It’s pretty common these days for people to refer to successfully quantizing general relativity as “the Holy Grail of Physics”, but it seems to me that there is a different problem that better deserves this name:
“Why does the vacuum state break electroweak gauge symmetry?”
If we could answer this question, we’d probably understand where masses of particles come from, as well as just about all of the undetermined parameters of the standard model (except for a couple ratios of the strengths of the gauge interactions). The exciting thing about this problem is that we have good reason to expect experiments to give us some new clues about it in 2008 when data from the LHC begins to come in.
The standard unification paradigm these days explains this in terms of the potential for a Higgs field, with various grand and super-unification schemes allowing an appropriate Higgs field but somehow never being able to predict anything at all about it. Even worse, such schemes not only don’t explain anything about this field, but also require the addition of extra Higgs fields beyond the single one required by the standard model.
An idea I’ve always found appealing is that this spontaneous gauge symmetry breaking is somehow related to the other mysterious aspect of electroweak gauge symmetry: its chiral nature. SU(2) gauge fields couple only to left-handed spinors, not right-handed ones. In the standard view of the symmetries of nature, this is very weird. The SU(2) gauge symmetry is supposed to be a purely internal symmetry, having nothing to do with space-time symmetries, but left and right-handed spinors are distinguished purely by their behavior under a space-time symmetry, Lorentz symmetry. So SU(2) gauge symmetry is not only spontaneously broken, but also somehow knows about the subtle spin geometry of space-time. Surely there’s a connection here…
This idea has motivated various people, including Roman Jackiw, who has several papers about chiral gauge theories that are very much worth reading. The problem you quickly get into is that the gauge symmetry of chiral gauge theories is generally anomalous. People mostly believe that theories with an anomalous gauge symmetry make no sense, but it is perhaps more accurate to say that no one has yet found a unitary, Lorentz-invariant, renormalizable way of quantizing them. In the standard model, the contributions to the anomaly from different particles cancel, so you can at least make sense of the standard perturbation expansion. Outside of perturbation theory, chiral gauge theories remain quite mysterious, even when the overall anomaly cancels.
So, this is my candidate for the Holy Grail of Physics, together with a guess as to which direction to go looking for it. There is even a possible connection to the other Holy Grail, I’ll probably get around to writing about that some other time.
You will kindly refrain from putting words in my mouth, especially when they are incorrect ones.
If there were, indeed, a plenitude of “realistic looking vacua”, then string theory would be reduced to the level of quantum field theory, where the particle content, gauge groups, and coupling constants are input parameters, not calculable from some underlying principle.
This would not be a disaster for string theory, but it certainly would be a disappointment. I, for one, would hope that at least some of these seemingly arbitrary parameters (say, the electron-muon mass ratio, or the ratio of the QCD scale to the Planck Mass, or the values of the KM mixing angles) would be calculable in a fundamental theory.
It could turn out that they are just as arbitrary in string theory as they are in field theory. Disappointing? You bet! A disaster? Not exactly.
But, then, for a variety of technical reasons, I don’t think that’s the way things work in string theory.
Jacques means it is good for string theory if there are few realistic KKLT sorts of vacua because the alternative is a huge problem. If, as some people believe, there are 10^500 or so relatively realistic looking vacua, string theory is utterly useless for ever predicting anything. In this case, those who take string theory on faith will keep trumpeting how wonderful it is, while anyone who believes in the scientific method will stop paying attention to it.
His preferred situation is that either
1. Just a small number of the vacua now under study are realistic, and one of them is an approximation to the real world.
2. Some new non-perturbative insight will explain why the vacua now under study are not true vacua, at the same time identifying the true vacua, one of which we live in.
Needless to say, there is no evidence for either 1. or 2. other than wishful thinking.
” Vacua of this sort which look even vaguely like the real world: acceptably small rate of proton-decay, suppression of flavour-changing neutral currents, etc, etc, are very rare indeed — if they exist at all.”
What, why is this good for String theory? You better hope they exist, or else you have a close to falsified theory on your hands.
