CM theorum. Why? The exceptional Lie algebras F4, E6, E7, and E8 have some unusual (for Lie algebras) characteristics: they are based on Octonions and they are combinations of adjoint representations and spinor (or half-spinor) representations of Spin(n) Lie algebras. It is the second characteristic that lets you use both fermions and bosons.

reader Luboš Motl said...

Dear french, no, your comments are wrong and they have already been discussed in the fast comments, slow comments, and the main article itself.

A nonzero cosmological constant doesn't prevent one from proving the Coleman-Mandula theorem and from excluding the kind of mixed symmetry proposed by Lisi and many others. There are several ways to see it.

First, the C.C. is a tiny correction, so the original conclusions for the Poincare case must hold with a great accuracy. Quite clearly, they are 100% broken.

Second, full-fledged versions of the theorem have been proven even for nonzero cosmological constant cases.

Your second comment is wrong at several different levels and this basic confusion of yours has been discussed many times, too.

First of all, you confuse fermion vs. bosons with fundamental vs. adjoint. These are two completely different criteria to distinguish objects. Bosons don't have to be in adjoint and fermions don't have to be in fundamental. There is actually a third distinction that you completely omit - integer vs. half-integer spin.

This thing (spin) is correlated with statistics for conventional physical fields but may be violated for various kinds of unphysical fields. There are thus at least three different criteria - spin, statistics, representation of the gauge group - that you confuse but you shouldn't.

Second, all these three different problems show that the paper is wrong. In a correct theory, one cannot add bosons and fermions (meaning commuting and anticommuting objects), one can't add integer spin with half-integer spin objects, and one can't add adjoint representations with fundamental representations either. The gauge bundle is always in the adjoint.

Fields or particles with different spins or kinds of representations can only be linked to each other if one has a symmetry - such as supersymmetry - that either carries half-integer spin, or is anticommuting (as in SUSY, both cases), or transforms as a non-adjoint representation of the gauge group. Neither of these things is present is Lisi's paper. Each of these problems separately would be enough to see that the paper is wrong but he seems to have all these mistakes (and many more) simultaneously.

You are also clearly using many words whose meaning you completely misunderstand and you shouldn't be doing so. You can only learn physics step by step, assuming that you are sufficiently comfortable with each concept that you include into your vocabulary. If you get used to using the word "fundamental" while not knowing the difference of this word and this word "fermionic", you just become guaranteed to emit the same kind of nonsense as you wrote above all the time.

reader Professor R said...

Apologies Lubos, I hadn't realised Sidney Coleman had recently passed away. Unfortunate timing for drawing attention to the O'Raifeartaigh theorem...

The tribute on your blog is lovely - Sidney was clearly a well-liked, self-effacing man (like so many of the top theory guys) and deserved his fame many times over.

You're quite right about SUSY breaking, Lochlainn always considered it was his most important contribution (as well as a way around the no-go theorems!). Too bad he didn't live to see next year's experiments, along with his dear friend Julius Wess (another gentle giant of physics)...

In fact, if SUSY particles are detected, I wonder is it the first time in physics that experiment lags theory to the extent that a whole generation of theorists have gone on to the great blackboard in the sky before results are available....Cormac

reader jrc said...

The socilogy of this thing is wrong: Garrett Lisi contacted the press to indicate he was a new Einstein (where is the bomb?) - last time this was done was for cold fusion. And of course, the physics is wrong as well.

reader Gandolf said...

Find a group big enough (and E8 is huge) and you will find a spot for all the particles, especially if you do not worry about their spins. So you can claim that Coleman and Mandula were wrong, mix things in an arbitrary way, and claim you are a genius. Did someone try this with E6 or SU(10)? Bigger is better... especially in the surfing community. The good thing about Garrett Lisi's paper is that the color pictures can be used as Christmas ornaments. Soon to be found at a K-Mart near you?

reader Unknown said...

I note Garret Lisi's TFE geometrical similarity to "trisine"

particularly the triangular nature.

As a general comment:
All of these particles represent a breakup of the trisine resonant structure, like taking the 3 dimensional object (trisine) and breaking it into pieces. More energy more pieces. But the trisine form stands on its own at all dimensions from nuclear to cosmic scales.

