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. Tyler,

    I don’t know about the noise drowning out the signal. The raised hackles are indicative of the significance the various scholars place on the discussion.

    And putting aside the human bits of personality, the discussion has been extremely valuable as we all start exploring different ways of looking at the actual physics. I’m certainly learning a lot, and I doubt I’m the only one.

    –Nathan

  2. Thank you everyone. Now that the discussion has come to a reasonable conclusion, it is time to summarize:

    LS: I have said 2+1 = 4 . Distler does not point to a specific step in this which is incorrect.

    JD: Try reading again what I wrote (not just here, but in the blog post I linked to): 2+2=4 .

    LS: I haven’t checked in detail, I am puzzled that there is no mention of subtraction.
    If it is just a terminological mixup that is of course fine for this issue, and what you mean by 2 is different from what I meant by 2, so although I agree I may have been imprecise, the essence of my statement remains correct.
    It matters not the context in which you do this.

    Anon1: The problem is that JD was not polite in his explanation.

    Anon2: Oh boy, here we go again with smokescreen tactic that Woit/Smolin use whenever they’re losing an argument of accusing the other side of being impolite.

    PW: I really think string theorists like yourself should, instead of attacking me and Lee for pointing out a problem, give some thought to how much damage your own partisans (anonymous and not) are doing to your own interests.

    LS: It is true that the statement 2+2=4 is disrespectful and therefore unconvincing.
    The point is to convince other scientists to change their minds and to do this you must show your respect for them and you must reason with them. Suppose I work in a Lorentzian metric, then is it not true that 4-1=2 ?

    JD: 4-1=3 . If you really want to have a technical discussion, with equations, you might consider moving things to my blog, where the fonts are better.

    Anon1: why are string theorists always so nasty?

    B: I’ve been pretty damned close to quitting physics, more than once, because people are so impolite. Best, B

    PW: It’s not just the public that is coming away with the impression that there’s something quite odd about how string theorists choose to engage in scientific discussion. Even if what he says is true and not so impolite, it still can never be tested.

    LS: Thanks for your kind words, but with respect, this resolved only the point I queried. I have more technical questions about missing steps in Jacques’s arguments which would need to be filled in before I understand it.
    Unless I am having a particularly opaque day, his remarks on 2+1 are incorrect.
    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.

    Anon3: Of course, I cannot follow the technicalities of this exchange.
    This being said, on the other hand we are all profesionnals, at least those of us who know how to spell.

    LS: He was largely wrong in his previous post as he been several times before in discussions on most other issues.
    Even ignoring the condescending tone, this seems to me sloppy and makes me cautious about accepting his conclusions about other things without checking. There are many logical gaps in his argument which need to be resolved.
    You understand that to be taken seriously a scientist who wants to criticize other scientist’s work must be professional and precise in its criticisms. It’s quite likely that we use ‘=’ to mean different things.

    Anon5: The problem with “tone” is a real one.

    B: I’d hope any discussion about the “tone” and similar issues would just be unnecessary. It certainly wasn’t my intention to distract from the technical argumentation with a ‘rhetorical strategy’. Best, B

    Anon3: There are too many comments like this one complaining about the lack of physics content making it difficult to find the physics content.

    JD: The complete triumph of form over substance. For the correct meaning of the ‘=’ sign, see my blog where it occurs in the correct font

    LS: Perhaps if what you say is correct, it could still be that 1+1+1=4.
    Finally, what is the best reference to understand why there are only these ways of decomposing 4 into positive integers and where the results you quote come from?

    Anon6: why don’t you crack open a book about integers

    PW: I suppose one could have predicted that the response to pointing out that anonymous insults on physics blogs are a problem would be anonymous insults.

    Anon6: once again i am not anonymous. i always use the pseudonym anon6.

    TS: there’s a 7-grading of e8

    Anon3: It’s difficult to concentrate with all this noise.

    WS: A pox on both your houses

    Anon7: There you go again,

    Anon8: Hey, stop kicking.

    Anon9: You started this.

    Anon1: You embarrass yourself with namecalling.

    Anon6: You embarrass yourself more by complaining about the namecalling.

    Anon2: Can you imagine seeing transcripts of your heros acting like this?

    PW: I just finished reading (and writing about on my blog), an excellent book about borderline mental illness and the temptation of anonymous comments on internet forums.