I think I agree however, it would be nice if the vacua that describes are world would look like an isolated point. It makes it in principle, easier to single out sometime in the future if we ever get a realistic mechanism that picks out vacua.
In short, I believe that de Sitter vacua with small cosmological constant exist, but are not as dirt-common as KKLT would have you believe. Vacua of this sort which look even vaguely like the real world: acceptably small rate of proton-decay, suppression of flavour-changing neutral currents, etc, etc, are very rare indeed — if they exist at all.
To say more would require equations and stuff. Perhaps I will post something on my own blog.
You didn’t. Peter did. Maybe, in the meantime, the two of you could settle between yourselves whether KKLT being right/wrong would be a triumph/disaster for string theory.
Jacques Distler wrote:
My personal opinion, contra KKLT, is that it is hard to find appropriate (meta)stable de Sitter vacua. And I view that difficulty as a good thing.
I’d be genuinely interested to hear what you mean by this. Note that I never said that it would be a disaster if KKLT can be made to work. I don’t agree with that claim. If deS can be extracted from string theory, even in a lame way, that would be major progress, provided of course that everyone admits that it is indeed lame….. The *worst* thing that can happen is for everyone to run off and hope that the cosmological constant will somehow go away while they work on something else.
It certainly seems to me that if KKLT is right, it’s a bad thing for string theory, if it’s wrong it’s a good thing but just in the sense that a bad thing didn’t happen.
If I understood what a Rutgers post-doc was trying to explain to me on the shuttle bus there a few weeks ago, he and others had found that certain conditions needed to make KKLT work were not so easy to achieve, although they did have some solutions for these conditions. So, my impression was that they thought there were fewer viable solutions than the vast numbers that were initially expected (no idea whether “fewer” means 10 or 10^50). Caveat: no, I’m no expert on this and I’m just recounting what I understood of a conversation on a short bus ride. Maybe I’ve got this wrong somehow..
I see. So, if KKLT are right, it’s a disaster for string theory. If KKLT are wrong, it’s also a disaster for string theory.
Poor bastards, they’re doomed either way!
My personal opinion, contra KKLT, is that it is hard to find appropriate (meta)stable de Sitter vacua. And I view that difficulty as a good thing.
“The rate of progress in any field is far from uniform. I’d be the first to agree that the rate of progress in string theory recently is slower than we have been accustomed to. But to call that a “crisis” is seriously overblown.”
I agree that *that* is no sign of crisis. But
the persistent failure to get de Sitter out of
string theory—that *is* a crisis. I am reliably
informed that the Rutgers gang has been trying
hard to get the KKLT proposal — and it is no
more than that — actually to work. And they
are getting badly discouraged. But Lubos Motl
isn’t, of course — he just claims, apparently
with a straight face after that nasty tic is
modded out, that it is “premature”
to worry about this! Well, the latest data
show that the Big Crunch is at least 40 gyr
away, so we still have time to get string
cosmology to work.
You really can’t help yourself…
“Just because SU(3)xU(1) is nonchiral doesn’t mean it is well-understood nonperturbatively.”
Did I say anywhere that SU(3)xU(1) gauge theory with fermions is well-understood?
“If you turn off SU(3)xU(1), you obtain an SU(2) gauge theory that is nonchiral.”
Did I say anything about turning off SU(3)xU(1)?
“Your repeated dismissal of the twistor stuff as insignificant”
Did I ever refer to Witten’s work on this as “insignificant”?
I don’t think so, since that’s not what I’ve ever thought about it. I have repeatedly, here and elsewhere, said I don’t really understand its significance, hoping to get explanations of its significance from others more knowledgeable than myself. The comment explaining to me its significance for calculating tree-level, multi-gluon amplitudes was the first response I’ve gotten to the question from someone knowledgable. The only other responses I’d gotten were incoherent rantings from Lubos Motl.
No, I’m not going to tell you who the postdocs and more senior theorists were that I was referring to, and they are unlikely to speak publicly. Besides the obvious reasons, they are unlikely to want to get publicly attacked as incompetent fools by various fanatics
I doubt it. Uninformed anti-string rants get real old, real fast. You’ll have to come up with something more interesting if you want to hold my attention.
