Garrett Lisi’s Theory of Everything!

Garrett Lisi has a new paper, “An Exceptionally Simple Theory of Everything.” Many people seem to think that I should have an opinion about it, but I don’t. It’s received a good deal of publicity, in part because of Lisi’s personal story — if you can write an story with lines like “A. Garrett Lisi, a physicist who divides his time between surfing in Maui and teaching snowboarding in Lake Tahoe, has come up with what may be the Grand Unified Theory,” you do it.

The paper seems to involve a novel mix-up between internal symmetries and spacetime symmetries, including adding particles of different spin. This runs against the spirit, if not precisely the letter, of the Coleman-Mandula theorem. Okay, maybe there is a miraculous new way of using loopholes in that theorem to do fun things. But I would be much more likely to invest time trying to understand a paper that was devoted to how we can use such loopholes to mix up bosons and fermions in an unexpected way, and explained clearly why this was possible even though you might initially be skeptical, than in a paper that purports to be a theory of everything and mixes up bosons and fermions so casually.

So I’m sufficiently pessimistic about the prospects for this idea that I’m going to spend my time reading other papers. I could certainly be guessing wrong. But you can’t read every paper, and my own judgment is all I have to go on. Someone who understands this stuff much better than I do will dig into it and report back, and it will all shake out in the end. Science! It works, bitches.

For a discussion that manages to include some physics content, see Bee’s post and the comments at Backreaction.

241 Comments

241 thoughts on “Garrett Lisi’s Theory of Everything!”

  1. Sandra,

    E8 is a symmetry group, a mathematical structure. Expanding E8 to the size of the universe is a statement that makes no sense. The statement that a “theory of everything” is described by the E8 symmetry group is a statement that the most fundamental constituents of the universe are invariant under rotations in the E8 symmetry group.

    A way of visualizing this is if you imagine that the fundamental constituents of the universe are fully described by a series of numbers (I couldn’t tell you how many, I’m not familiar with the particulars of E8), then the obedience of E8 symmetry means that changing those numbers in a specific way (an E8 rotation) does not change the physics: the particle behaves the same whether we describe it with the numbers before the rotation or after the rotation.

    For a more down to Earth example of how such symmetries work, we can take spatial symmetry. If you want to describe the motion of a ball rolling on a table, you can do so using a variety of possible choices of axes. You can place the origin at the center of the table, or at any of the four corners, or anywhere else you like. You can also label the numbers with inches, or centimeters, or meters, or anything else. No matter how you label the table with numbers, though, the ball behaves the same.

    This can be decomposed into a discrete set of symmetries. Some of them are simple translations: if you move your coordinate axis left or right, forward or back, and the equations that describe how the ball moves remain identical (because the table is flat). This simple fact ensures that momentum is conserved. If you instead rotate the table, you find that once again the equations that describe its motion remain unchanged. This symmetry ensures that angular momentum is conserved. Then you can show that as time moves forward, the equations that describe the motion of that same ball still remain unchanged, and this ensures conservation of energy.

    The E8 symmetry is a similar statement: if we make an E8 transformation to the numbers that describe a particle, if the equations of motion obey E8 symmetry, then the equations of motion will not change after the transformation. What would be conserved in this situation would be a set of charges, much like the electric, weak, and strong charges which are described by known physics.

    Hopefully this wasn’t too cryptic.

  2. 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.

  3. Any enthusiast who has read Garrett’s paper front to back even without understanding all the math can get an excitement about the unification of what we all expected was unifiable but didn’t expect would be so hard to unify.

    I’m wondering if the mapping of these into E8 will eventually in some way correlate to the mapping of living systems in terms of what their real functions are versus those which the consciousness insists exists. For example our consciousnesses insist on a certain smoothness which the sensory systems don’t actually exhibit. Our mind fills in.

  4. I wish Lee Smolin would read Jacques Distler’s blog more often. The group theory part of Lisi’s paper has been completely debunked and yet, Smolin completely ignores this and gives Lisi his stamp of approval. The scientific standards of the LQG community seem to be really low these days.

  5. I am not an expert, but here is my take, based in part on statements by Lisi at PhysicsForums.com. You say you’re a neophyte, so I’ll emphasize one idea, and that is the construction of a quantum theory from a corresponding classical theory through “quantization”. Physically that means introducing the uncertainty principle; mathematically it means reinterpreting the basic equations as operator equations.