    B: Sadly, I have heard remarks like this very often. That’s not a single sorry story, that’s the way I have seen it happening over and over and over again. Best, B

    JD: 1+1+1=3 . It’s called thoroughness. There are more details in better fonts on my blog, and a recipe for goose. Now back to etiquette and anonymity.

  3. Nathan, by “noise” I meant the meta-discussion. Not the heat; the ad nauseam discussion of the heat, its validity, etc, the minutiae of netiquette – all of which is really a solved problem, the answers are known, though sadly rarely applied. A small meta-discussion is valid to keep that heat at a level where communication can still happen. Of course people get upset, snarky, and even downright mean at times. It’s when this causes the whole discussion to spin off in postmodernist self-analysis that it counts as noise.

    Since the technical content of this thread has dropped to zero I don’t feel guilty about the dense irony field surrounding this post, which is a meta-critique of the above-mentioned meta-discussion.

    amused, as a nonprofessional, group theory is even more above my head than usual. The degree to which I fail to care whether Mr. Lisi’s paper is correct or not cannot be adequately expressed in written English. As an outsider I have the luxury of viewing the progress of science on long time scales. However there were a lot of interesting things happening in this thread that, for me, counted as “signal” – and it seems that a lot of professionals were finding signals of interest in the thread as well. But naive discussions of functional netiquette were last interesting in 1996 by my reckoning.

  4. Thomas Larsson said “… the anthropic landscape proves that string theory is unable to say anything definite about our universe, and the non-discovery of SUSY and extra-dimensions at the LHC will (if it happens) disprove the scientific part of string theory”.

    If I were a string theorist, I would certainly be interested in explanations of electroweak symmetry breaking that would look maximally dull at the LHC – by which I mean not only no low-energy supersymmetry or Kaluza-Klein modes showing up, but not even a Higgs. It would be a bet against the belief that there must be something exciting around the next corner just because we haven’t looked yet.

    I was surprised to read at Jacques Distler’s blog that it’s actually very hard to find something that emulates the Standard Model in string theory (1, 2), despite the variety of phenomenological avenues being considered (see section on “Phenomenological attempts” here). That the landscape implies no predictions may be a gross exaggeration. Even if there are very large numbers of stable vacua, just knowing a posteriori that there are (e.g.) three generations of chiral fermions may narrow things considerably.

  5. I was mercifully away from the internet all day, glad to see that string theory partisans took the opportunity of not having noise produced by me to have a high-level discussion. It seems like I was wrong about Jacques, I guess he was just having an off-day yesterday.

  6. If I were a string theorist, I would certainly be interested in explanations of electroweak symmetry breaking that would look maximally dull at the LHC – by which I mean not only no low-energy supersymmetry or Kaluza-Klein modes showing up, but not even a Higgs.

    This isn’t possible — a Higgs or some other new physics is necessary to satisfy unitarity.

  7. Dear All,

    Yesterday was a bit too nasty, but before we close this discussion let’s talk about what actually happened. First, if one ignores all the posturing and blustering, the points I made about Pati-Salam stuck. Notice that in the last few exchanges between Distler and I he doesn’t disagree with my points, he just changes the subject, for example by suggesting we move the discussion to his blog. What were these points? What we established before it got too nasty was that the fermions are in a rep r which has all the following properties:

    1) It is chiral in the standard sense (see 99 and 151)

    2) When taken in full as a rep R_ps, as defined in previous posts, of lorentz+H where H=su(4)+su(2)+su(2) it is parity invariant.

    3) R_ps is also pseudo-real.

    It was important to establish these points, because they bear on Lisi’s proposal and more generally for model building of this type. Pati-Salam is not a trivial point to be filled in, it is the key to whether Lisi succeeds or fails. This key point was not commented on by Distler or anyone here until I brought it up.

    I also asked what properties a Lie algebra G has to have so that it has a subalgebra of lorentz + H, with a representation that on breaking to the subalgebra gives R_ps. My question, central to understanding if anything like Lisi’s proposal can work, was based on the fact that the situation was rather different than the case of the usual standard model where 2 and 3 don’t hold.

    Distler did in 165 offer a general statement, “If the embedding of SL(2,C) in the non-compact real form of G is related by Wick rotation to an embedding of Spin(4) in the compact real form of G, then R is non-chiral.” So far as I can tell this is false because G=SO(3,1)+H is itself a counterexample to it, given the above. Were there further discussion this would be the place to start.