Just because SU(3)xU(1) is nonchiral doesn’t mean it is well-understood nonperturbatively. The U(1) does not exist nonperturbatively. You identified the SU(2) gauge theory as the part that is chiral (and hence hard to understand nonperturbatively). This is incorrect. If you turn off SU(3)xU(1), you obtain an SU(2) gauge theory that is nonchiral. It is very hard to come up with an interpretation of your post, and of your responses to Mark that does not involve your asserting the contrary. Take, for instance:
There are other misapprehensions in your post. Most importantly, as Mark says, the generic quantum field theory is chiral, so “chirality” is hardly a puzzle to explain. But it’s hard to discuss the big picture when you persist in misapprehensions about the basics.
There are dozens of recent papers I find as interesting, or more interesting than the developments in twistor theory.
The rate of progress in any field is far from uniform. I’d be the first to agree that the rate of progress in string theory recently is slower than we have been accustomed to. But to call that a “crisis” is seriously overblown.
Your repeated dismissal of the twistor stuff as insignificant (a dismissal you’ve made repeatedly, both in this venue and elsewhere) is, I think, indicative of the general fact that you haven’t the context necessary to evaluate the significance of the talks you’ve heard and the eprints you’ve tried to read.
I might take seriously the opinions of the unnamed “senior theorists” and “string theory postdocs” if you’d care to tell us who they were, and exactly what they said.
Or, better yet, they can speak for themselves.
Glad to see that you’re following my weblog so closely. If you keep doing this I’m sure you’ll find many more opportunities to take something imprecise that I write, make up an interpretation of it that is incorrect, then use this to demonstrate my ignorance of basic facts. In the future when you do this, if you’re more careful, your correction might even be correct. You’re quite right that “this is getting really embarassing”, but I think we probably disagree for whom.
To try and say things in a way that will be less easy for you to misconstrue, all I was saying was the following. If you turn off the weak interactions, you have a SU(3)xU(1) non-chiral gauge theory. Turn on the weak interactions and you have something much trickier and less-well understood non-perturbatively: a chiral gauge theory with spontaneously broken gauge theory.
No, I wasn’t the guy who “had no clue as to why anyone would want to calculate multigluon perturbative Yang-Mills amplitudes”, that guy lives only in your over-worked imagination. I was the guy who knew very well that multigluon perturbative YM amplitudes were important things to calculate in collider physics, but would have guessed that the calculations were pretty straight-forward for tree amplitudes, only really difficult when you put in loops. I was very pleased to learn something new from the comment posted here.
As for whether there is any progress being made in the last few years in string theory, I base my judgment on the following evidence:
1. Multiple string theory postdocs who have recently told me they find the field in crisis, very depressing, no new ideas, to the extent that they are thinking of quitting.
2. Multiple senior theorists, string theorists and others, who have told me that there are no interesting new ideas in the subject (with the possible exception of Witten’s twistor stuff).
3. Attending talks about string theory, looking at recent talks on the web, scanning the new papers on the arxiv. No, I don’t understand everything I read or hear this way, but do understand enough of it to note that the experts I talk to seem to be right.
So, let’s get this straight: the students I mentioned are “fools”, I’m an embarassing, incompetent fool and the post-docs and senior faculty who think string theory is in crisis are also probably fools. The only people in the world who aren’t fools are you and perhaps some of the few other string theorists out there who spend their time hyping a theory which has utterly failed to provide its promised new insights into unification of physics. Have I got this right?
Make that “real,” not “pseudoreal.”
This is getting really embarassing.
For the last time. The left-handed fermions of the standard model form a real representation of SU(3)xU(1), and they form a pseudoreal representation of SU(2). It’s only when you look at the full SU(3)xSU(2)xU(1), that you find that they form a complex (ie, chiral) representation of the gauge group.
Weren’t you the guy who, until yesterday, had no clue as to why anyone would want to calculate multigluon perturbative Yang-Mills amplitude, much less how the recent work on twistors represents a revolution in our ability to do so?
What makes you competent to decide whether progress is being made?