As such, I would interpret Garret's TFE model as expressed in Tables 6-8 and animation as various "breakup" expressions of trisine through the z axis.

Richard D. Saam

reader AHAU SURFBOARDS said...

muy bien chicos, esto esta muy bien. yo no soy fisico, nisiquiera matematico, jejeje, soy artista, y muchos diran que cojones hace este personaje aca opinando. tengo alguna pregunta para ustedes.
1 cual es el problema de que haya una tehoria nueva en el planeta, acaso las anteriores se han demostrado ya como realidades tangibles?
2 si esta tehoria del todo no es cierta, como funciona el todo en este universo ?
3 creo que ya se demostro que einstein, no tenia razon? pero sin embargo segimos arrastrando desde entonces sus consecuencias
4, por que un fisico cuando no le cuadra una formula se saca una constante de la manga y nadie le dice nada, acaso no vivimos bajo unos conceptos de fisica falseados?
ok i just write first on spanish sorry i just need a refernce for translate from.
ok guys this looks so beautifull, i´m no physicist, not even matematics, olso my english its patetic, hehehe, i´m just an artist, closer to the filosofy tham the empiric science, and probably many of u guys would think about what a fuck is this guy it´s doing round here.i just got few questions about.

1 which one it´s the problem about "new tehory " on the planet. did the ones before has been demostrated as absolute true? i mean the ones supously makes run this universe from some body star thinking about.
2 if this tehory it is´nt rigth, them how things relay works on this universe?
3 i hear ones that eintein was´nt rigth at all, if that´s true , why we still working unther thouse parameters?
4 why when any physicist has a theorem or theory who does not realy work by itself, them they take a contant or number from the poket of any of his old pants to make it work? and no body says nothing, i mean, are we living unther false fisics concepts?
5 what do you think about making think people that some thing its the reallity when it just a theory?
do you guys still thinking that we realy come from the monkey? or that every thing starts at the "big ban"?
whats the way to say or to think that a theorem or theory can be use as an "elementary relative true"?, making shadow to others hundred of theories, that will never be show to the normal people, while sistem insist on that we should believe?

sorry for my bad english .
i just post it cause probably you guys are smarter and full of knowege tham me on this field.

i´ll hope you guys will understand my point and my curiosity thats all about.

greeting from spain guys

reader Alex said...

I'm not a physicist, but you bring up the analogy of a chess board to illustrate the point that given enough placeholders all the elementary particles can be fit into some shape given enough placeholders. How is this any different from the extra dimensions being added to string theory in order to make the equations fit what has been observed?

Thank you.

reader Luboš Motl said...

Dear Alex,

the difference is that extra dimensions (as you correctly anticipate) actually do generate the physics - interactions, cross sections, forces, spin - that has been observed while the chessboard or Garrett Lisi's pictures don't.

It's the same difference as the difference between pouring oil and pouring water to your SUV. One of them works and the other doesn't. Not sure whether this difference is sufficiently important for readers but I happen to think that it is important.

For example, it can be easily shown that the simplest Kaluza-Klein background with an extra circular dimension reduces to general relativity plus the Maxwell system (plus an extra scalar). It was shown as early as in 1919. It can be equally easily seen that the Lagrangians written in Lisi's paper don't reproduce a single kind of force or matter particle that they should, neither their spins, nor their statistics, nor their interactions etc.


reader Berlin said...


I think that in a period that nobody has come up with a complete, predictive theory, everyone with a new and maybe promising approach should be taken seriously. You point at flaws in Lisi's proposal and say its completely different from string theory. I am not so sure. In the birth of QM Heisenberg came up with matrices nobody understood. Schroedingers picture was much easier to grasp, allthough it took a Max Born to interpretate its statistical nature. Someone else (Dirac?) proved that both approaches are identical. I think that you should investigate the possibility that both approaches will turn out to be the same. Nobody has seen extra dimensions and they could easily be a maths trick to get the right answers. The same with complex calculus where you go to complex space to solve certain real integrals!

reader Luboš Motl said...