    Lisi starts with a field theory which can be called “BFE8”. The fields and their interactions all follow from the E8 symmetry. Then he adds some extra terms, in the way described in Smolin’s paper. The resulting theory has a MUCH smaller symmetry, first appearing in the “Pati-Salam model”, so I’ll call it a Lisi-Pati-Salam model.

    It looks to me as if BFE8 theory exists classically, and as if this Lisi-Pati-Salam model exists classically AND as a quantum theory; but that there is no evidence that BFE8 theory exists as a quantum theory, and that one has good reason to think it does NOT exist as a quantum theory, namely, the Coleman-Mandula theorem. If there is no “quantum BFE8 theory”, then the use of E8 structure constants as coupling strengths in Lisi’s extended Pati-Salam model is just an eccentric way to specify their values and has no particular logic to it.

    I should back up here and say that in generic quantum field theories, coupling constants (field interaction strengths) are parameters that mathematically you can choose as you wish; but in a theory with a particular Lie group as a symmetry, those numbers will be determined by the algebra. So it would make sense for a theory which REALLY has an E8 symmetry to have couplings determined by the E8 algebra. But if Lisi’s Pati-Salam model is not actually descended from a genuine quantum E8 theory, the use of those numbers is quite arbitrary.

    Lisi and Smolin both say (in effect) that a quantum BFE8 theory exists and that it evades the Coleman-Mandula theorem because… well, sometimes the reason is that it has a de Sitter metric rather than a Minkowski metric, sometimes the reason is that it has no metric at all and is purely topological. My hunch is that this is a mistake, that their critics are right in this regard, and that quantum BFE8 theory simply does not exist. Certainly, if they wish to claim that it does, they need to exhibit it, somehow.

    As for Distler’s debunking… Lisi’s attempt to squeeze the Standard Model and gravity into (his preferred representation of) E8 appears to be doomed for algebraic reasons independent of the quantization problem. So the reports about ’20 new particles’ whose masses need only be calculated are wrong. Any particular equation that can be written down right now is known to be wrong even before one tries to calculate particle masses. So any attempt at E8-based unification is going to involve changing one or more of the premises defining Lisi’s original approach. Change them enough and you could end up just reinventing string theory, in which E8 also features.

  6. I did look at Dsitler’s blog and there is, to my understanding, only one issue was raised in his discussion of Lisi’s paper that was not already raised by Lisi himself in his paper and talks: this is that Lisi muffed the nomenclature for non-compact forms of E8.

    The question is whether the open issues are solvable issues or not. Distler thinks not, Lisi thinks perhaps yes. I don’t see what there is to be gained by arguing, the burden of proof is on whether the issues can be solved and so the only thing to do if one is interested is to work on them. Some of the open issues are straightforward to address, given that there is a literature on this kind of unification, beginning with Peldan in 1992. So in my recent paper I describe how to make a fully gauge invariant action for proposals of Peldan and Lisi’s type, and I also suggest an alternative approach for the fermions which mght resolve some of the other open issues. The gauge invariant action is, btw, the starting point for quantization using LQG and spin foam methods.

    I don’t understand the fuss about the CM theorem, which concerns global symmetries of the S matrix. In a gravitational theory, which Lisi’s is, global symmetries are symmetries only of solutions or of asymptotic conditions and are not the same as the local gauge symmetries. Indeed, even though my local gauge symmetry is some semi-simple G, I display a solution whose global symmetry is a subgroup of G, namely SO(4)+H where H is the largest compact subgroup of G/SO(4). (The same would work with Lorentzian signature.)
    Even if G=E8 this is in accord with the CM theorem.

    In case it comes up, let me emphasize that while I do think that Lisi’s paper has enough interesting about it that it is worth working on the open issues, I also think that the press coverage was premature and told that to the journalists who contacted me. The “Fabulous…” quote by me was taken out of context-it was a remark made spontaneously to a few people just after hearing his talk and quoted-in some cases without permission-and without the cautionary statements that I empahsized to the journalists that contacted me.