Then they are fools. The job market, at the moment, for good young phenomenologist is considerably better than that for young string theorists. (Not that the latter is bad, just that good young phenomenologists are much sought-after nowadays.)
About chirality again:
It’s surprising if you think geometrically and take the standard view that internal and space-time symmetries have nothing to do with each other. The U(1) and SU(3) gauge symmetries are not chiral and are truly independent of the space-time geometry. The SU(2) gauge symmetry knows the difference between right and left-handed spinors so in a subtle way it knows something about space-time geometry. More precisely, it knows about the spinor geometry.
Is it a coincidence that the piece of the standard model gauge symmetry that is chiral is also the piece that is spontaneously broken? Maybe, or maybe there’s GUT lore about this I’m not thinking about. Is it a coincidence that, besides having its gauge symmetry spontaneously broken, the SU(2) chiral gauge theory is also really hard to understand non-perturbatively? Maybe.
I’ve never, anywhere, denigrated string theorists as “diletantes and poseurs”. That’s not what I think about them. Some of my best friends are string theorists, and most people doing string theory are very smart and harder-working than I am. On any metric for how smart and hard-working someone is, Ed Witten is off the scale.
Sure, I think the NSF and DOE should stop funding theorists who send in grant proposals that say “String theory has made huge progress in the last few years, we intend to keep doing the same thing”. The fact of the matter is that string theory hasn’t been making any progress and this needs to be honestly addressed. The panels that allocate very scarce funding for theoretical physics are the place this is supposed to happen.
The over-hyping of string theory is doing more damage to theoretical physics than any cut in government funding ever could. I personally know quite a few really good young students who have left physics because they saw no way to make a career for themselves in the field other than by working on string theory, which they didn’t believe in.
“As far as I can tell your point is essentially just the obvious one that since we know how to write down chirally asymmetric theories, a generic theory is going to be chiral.”
If this point is obvious, why did you say that it is “in some sense surprising” that the QFT that describes the real world is chiral?
As for anomalous gauge theories, if you (or Roman Jackiw or anyone else) can construct them, great! I’d be very interested. But I think there are very good reasons why it can’t be done, reasons that are as close as we ever get to a proof in QFT. I don’t agree that it’s “more accurate” to say that these theories just haven’t been quantized yet.
As for arrogance, when you denigrate a whole group of dedicated, hard working scientists as diletantes and poseurs because you don’t share their taste in interesting problems, it’s hard to want to be polite. Change the name of this blog from “Not Even Wrong”, a famous insult in physics, to something more neutral, and I’ll be a lot more polite in the future.
You say that you’re “not in the business of telling people what they should work on and there is no danger they would pay much attention to me if I was”. But there is. You are seeking publicity in the larger public arena, via your article in American Scientist and this blog. You denigrate a lot of hard honest work done by brilliant people. There is a small but significant chance that this denigration could ultimately have a detrimental impact on science funding.
You think that it is a terrible crime that string theory has been overhyped. But if science was better funded, more young people would have more of a chance to make an impact, however they choose to try to do it, before irrevocable decisions have to be made about their futures.
That’s why I took the time and effort to respond in the first place.
We probably did overlap somewhere back in the 80’s, I was a grad student at Princeton 1979-84. Unfortunately one aspect of middle age for me involves the inability to remember exactly people I was glancingly acquainted with back then.
Your latest post starts with the generic argument for string theory in terms of quantum gravity. Responding to that seriously would take a while and someday I’ll get around to it on the weblog.
The other comments you make about the sociology of why people do string theory are interesting and worth responding to. Again, I’ll try and do so at length at some point soon, but a couple quick comments: No, I don’t think it’s a conspiracy and I’m sure most of them do so because they think it is the best bet for making some kind of progress (this is less true of those poor bastards trying to get a permanent job). On the other hand I don’t agree with you at all that the community is now open to new ideas.
I’m not in the business of telling people what they should work on and there is no danger they would pay much attention to me if I was. My interest here is in trying to do two things:
1. Explain exactly what the present state of string theory is, minus the hype. You and others are welcome to argue with me when I do this. It’s a complicated subject and probably I’ll get some things wrong.