    Let’s look next at what happened in my dialogue with HIGGS. It was somewhat useful until I made a precise point explaining how two of the criticisms he made of Lisi were answered by my construction in a paper of a gauge invariant action. His answer was to make an unprofessional content free insult.

    I want to emphasize that I entered this discussion late and reluctantly after being asked my views by people on it. The reason for my reluctance was that I believed it would have more value to actually solve one of the issues facing Lisi’s proposal than to just argue about it. It happened to be possible to solve a key issue-that of exact E8 gauge invariance- quickly and make a conjecture about other issues. I wrote a very carefully worded paper explaining these. I also took the time to explain carefully why the CM theorem was not relevant and also, on the other side, to make it clear that there are open issues with aspects of Lisi’s proposal not addressed in my paper.

    Notice that in the subsequent discussion here and on Distler’s blog, not one of the Lisi’s detractors show any evidence of having read or understood this paper. This speaks volumes about the extent to which we are dealing with a one sided situation. One side is fair and open minded, easily admits mistakes and points out open issues and weaknesses in their proposals (no one does this more than Lisi himself.) The other side rarely admits mistakes, and never retracts claims even when they have been thoroughly debunked. (Notice how many people wrote to say they were wrong about the Coleman-Mandula issue: zero.) Notice how they construe everything I say in the worst possible light, as indicating ignorance or error on my part, this is, friends, nothing but a classic debating tactic of people without the truth on their side.

    Unfortunately this is not the first time myself and other people who see a value in being fair minded have tried to have a constructive debate with Distler, HIGGS and others of their posse of anonymous detractors. They always use the same tactics and the result is always the same. They never admit error but they decrease their credibility in the eyes of fair minded people.

    So here is what took up the space that could have been devoted to a genuine scientific discussion: When I made a simple mistake of notation I was insulted by anonymous people piling up. And when I made correct points which were not rebutted, the same people just pile up even more insults.

    The overall impression is very sad. In a recent conversation Lenny Susskind urged that in judging the behavior of any scientific community you should judge by the best people in it, not the worst. I agree and have tried to do so. But the people posting here anonymously make this hard to do.

    So what is really happening here? What has happened is that one very smart, but intellectually isolated young theoretical physicists has made a bold and risky proposal for unification of physics. Due to his personal circumstances, he got much too much media attention-something everyone including him agrees about and several of us including myself tried to stop. A bunch of people who think they own the territory of unification are enraged. They react with all the classic symptoms of territory defense that the sociologists of science have catalogued. More troubling for them, Lisi’s proposal is set in the language of LQG, a rival approach which they already irrationally oppose because they think it threatens their hegemony over the territory of unification. The resulting behavior displayed makes my tentative conjectures about group-think look way too cautious, here we see all the classic signs of intellectuals acting irrationally because they feel their territory is threatened.

    Now, it is the case that there are open issues with Lisi’s proposal. He himself emphasizes them in his paper and talks. So there is intellectual work to do to develop and understand if the proposal can work. In a professional atmosphere there is a lot to talk about and examine, for those who judge it worthwhile to put the time in, but that is not what happened here.

    What did Distler contribute? He made a first post, where he mainly pointed out issues that Lisi himself had already emphasized. He also made a proposal about which non-compact form of E8 Lisi was using, which he then retracted in a second post, where he also claimed to make a clinching argument that Lisi’s proposal must fail. The main issue that is highlighted is the brittleness of the structure of the two non-compact real forms of E8 and the possibility that Lisi’s proposal cannot fit any of those forms.

    Does Lisi’s proposal survive Distler’s second post? Even if there is some truth to Distler’s argument, is the result the end of Lisi-like proposals or are there alternatives which evade it? For example, by going to the complexification? Or might it be that Lisi’s proposal works for the Euclidean spacetimes but not for lorentzian? Might it be that it only works if only part of the lorentz algebra is gauged, as in the Ashtekar or Thiemann formulations? All these are interesting possibilities and I would have liked to have participated in a debate that resolved these issues. I do think we made some progress. If we could have stuck to a serious discussion we might have gone further. But just at the point where we made progress, Distler decided he was not interested in continuing the discussion here and the anonymous hecklers piled on. And it got so nasty that, unless there is a big change of tone and the anonymous hecklers apologize and withdraw or are deleted and banned, I see no point in trying to continue to have a constructive discussion here.