    Finally, let’s put this in context. Often the first publication of an important new idea is incomplete and comes with open issues. (Consider Glashow’s 1961 paper on the weak interactions or the 1954 Yang-Mills paper, among many others.) Lisi’s paper is a candidate for such an idea. He himself is honest and consistently emphasizes the high risk nature of his proposal and the open issues and weak points, in his paper, talks and conversations. My view is that the idea deserves some time to see if it works out. Meanwhile, there are better developed ideas about unification such as Chamseddine-Connes that deserve more attention and investigation than they are getting.

  7. This is really not the place to argue about the technical merits of Lisi’s theory. My whole original point is that the paper did not, on the face of it, look nearly interesting enough to warrant all this attention, and the subsequent discussion has borne that out.

    Saying “there are still some issues to be ironed out” is a cop-out. In addition to the mentioned problem with mixing gravity and internal symmetries, the original theory was not unified, not quantized, and somewhat ad hoc. Jacques pointed out in his first post that you couldn’t embed all three fermion generations in E_8, which Lisi admitted was true, and in a new post he shows that you can’t even embed one generation. If anyone does not agree, it would make sense to point out why over there. And “new proposals sometimes don’t fully work at first” doesn’t count; if the Standard Model can’t be fit inside E_8, there is nothing even conjecturally interesting about the proposal.

    This is a sad case where media attention gave an utterly incorrect view of the scientific process.

  8. Lee: “I did look at Dsitler’s blog and there is, to my understanding, only one issue was raised in his discussion of Lisi’s paper that was not already raised by Lisi himself in his paper and talks: this is that Lisi muffed the nomenclature for non-compact forms of E8. ”

    Dear Lee, Jacques has a second posting about Lisi’s paper where he makes another explicit group-theoretical on why his idea does not work. I’d like to hear what your opinion is.

  9. Dear Sean,

    We agree that there was too much media attention. I advised every journalist I communicated with to delay writing about this until the paper could be digested by experts, to some of them I suggested waiting a year. At the same time, there has been way too much hostility and nastiness on the blogs. Only with the greatest hesitation did I post something about this. Several of the issues you mention are directly addressed in my paper, as I give an action which is fully gauge invariant, not ad-hoc and is directly amenable to quantization with known techniques. And I exlain there and above the full answer to the CM issue about mixing gravitational and internal symmetries. My view is that getting the gravity-Yang-Mills unification right makes it interesting enough as there is already an interesting idea about how to proceed to incorporate the fermions, which I also mention in my paper. I worded my paper carefully and I would much prefer to spend my time working and writing papers or discussing the technical issues going forward than repeating things that have been already said.

  10. I would also like to hear what Lee (or other people who believe that Lisi’s idea is somehow interesting) has to say about Distler’s second post, where he shows that one cannot even get one generation right, since the embeddings lead to non-chiral fermions. And about his idea (still unproven though) that perhaps all embeddings in E8 lead to non-chiral fermions, which would render the whole idea useless. Perhaps Distler’s blog is a better place for that though, if Lee or other people feel like replying to these arguments.

    I’m quite amazed to see that no one in the people who think that this theory may be interesting have bothered replying to Distler’s arguments, which are rather clear and purely group theoretic, and to say the least rather crucial…

  11. “E8 is a symmetry group, a mathematical structure”

    Well I can’t see what sense E8 makes as a symmetry group here. Lets talk about the algebra here. It is defined by its commutation relations. Sometimes a symmetry is spontaneously broken, but then the commutation relations are still valid; some of the generators are then non-linearly realized. So the symmetry is still there, but in a sense hidden.

    In this case, some of the generators, namely ones related to spinorial roots are declared fermionic, and thus must anticommute rather than commute. Such a construction works in the case of superalgebras resp groups. But E8 is not a superalgebra, and has only commuting generators. So declaring some of them to be fermionic, doesnt make any sense to me. There is no way that E8 as a symmetry group is realized in this theory, not even “broken”. The theory does not provide the correct commutation relations.

    So why speak about E8 at all in this context? It is simply not there!

  12. From my understanding of the Lisi business, which is very limited due to lack of interest, there are two aspects which need to be distinguished.