2. Explain some highly speculative ideas of my own. These are also “Not Even Wrong” at this point and will be clearly labeled as such.
As far as I can tell your point is essentially just the obvious one that since we know how to write down chirally asymmetric theories, a generic theory is going to be chiral. If you are a believer in Susskind’s landscape then maybe our world is governed by a generic theory and of course it is not surprising it is chiral. I may be wrong, but my point of view is to try and find something special about SU(3)xSU(2)xU(1) and the standard model representations that would explain where this symmetry comes from. The chirality of the SU(2) couplings in this case may be a clue. You may think this kind of speculation is pointless, a waste of time, has all been done before, whatever. But it’s clearly labeled as speculation, it’s just as “Not Even Wrong” as string theory. If you think my speculative ramblings are wrong-headed, don’t read them.
Anomalous gauge theories:
You seem really exercised that someone would even implicitly question conventional wisdom. Clearly we’re not going to get along here. At most points in the history of science spending one’s time figuring out the implications of new ideas is a more fruitful thing to do than questioning conventional wisdom. I think this point is different: there are no new good ideas and we need to question how we got to this point. Certainly something goes wrong with our standard understanding of gauge theory when you try and quantize an anomalous theory. I happen to think it’s worthwhile to think about this and try and better understand exactly what happens. One of my reasons is that in 2d there is some really beautiful and new mathematics that makes its appearance. Maybe this is irrelevant to 4d, maybe not.
My “tone about poor benighted theorists”:
Well, for 20 years the smartest people in the business have been to a large extent off thinking about quantizing gravity instead of electroweak symmetry breaking. Right now when I talk to them they are bitching and moaning that in string theory there are no new ideas, everything that anyone has tried either has failed or can’t be pushed further. Under the circumstances I do think it would be healthier if more of them would stop doing this and would start instead bitching and moaning about how hard it is to come up with a new idea about electroweak symmetry breaking.
First of all your initial post was simply rude and insulting. Today also brought an even more juvenile string of insults from a Junior Fellow at Harvard, Lubos Motl. What is with you people? Grow Up! Do your parents know you behave like this? You don’t know me and seem to think it’s all right to start insulting someone you don’t know on the basis of your interpretation of a couple vague sentences they write about complex issues in QFT. What about posting a comment saying you disagree with something I wrote, explaining why and asking me to justify what I wrote? Then when I can’t justify it, you’re welcome to start accusing me of ignorance.
While I was about to finish this, another post from you came through. I’ll stop this one, continue with another after reading your latest.
Looking at your credentials, I see that we must have overlapped at Princeton in the early ’80s. I confess that I thought you were a mathematician who was dabbling in physics.
As for string theory being “not even wrong”, the title of your blog, it is QFT that deserves this description.
Pick up a book. Hold it at arm’s length. Let go. Did it fall? You just disproved the Standard Model, which does not incorporate gravity.
The only known way to deal with gravity in QFT is to put in an ad hoc cutoff at the Planck scale. Then you lose either Lorentz invariance or unitarity or both. We could perhaps live with violations of Lorentz symmetry, but before giving up on it, perhaps we should search for a more clever cutoff.
And that’s exactly what string theory provides. It *may* be that it doesn’t work in the end; that’s still an open question. But *this* is why string theory is exciting: it’s an extension of quantum field theory that (1) incorporates gravity in a natural way and (2) provides the *possibility* of a finite theory that does not require an ad hoc cutoff.
The tradeoff is that it’s *much* harder to find specific quantum field theories as the low energy limit of string theory. There’s been a huge amount of work on this, work that continues at a feverish pace. A QFT that looks like the Standard Model has not been found yet. Whether or not one exists is an open question.
Senior string theorists work on string theory because they think it’s the best bet for a more fundamental theory than QFT with an ad hoc cutoff. That’s all there is to it. No vast conspiracy. People with tenure who want to work on other things, do. People without tenure have to hedge their bets on what to work on. One can certainly criticize the fairness of the tenure system in general, but there is nothing unique or special about string theory in this regard.