    Of course someone will follow this with a re-assertion that the issue is settled. Remember that these are the same people who have refused to acknowledge it when a paper is posted with results that answer some of their criticisms. So we are not dealing with people who play fair, and argue honestly. I am afraid those claiming the issue is settled have done nothing to increase my belief in their claims in this discussion. I entered this discussion hoping we could find resolution, what I encountered was a toxic and nasty atmosphere in which it was impossible to get a simple yes/no answer to a simple question without facing a lot of blustering and nastiness. One needs a clear head to think through this stuff and this is not a context conducive to gaining that clarity.

    Part of the posturing of Distler and his friends is to suggest that the math is trivial-at least to them-and that anyone who doesn’t agree with them is simply incompetent or incapable. I suggest anyone who is tempted to fall for this act either talk with a mathematician who is actually an expert on E8 or try to work through the details of its construction in the math books. In fact, I am told that behind the scenes all the key actors in this little melodrama have been consulting with pure mathematicians in their efforts to get the fine points right.

    I’m sorry if we can’t go further in this context, but I’m sure further study will clarify the issues in due time. Meanwhile, if something thinks they indeed have a careful argument that Lisi’s proposal fails, I’d be grateful if they explain it clearly in an email and send it to me. I’ll study it. And if its right I’ll say so. As I noted before, I have no particular stake in the outcome, especially since there are a number of interesting alternatives if the precise form Lisi proposed fails. Indeed, as one of the authors of a different unification scheme within LQG, if anything, I have a stake in Lisi’s proposal failing. If fact, I simply want to know what is true.

    So I have some proposals to make:

    1) I propose we either improve the tone drastically or close this discussion now. There were a few flashes of science above, but this has turned into too much of a gladiator fight for reasonable discussion. I could have dealt with Jacques alone but I have lost patience arguing with people without names who do not play by the least rules of fairness. Maybe in another forum where people have self-respect and manners-or where the moderators have a policy of deleting and banning personal attacks- this discussion can continue, but not here.

    2) As I said before it’s in any case time for the experts to consult off-line. I’m happy to discuss off line any of these issues with anyone, so long as they put their name behind their words. But if you are someone who lacks the courage to put your own reputation at stake when you trash someone else’s then I don’t care what you have to say, and I don’t see why anyone else should care either.

    3) Anonymity is a big issue. While I prefer a gentler intellectual environment I can handle arrogance and nastiness face to face. I grew up in one of the toughest environments, the Harvard physics department of the late 70s. But there were two differences. One, people said what they had to say, face to face. When someone called you an idiot he was right there and he listened when you argued back. And if you miffed a definition or a factor nobody cared, we all did, it was not about debating points, what was important was to invent, play with and discard ideas on the way to the truth. Further, the people setting the tone had earned the right to their arrogance by doing the one thing that really matters in science, which is publishing predictions that turned out right when the experiments were done. No one here has earned that right. It took courage to stand up to them, and after that education I can’t imagine how anyone who has pride in their views and accomplishments could hide an attack on the reputation of a colleague behind anonymity.

    4) Those running blogs need to take a hard look at examples such as this and ask what is being gained by allowing nasty, unprofessional and destructive comments, especially from anonymous people. Some bloggers already have a policy of deleting personal attacks such as those that dominated here or even comments by anonymous people altogether. Those of us who actually want to discuss science in a professional atmosphere will I predict be drawn to limit our reading and writing to such blogs.

    There is a beautiful vision of a blog as a place which extends globally and transparently the community of scientists, where we share in the adventure of discovery, in the context of a global community where strict ownership of ideas gives way to the joys of collective progress. Those who care about such visions should see how they are made impossible when a thread is taken over by people who want to use the context to enforce their notions of entitlement, hierarchy and ownership over issues.

    5) The physics community should take a look also at what these kinds of episodes are doing to our reputation and to our professional standards. There is no other context in the scientific community where someone can hurl schoolyard insults anonymously at a colleague, without risk to their own reputation. Since reputation is crucial for the workings of a scientific community this is not something we should allow without careful reflection as to the consequences.