Dear berlin,

I respectfully but completely disagree with your opinion that a "special era" justifies to take anything seriously, including blatant nonsense.

First of all, I don't think that we live in a special era. As far as all criteria go, the progress in the recent era is close to the historical average and the very notion that something is slower these days is generated by grumpy crackpots and charlatans.

Second of all, I think that both in normal eras as well as in special eras, science must respect certain scientific standards and avoid nonsense, irrationality, and mistakes. The only reason why certain people vehemently disagree with insisting on the scientific method is that they want to flood theoretical physics with nonsense because it is the only thing they can do and it is what they want to be paid for.

Lisi's theory might be more different or less different than string theory but this is not a key thing. The key thing is that it is wrong. It doesn't agree with very basic facts about Nature such as the existence of fermions.

It doesn't reproduce any kind of interaction between matter particle, not even qualitatively, and can't agree with basic properties of particles such as their different spins. The only role that string theory or grand unified theory or anything else can be relevant for making this argument is to show you frameworks where these things actually work. If Lisi knew grand unification or even string theory - I mean physics, not just some basic facts about group theory - he would know why his theory is wrong, much like particle physicists know it.

The role of groups including exceptional groups in grand unification has been analyzed for 30+ years and people who do it have tested certain possibilities and know which of them work and which of them don't. Of course that an outside can learn relevant things from the scratch and bring a new theory. On the other hand, most outsiders propose nonsense and this one is no exception.

Most random deviations from a working GUT-like theory simply end up with a theory that doesn't work at all - and this is exactly what Lisi is doing: adding random mutations to a grand unified framework. Using similar words and mathematical tools but using them incorrectly and ignoring all kinds of physical "details".

Concerning your Dirac analogy. Two a priori completely different approaches to a set of physical phenomena may be equivalent - we say "dual" these days and we know dozens of major very non-trivial and fascinating examples.

On the other hand, slight modifications in a simple framework that uses similar concepts is almost always guaranteed to lead to a different outcome. In this case, we don't have to rely on probability estimates: we can actually see that the theory written by Lisi can't include almost anything from particle physics. His proposed theory is not a mysterious bombshell that might revolutionize physics next year. It is an exceptionally simple set of equations - he says it himself - and it is thus exceptionally simple to see whether it works or not. It doesn't.


reader Dany said...

Lumo said:”This means that not all 16 degrees of freedom in the vierbein are physical: only 16-6 = 10 of them are, precisely matching the metric tensor.

The local Lorentz transformation that changes the vierbein but not the metric is a gauge transformation, analogous to those in Yang-Mills theory. It must be - otherwise new particle excitations would appear in the spectrum (many of which would have negative norm - negative probabilities - bad). However, the action is different.”

Notice that U(4) matches your arithmetic’s.

Regards, Dany.

reader danfitzpatrick said...

Lisi might be right and Lubo might be wrong.

Lubo says:

How fields of different spins can't be unified

The local Lorentz group in general relativity is sometimes used analogously to other gauge groups - when we write down e.g. anomalies in supergravity-super-Yang-Mills coupled system - but it is essential that physics of gravity is technically different from physics of Yang-Mills forces. Gravitons have spin 2 while gauge bosons have spin 1. It is a technical difference that doesn't spoil certain philosophical analogies between gravity and other forces. Nevertheless, it is a huge technical difference that certainly prevents you from combining the graviton and gauge bosons into the same multiplet (unless you have supersymmetry).

It might be a tempting idea to combine fields of a different spin but in field theory, it simply can't work. That's why all of the hundreds (?) of papers that tried to do such a thing have failed and hundreds (?) of similar papers will fail in the future.

You are correct Lubo that these fields are entirely different but there must be some similarity because why does a high gravitational star bend starlight?

What if gravity and inertia are caused by quark spinors which are at an exact square of the electron spin frequency?

What if the quark spinor is an exact harmonic of the electron spinor?

E-8 seems to be telling us that there is some harmonic relationship here.

Lubo mentioned general relativity. Now the tensor math of general relativity has tensors for space but no tensors for force. then how is force derived in general relativity?

Repulsive force is seen as more space than average between the two items and attractive force is seen as less space than average between the two items.