    First, both fermions and bosons belong to the same E8 multiplet. This is surely plain wrong. Second, bosonic internal and spacetime symmetries might be unified in de Sitter space with a bosonic algebra. Although I am skeptical about this, it does not seem obviously wrong. The CM theorem depends on the S-matrix, but there is no S-matrix in de Sitter so there might be a loophole here.

    Alas, there is another way to evade the CM theorem which I have not seen mentioned: don’t unify internal and spacetime symmetries. 🙂 In fact, it is an underappreciated triumph of the non-unified SM that it very economically explains baryon number conservation and the longevity of the proton.

  13. Dear Vincent,

    I haven’t responded because unfortunately I’ve been swamped with other priorities and haven’t had time to check this out in detail. But since there have been repeated requests, here is what I am thinking about this.

    1) There is no issue for the euclidean, compact case.

    3) Distler does not point to a specific step in Lisi’s paper which he claims is incorrect. This makes me wonder if Distler’s claim is a non-sequitor or based on a misunderstanding. While I haven’t checked in detail, I am puzzled that there is no mention in Jacques’s post of the Pati-Salam chirally symmetric theory, as that is what Lisi’s paper shows is embedded in E8. While I haven’t worked out the details, the Pati-Salam is a vector theory where parity is only broken spontaneously. Fermions in the Pati-Salam model are in parity symmetric reps, because of the overall parity invariance of the theory. In Pati-Salam parity is broken spontaneously, leaving chiral fermions at low energy. As I haven’t checked the details I don’t know if this is the answer to Distler’s objection but the fact that it is nowhere mentioned is worrying.

    4) Distler was largely wrong in his previous post as he been several times before in discussions on other issues. (The one criticism he made that was correct and not mentioned already by Lisi had to do with the nomenclature of non-compact forms of E8.) So I would urge caution. This is a highly technical issue that needs care to get it right.

    4) Distler’s last remark “And, no, I don’t intend to comment on the REST of Smolin’s paper….” implies he believes that something in his post addresses something in my paper. But there is nothing at all in this post relevant to the results of my paper. Even ignoring the condescending tone, this seems to me sloppy and makes me cautious about accepting his conclusions about other things without checking.

    If I can add, I fail to see the value of these one sided arguments where one side plays fair and admits mistakes and open issues and credits strong points on the other side, but the other side plays nasty hardball. Not only is it not fun, it is of little positive scientific value and indeed it’s counterproductive as this kind of nasty debate has been the source of many falsehoods and misconceptions, because those who originate them never apologize or admit error. In the exchanges with Lisi so far we have Lisi himself emphasizing the open issues and questions, and the other side making a spectacle of arrogantly criticizing him for issues that they didn’t realize he had already discussed.

    There is nothing wrong with making mistakes, but the spirit of science requires that we acknowledge them. I would strongly urge those who want to criticize other physicists’ work in a public forum do it professionally, without personal attacks and with a constructive and fair attitude. Most importantly, if you criticize, then be fair and acknowledge when your own criticisms have turned out to be wrong and be generous about acknowledging when your criticisms have been answered by further work. If we all played fair in these ways I think that more of these online debates would end in agreement and increased understanding.

  14. Lee,

    If you have any technical critiques of my two posts on this subject, please leave them in the comments on my blog. If you just want to make ad hominem attacks, please go ahead and do that over here.

    However, this cannot go without a response.

    If I can add, I fail to see the value of these one sided arguments where one side plays fair and admits mistakes and open issues and credits strong points on the other side, but the other side plays nasty hardball.

    Who’s the one not playing fair, here, and admitting to mistakes?

    I cheerfully admitted to several mistakes in earlier versions of my post(s). They were either

    a) inconsequential, so that, when corrected, they made no difference to the result, or
    b) overly generous to Lisi’s case, so that, when corrected, they made the situation worse for him.

    Distler does not point to a specific step in Lisi’s paper which he claims is incorrect.

    No, instead I point out numerous such steps.

    This makes me wonder if Distler’s claim is a non-sequitor or based on a misunderstanding.

    My claim is very clear. And, since it cuts to the heart of what Lisi is trying to do, I cannot understand how you could possibly call it a “non-sequitor” [sic].

    While I haven’t checked in detail, I am puzzled that there is no mention in Jacques’s post of the Pati-Salam chirally symmetric theory, as that is what Lisi’s paper shows is embedded in E8.