    As I said before many times, I have no fear of admitting error, I enjoy shooting from the hip in informal situations and I recognize this means one often makes mistakes and learns from them. In the above debate I tried to be open minded, polite, reasonable and fair and was met with nastiness and personal attacks which persisted as much when I was right about something as when I made a mistake. In fact, the key points I made were all sustained, even if I erred a bit on the way. But it was too hard to get there because most of what I had to deal with was displays of posturing and bullying with precious little reasoning of the kind that scientists do face to face.

    As for myself, I like to keep a clean distinction between informal contexts, where I can be spontaneous, make mistakes, and still sometimes come up with an important idea or insight, and writing papers, where I am extremely careful about what I present and how it is worded and argued. I am happy to participate in the experiment of opening up the informal process online so all may participate and watch. But I insist on the primacy of the publication. This means that I cannot take very seriously people who claim to be interested in an issue and yet, in spite of the abundant time on their hands that their blogging participation shows, do not take the time to read a paper that presents new results relevant to the issue under discussion.

    I still hope that the blog format can be made to work for science. But people, it did not work here, because of the corrosive effect of personal attacks from behind veils of anonymity and because key players do not see an obligation to argue fairly, openly and in good faith. Fix these issues, and blog formats may thrive, fail to fix them, and a lot of time and effort will produce little of actual value.

    Thanks,

    Lee

    Ps I apologise if any of this seems like a personal attack. In fact, in person, Jacques and I have a friendly relationship, the last time we saw each other we had a very pleasant dinner together. I hope that fair minded people will allow me to respond to the nastiness directed at me above by at least trying to point out the tactics that are being employed which are, after all, deliberately aimed at my credibility and reputation.

  8. First, if one ignores all the posturing and blustering, the points I made about Pati-Salam stuck.

    Let’s roll the tape.

    In #90, you said

    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.

    1. Pati-Salam is not a vector-like theory. It is inherently chiral.
    2. The spontaneous breaking of parity symmetry is a complete red-herring. You can never turn a vector-like theory into a chiral theory, “leaving chiral fermions at low energies” by spontaneously breaking parity.

    In #102, you said

    In Distler’s post he asserts to the contrary that in the Pati-Salam model the fermions are in the representation he calls R_ps= (4,2,1)+(4-bar,1,2) of SU(4) x SU(2)_L x SU(2)_R, which is not parity invariant.

    It seems to me this invalidates Distler’s discussion of Pati Salam and by extension suggests that his second post on Lisi is incorrect.

    which, again, was completely wrong.

    When H-i-g-g-s pointed out your errors, you (#108) put this off to a “terminological mixup.” It is clear that the “mixup” is far more than “terminological.”

    2) When taken in full as a rep R_ps, as defined in previous posts, of lorentz+H where H=su(4)+su(2)+su(2) it is parity invariant.
    3) R_ps is also pseudo-real.

    My question, central to understanding if anything like Lisi’s proposal can work, was based on the fact that the situation was rather different than the case of the usual standard model where 2 and 3 don’t hold.

    No. In the sense you are using it (viewing the complete fermion representation as (2,r)+(2bar,rbar) of SL(2,C)xH), property 3 holds for the Standard model and, indeed, for every unitary quantum field theory under the sun.

    What is true of Pati-Salam, which is not true of the SM, is that there is a definition of “parity” such that property 2 holds.

    But that is completely irrelevant (as far as I can tell) to the rest of your argument.

    So far as I can tell this is false because G=SO(3,1)+H is itself a counterexample to it, given the above. Were there further discussion this would be the place to start.

    Further discussion would require your understanding what the phrase “chiral fermions” means.

    Notice that in the subsequent discussion here and on Distler’s blog, not one of the Lisi’s detractors show any evidence of having read or understood this paper.

    I think it’s fair to say that the shoe is on the other foot.

  9. Jacques,

    I guess with

    “Further discussion would require your understanding what the phrase “chiral fermions” means.”

    we have your response to Lee’s

    “I propose we either improve the tone drastically or close this discussion now.”

    Why do you think it it’s a good idea to try and discuss a scientific issue with someone in the nasty, insulting way that you do? It’s completely unnecessary, just impedes the process of understanding each other’s arguments, sets a really bad example for the young, and discredits this subject in the eyes of outsiders. Why keep doing it?

  10. And I will further note that I explicitly computed what “fermion” representation arises from all possible embeddings SL(2,C)x(Pati-Salam) in a noncompact real form of E_8, which proceed (per Lisi) via a D_4xD_4 subgroup.