This means force can be substituted for space!

Are these spinors producing space as well as force?

This is what Lisi's concept may be telling us!

If the electron spin causes magnetism and sigma and pi chemical bonding then can the more massive quark spin, at the square of the electron's spin frequency, be causing gravity and inertia?

Is this why we have the principal of equivalence and the quantity c squared?

I believe I'm going to listen more to Lisi and less to Lubo!

reader Luboš Motl said...

Dear Dan,
why gravity bends starlight?

Because gravity acts on every form of matter or existence. In fact, it acts equally on all of them - because of a basic property of gravity called the equivalence principle.

Even in Newton's picture, it would bend light - just 50% of what it does in general relativity.

But the fact that gravity acts on something doesn't mean that it is unified. ;-) It means that these two things interact with each other. Indeed, virtually any pair of two things in the world interact with each other.

But that is a very different thing from their being unified. The Sun acts on you when you are getting suntan but that doesn't mean that you are a Sun.

Sorry but I won't reply to the rest mixing spinors, light, harmonic E8, gravity, and all words with each other because it doesn't sound that it was written by a mentally healthy person and I will be erasing the same kind of crap that someone else tries to post.

I didn't write this text to attract the craziest lunatics in the world.

reader Stuntman said...

Don't knwo squat about physics except that if I jump I land. My science is to do with things that bleed, and even that is behind me. I work with people now - much more interesting than test tubes.

What strikes me here is that there is a lot of ego stuff flying around. I know careers and funding streams can hang in balance but if you are realy up for a theory of everything then surely Lisi's theory is worth looking at. At least it is potentialy testable when the Large Hadron Collider comes on line.

And if Lisi's theory turns out to be wrong? Well he'll go back to the surfing and snowboarding with a bit of egg on his face - no harm done and you string theory boys can get on with your smug we told-you-so we're so brainy-it-hurts theorising that is not even testable in our current understanding of the universe.

If, on the other hand, Lisi is correct and his theory does come up with particles that the Large Hadron Collider demonstrates, you boys (and girls) will be choking down humble pie for the rest of your pitiful careers, whilst Lisi laps up the Nobel. You won't even have the surfing to fall back on.

Think on it...

reader Unknown said...

All the personal attacks by Lubos just demonstrates how desparate the string theorists are. Their world is crumbling beneath them and there is nothing that can be done to save it. When it is said, "For example, the cosmological constant deforming the Poincare group to the de Sitter group is a tiny perturbation of order 10^{-120}. Such a tiny correction can only cause comparably tiny corrections to the conclusions of the Coleman-Mandula theorem.", we can see someone who has staked his whole career on the silly notion that something like out-of tune-guitar strings can be manipulated mathematically to represent the fundamental nature of the universe. If One want's to know what is wrong, examine so-called string theory. It produces an almost infinite number of wrong answers. In fact, most of Lubos's objections have already been addressed, or have been proven by more objective minds to be groundless. E8 may or may not provide additional insight, but with this post, Lubos has shown he is bitter and resentful of the media attention Lisi has received, and nothing more.

reader Mitchell said...

Pseudonymous commentators who understand no physics,

Please understand that string theorists are not idiots and that the criticisms made of Lisi's theory are in general correct! Under the most optimistic interpretation possible it is nowhere near being able to make relevant predictions, because it is qualitatively wrong (fermion generation structure) with no ideas about how to fix it (you can't superpose the "triality partners"). And then there is the whole problem of quantization. I see two avenues for Lisi here. One is the line he takes in his lecture, where he says "It's not an exact Poincare symmetry, therefore CM doesn't apply." That is exceedingly unlikely to work as the CM theorem has generalizations for such situations. The second approach is to say that since his action actually breaks the E8 symmetry, it doesn't really put fermions and bosons into the one multiplet, and so those fields can just be quantized normally. That would mean it's not really an E8 theory (the full set of fields would still be nominally E8-valued, but would no longer have E8 symmetry), so I can't think that it's a very appealing option to its author, but at least you might have a well-defined theory. There's also a third handwaving idea about getting fermions from BRST ghosts.