    Maybe you should read my second post more carefully.

    While I haven’t checked in detail,…. While I haven’t worked out the details, … As I haven’t checked the details …

    That would be a place to start, then, wouldn’t it?

    There is no issue for the euclidean, compact case.

    Could you explain what you mean by that remark? What is it that you claim “succeeds” in the Euclidean case?

  15. A hint to those too young to remember the Pati-Salam model. The left-handed fermions in that model transform in a complex representation of SU(4)xSU(2)xSU(2), specifically, the (4,2,1)+(4bar,1,2).

    Lisi also has the electroweak SU(2) embedded in an SU(2)xSU(2). There, however, the similarity with Pati-Salam ends.

  16. Thomas Larsson said, about “the Lisi business”:
    “… both fermions and bosons belong to the same E8 multiplet. This is surely plain wrong …”.

    Could Garrett Lisi’s model be understood in terms of a 7-grading of e8 that was described in a sci physics research thread Re: Structures preserved by e8, in which Thomas Larsson said:

    “… … e_8 also seems to admit a 7-grading,
    g = g_-3 + g_-2 + g_-1 + g_0 + g_1 + g_2 + g_3,
    of the form

    e_8 = 8 + 28* + 56 + (sl(8) + 1) + 56* + 28 + 8* .

    …[in]… the above god-given 7-grading of e_8 … g_-3 is identified with spacetime translations and one would therefore get that spacetime has 8 dimensions rather than 11. …”.

    So, if you used g-3 for an 8-dim Kaluza-Klein spacetime,
    could you see the 28* and 28 as the two copies of D4 used by Garrett Lisi to get MacDowell-Mansouri gravity from one and the Standard Model gauge bosons from the other
    and
    see the central sl(8)+1 being related to transformations of the 8-dim spacetime
    (actually being a 64-dim thing that is substantially 8×8* ).

    The even part of the grading would then be the 112 elements
    28* + 8×8* + 28
    and
    the odd part of the grading would then be the 128 elements
    8 + 56 + 56* + 8*
    If the 8 and 8* are used for 8-dim Kaluza-Klein spacetime
    so
    could the 56 + 56* be used for fermion particles and antiparticles ?

    Even if the above assignment needs improvement,
    my basic question is

    could Thomas Larsson’s 7-grading of e8 be useful in making Garrett Lisi’s model a realistic description of physics ?

    Tony Smith

  17. Ask, and ye shall receive.

    Lee complained that I didn’t use the phrase “Pati-Salam” in my post, so I added an appendix, where the phrase is used liberally.

    It’s not clear why that is supposed to make things better. But if it helps Lee understand that Lisi does not even get one generation of quarks and leptons, let alone three, then it’s worth it.

  18. Dear all,

    I do agree that being condescending is not only annoying but also not useful to the point you want to make, since other people tend to stick to the condescending part of the argument rather than the technical part (as we can see, as an example, from Lee’s reply above). It would be great one day if we, as theoretical physicists, could discuss issues politely, with humility, in a nice and friendly fashion, as we usually do when we discuss with friends around a beer. However, I fear this is not what is happening on blogs; in the present case, on both sides of the story (to Lee: saying that one side is nice and friendly after having produced a few “kind of personal” attacks is not very honest I feel — and I am not attacking you on this, just trying to understand your comment above; similarly to Lisi calling his paper a Theory of Everything is not very humble, nor honest, assuming he understood (as he claims) that his theory was very far from being a Theory of Everything — if such a thing exists — etc. I could give plenty of examples of hype, non-honesty, non-humility from both sides, if there is such a thing as “sides”).

    In any case, I dream of the day when we can talk to each other on blogs with humility, as friends. And this we do all the time when we meet in person. But on the other hand, I can also understand some people’s comments on blogs, following from years of exasperation, which I fortunately haven’t experienced myself.