    I also computed what “fermion” representations arise for all possible embeddings of SL(2,C)x(SU(3)xSU(2)xU(1)), which proceed via an F_4xG_2 subgroup (about which Lisi goes on for pages and pages but which he ultimately abandons).

    Since, in both cases, the embeddings fall into the general rubric of this argument, it is no surprise whatsoever that they yield a non-chiral “fermion” spectrum.

    I would repeat the remarks of comment #156, but I feel that I have done altogether too much repeating myself.

  11. The schoolyard taunts about chiral fermions seemed oddly familiar, I just realized why. If you want to see the Distlerian method of scientific argumentation about fermion chirality in a simpler SM context, stripped of the complexities involved in non-compact real forms of E8, take a look at the comment section here

    http://www.math.columbia.edu/~woit/wordpress/?p=3

    which was one of the first postings on my blog more than three and a half years ago. Jacques started off by submitting anonymous insulting comments as “Field Theorist”, but his style was immediately recognizable, so he had to give up on that fairly quickly.

  12. Just curious, Peter, but do you have anything, anything whatsoever to contribute, vis-a-vis the substance of this debate?

    I thought you were a great fan of representation theory. And you do (I assume) know what chiral fermions are.

    If you have something of substance to contribute, now would definitely be the time to do so.

  13. Lee,

    Now that some of the cons of Lisi’s paper have been identified, would you be willing to give a summary of the remaining pros?

    I don’t think it was ever clear why you stated that Lisi’s work is “one of the most compelling unification models [you’ve] seen in many, many years” *, so I’m left wondering which parts of Lisi’s work led you to that conclusion, and which of those parts still remain valid.

    I realize that you’re very busy with organizing post-doc activities and with your own research, but it seems that you’re also very dedicated to responding to blog posts, so I thought it safe to take a longshot bet that you’d find time to reply to my question.

    Thank you,
    Shawn Halayka

    * http://www.cbc.ca/technology/story/2007/11/16/science-theory-everything.html

  14. Regarding the issue of chiral fermions in the Pati-Salam model with gauge group SU(4)xSU(2)_L x SU(2)_R, the main point is that the left-handed and right-handed fermions are not in the same representations. In particular, the left-handed fermions are doublets under one of the SU(2) groups while the right-handed fermions are doublets under the other SU(2) group. Thus, it is not a vector-like theory. Lee does not seem to get this point.

  15. Jacques,

    I don’t have enough interest right now in the particular technical questions you’re discussing here to try and contribute to the discussion, and, even if I did, the toxic, nasty, bullying and insulting way that you choose to carry on such a discussion ensures that I wouldn’t bother. The reason I’m spending some time writing comments here is that I think I do have something useful and substantive to contribute to this discussion, which is an argument that you and your anonymous fans need to stop insulting people and carry on scientific discussions in a professional manner.

    If you do that, I’ll be interested enough to try and follow the discussion and try and learn something, and may or may not have something to contribute. But the way you are going about this right now is not helping anyone understand anything.

  16. Peter,

    Having unequivocally expressed your opinion on “form” and having stated unequivocally that you have no opinion (nor any interest in forming one) on “substance,” you might consider doing what you can to reduce the background noise.

    Would that be too much to ask?

  17. I’m trying to decide whether the words “nasty”, “toxic”, “bullying”, and “insulting” are words which accurately describe some of the comments on display here. Those seem like pretty harsh words and they’re probably a more accurate description of some of the things which the characters of The Breakfast Club say and do to each other. I don’t really think these words do a good job at even remotely describing Jacques comments. I think Jacques’ comments are the most useful ones on display here (I learned a lot from them!), and I really think everyone should take a deep breath and relax and not take everything (including our egos) so seriously. I don’t think the act of learning something new and contributing something substantive to the discussion should be contingent upon improvements in tone. Just ignore it. Learning is good for you, and contributing substantive things are good for others and for physics. Maybe I’m being way too naive here. I also find that some of the long, bizarre comments above seem to be coming from people who seem to have no lives. Maybe something a bit more productive would be better in the long run.

    It’s the holidays! Let’s bring on some good old holiday cheer! Let’s all donate some old clothes, toys, canned goods, and money to our favorite charities. Above all: relax and let’s not take everything so seriously or personally.

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