I am a little more open than Lubos to the idea that Lisi's ideas might inspire something worthwhile (beyond people studying representation theory and eventually becoming string theorists, which is something I can imagine happening to myself), but then I wouldn't know a quarter of what Lubos knows about physics.

reader Zephir said...

Mr. Garett's work is a sort of geometric mysticism in its current state indeed, but it still doesn't mean, it CANNOT have robust physical meaning. The most important point (which wasn't mentioned till now) is, the Lie group is not just void geometrical structure. It's root system is describing the tightest structure of kissing hyperspheres, where the kissing points are sitting at the centers of another hyperspheres, recursively. The Aether Wave Theory proposes at least two dual ways, how to interpret such structure.

The cosmological one is maybe easier to realize: it considers, the current Universe generation is formed by interior of giant dense collapsar, which behaves like black hole from outer perspective. This collapse was followed by phase transition, which proceeded like crystallization from over-saturated solution by avalanche-like mechanism. During this, the approximately spherical zones of condensing false vacuum have intersect mutually, and from these places the another vacuum condensation has started (a sort of nucleation effect). We can observe the residuum of these zones as a dark matter streaks. The dodecahedron structure of these zones should corresponds the E8 group geometry, as being observed from inside.

The second interpretation of E8 is relevant for Planck scale, i.e. for outer perspective. The dense interior of black hole is forming the physical vacuum, which is filled by spongy system of density fluctuations, similar to nested foam. Such structure has even a behavior of soap foam, because it gets more dense after introducing of energy by the same way, like soap shaken inside of closed vessel. Such behavior leads to the quantum behavior of vacuum and particle-wave duality. Every energy wave, exchanged between pair of particles (i.e. density fluctuations of foam) is behaving like less or more dense blob of foam, i.e. like gauge boson particle. Every boson can exchange its energy with another particles, including other gauge bosons, thus forming the another generation of interacalated particles.

Therefore the E8 Lie group solves the trivial question: which structure should have the tightest lattice of particles, exchanged by another particles? And such question has even perfect meaning from classical physics point of view! Such question has a perfect meaning in theory, describing the most dense structure of inertial particles, which we can even imagine, i.e. the interior of black hole.

reader E.N. said...

reader blogger said...

As a software developer I just have to say, "there's more than 1 way to skin a cat" I won't pretend to have understood 1/10th of what was written in the blog and relevant comments, and I'm not saying that Lisi is absolutely positively right about everything in his paper; but, I agree with the few posts that even though not everything about it may be correct, perhaps it's worth looking into something a little more. With Lisi's popularity, perhaps more people will start to take an interest in physics and even the string theory people can get some notice.

Perhaps the moral of this story is not that one person is right or wrong, but that Lisi appears to know how to represent himself and furthermore speak about his theory in terms that more people will understand. Unless the point of physics is to simply confuse everyone so much that they can't prove you wrong, it may do some good for the physics community to learn some people skills. (pot calling the kettle black as a computer programmer here I know)

Anyway, interesting read even if it did make my head hurt. Open your minds to multiple theories and see if you can work with what they've given instead of jumping down their throat for being wrong.

reader E.N. said...


Let me put Mr Lisi's theory into a software developer's perspective.

Imagine you are a top notch programmer at some company, and you were tasked to lead a project with a colleague. You both agree to split the work up and integrate it at some future point.

One day you get to a point in your code writing where you need to ask how your colleague approach some particular problem; you go to his office and find multitudes of little tiny stickers of different shapes and colors pasted over his computer monitor, to the point that it would be impossible to see the screen. You later find out that your colleague couldn't even start his computer.

I think from this point you can finish the story...

reader Bohred said...

As I see it, Motl is a prof at a fairly decent university and is therefore likely to be speaking some sense much of the time. Lisi is a surfer dude and amateur physicist and therefore quite likely to be speaking less than sense a lot of the time. The Daily Telegraph writer seemed to be saying "Einstein wasn't part of the physics establishment when he made his most profound contributions to physics; Lisi is not part of the establishment, therefore he is the new Einstein". Lisi has a doctorate in physics. If he makes such basic errors, it makes me wonder whether doctorates are given away these days.

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