    This being said, on the other hand we are all profesionnals, and should all be able to ignore what we feel is condescending in someone else’s post and focus on the real, technical arguments. I try to think that we are not stupid, and raise above the “you attack I counterattack” level… If someone feels that someone else has been condescending, in the middle of a well-explained technical argument, then perhaps that someone should be able to ignore that thing he feels is condescending and concentrate on trying to reply to the actual argument. In which case, the condescending thing just loses it role, which was precisely that, to make the other one feels “lower” and reply to it by counterattacking. The best way to stop this “attacking the other one” tradition which is often present on blogs is just not to reply to the attack I feel, no? We should all be able to do that. And if one feels he gets too angered and needs to reply immediately, well just take a breath, relax, do something else, and come back a few hours later… just let the anger go away, and then we will be able to have meaningful discussions on blog. I like to follow physics blogs because very often there are insightful physics arguments and discussions hidden in the middle of useless personal attacks. But it would be so much better if the noise was reduced…

    And on the point at hand, I would, again, like to hear, in more details, what Lee, or other people like Lisi, have to reply to the technical points in Distler’s second post. This should probably be done on Distler’s blog, as he suggested. I do personally think that Distler’s argument is fundamental to make any sense of Lisi’s proposal, and can hardly ignore it or dismiss it because of whatever I could think of Distler’s behavior on his blog. 🙂

    Just my 2 cents 🙂

  19. Vincent said, about physicists discussing controversial non-mainstream things:
    “… we are all profesionnals, and should all be able to ignore what we feel is condescending in someone else’s post and focus on the real, technical arguments …”.

    Unfortunately, there is a long tradition otherwise in the USA physics community, going back at least around 50 years to the time Oppenheimer (as head of IAS) said of Bohm:

    “… Oppenheimer went so far as to suggest that “if we cannot disprove Bohm, then we must agree to ignore him.” …”.

    Tony Smith

    PS – The quote is from the Bohm biography Infinite Potential, by F. David Peat (Addison-Wesley 1997) at page 133. A bit more quotation shows that it is not an isolated quote out of context: “… Max Dresden[‘s] students formed a Bohm study group. … Dresden was forced to read Bohm’s paper. He had assumed that there was an error in its arguments, but errors proved difficult to detect. He had also read von Neumann’s “proof” and realized that it did not rule out the sort of theory Bohm had proposed. … Dresden visited Oppenheimer and asked his opinion of Bohm’s theory.
    “We consider it juvenile deviationism,” Oppenheimer replied. No, no one had actually read the paper – “we don’t waste our time.” …”.

    PPS – Anyone who was ever fortunate enough to have met Max Dresden knows that he was a brilliant physicist of impeccable honesty.

  20. A small clarification. Let us define a parity invariant theory to be one in
    which there is a Z_2 symmetry which includes inversion of the spatial
    coordinates (in three spacetime dimensions). Let us also define a chirally invariant theory as one in which, after writing all fermions as left-handed
    Weyl fermions, the fermions are in a real representation of the gauge group.
    Lee uses these two terms interchangably, which is unfortunate, and can lead to confusion. The Pati-Salam model with SU(4)xSU(2)xSU(2) gauge symmetry is
    parity invariant. To achieve this invariance one must extend the “usual”
    parity symmetry by a Z_2 which interchanges the two SU(2) factors in the gauge
    group. However, as correctly pointed out by Jacques, the PS theory is not chirally invariant because the fermions are not in a real representation. Since Jacques showed that the embedding used by Lisi gives a real fermion representation, he is correct in saying that the Lisi embedding does not contain the PS model. Lee is incorrect in saying the opposite, and indeed would be well advised to understand the details of work that he intends to build on. One can (and should) break the parity symmetry in PS spontaneously, but this does not suddenly generate chiral fermions from non-chiral fermions. The fermions were chiral to begin with.

  21. “Vincent said, about physicists discussing controversial non-mainstream things:
    “… we are all profesionnals, and should all be able to ignore what we feel is condescending in someone else’s post and focus on the real, technical arguments …”.

    Science is done by scientists. We are all human and should be able to pursue our research in a way that makes for a welcoming work environment. I’ve been pretty damned close to quitting physics, more than once, because where it seemed to be dominated by hostile, arrogant, immature men who are completely unable to grasp the essence of the words ‘collaboration’ and ‘communication’, not to mention essentials like politeness and reliability. Somebody can be oh-so-intelligent, if he’s not willing to express ‘real, technical arguments’ in an appropriate way, chances are he’ll end up being a hostile, arrogant, immature, bitter men who tells everybody he’s done everything already decades ago. The internet makes communication failures even more likely. Best,
    B.

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