Indeed, my experience is that the particle theory community is about as open to new ideas as a group of human beings can possibly be. Let’s not forget that 20 years ago, the string community was pretty much down to Green, Schwarz, and Brink. It’s grown enormously since then because people were genuinely interested and excited about it, not because they were forced to work on it.
I am *extremely* skeptical of *any* claim that scientists in general are working on the “wrong thing” and should be told to work on something else. I trust the community at large far more than the judgement of any one person.
“The arrogance of people in the particle theory community never ceases to amaze me. Assuming that anyone who dares to criticize what is going on in the subject must be ignorant is all too common behavior.”
I did not *assume* you were ignorant because you criticized what is going on (though your understanding of what is going on is mistaken, in my view). I *concluded* that you were ignorant because you made several statements that indicated misunderstandings of various issues in quantum field theory and particle physics.
“All I was saying was that if you think of SU(2) gauge theory as a purely internal symmetry, it is in some sense surprising that it is chiral, since chirality is an aspect of behavior under Lorentz symmetry, which is a space-time symmetry.”
This betrays a profound misunderstanding of the nature of chiral symmetry. One more time: if you start with three or more fermion fields, and one or more scalar fields, and include all couplings allowed by renormalizability, your theory will automatically be chiral, unless you choose special values for some of the couplings. Thus chirality in nature is no surprise; it’s a generic prediction of quantum field theory.
“I was just making the uncontroversial comment that if you take a classical chiral gauge theory such that quantizing the fermions produces an anomaly in the gauge symmetry, no one knows how to quantize such a theory.”
The conventional wisdom is that such theories DO NOT EXIST, not that we haven’t figured out how to quantize them. Your original comment questioned this belief. No one can prove anything either way. But the arguments against the existence of these theories are about as strong as any arguments in QFT.
All bets are off in two dimensions, where lots of special things happen.
“Maybe an elementary scalar field is what is causing electroweak symmetry breaking, and one has to ultimately understand this field and its couplings as coming from fluxes in a Calabi-Yau or who knows what. But theorists should not be so arrogant.”
Arrogance has nothing to do with it. Theorists have thoroughly explored all the alternatives they could think of (with some, like large extra dimensions, still under active investigation). Most died because they made predictions in immediate or eventual conflict with experiment. Theorists would be *thrilled* if something unexpected turned up at the LHC. The whole tone of your original comment was that poor benighted theorists are off thinking about quantizing gravity instead of electroweak symmetry breaking. This is wrong!
The arrogance of people in the particle theory community never ceases to amaze me. Assuming that anyone who dares to criticize what is going on in the subject must be ignorant is all too common behavior.
I won’t recite my qualifications extensively here, other than to note that the places where I first learned QFT included Weinberg’s course on the subject at Harvard that lead to part of the books Srednicki mentions. I also took Coleman’s QFT course there, as well as Gross’s course at Princeton where I got my Ph.D in particle theory in 1984 (Curt Callan was my advisor there).
It’s hard to extract from the torrent of personal abuse what Srednicki’s criticisms are. The weird thing is he doesn’t deal with my views on string theory, which are controversial, but here gets very worked up about what are accurate and not at all controversial statements.
“Wrong, Wrong, Wrong” number one. Hard to tell what he is getting worked up about here. All I was saying was that if you think of SU(2) gauge theory as a purely internal symmetry, it is in some sense surprising that it is chiral, since chirality is an aspect of behavior under Lorentz symmetry, which is a space-time symmetry. Chiral
gauge theory is tricky, as Srednicki should know well, since he started out his career, like I did, doing lattice gauge theory. If you try and put spinors on a lattice and couple them chirally to gauge fields, it’s surprising how much trouble you run into.
“Wrong, wrong, wrong” number two. I can’t see what he’s upset about here either. I was just making the uncontroversial comment that if you take a classical chiral gauge theory such that quantizing the fermions produces an anomaly in the gauge symmetry, no one knows how to quantize such a theory of coupled gauge fields and spinors in such a way that you end up with a unitary, Lorentz-invariant, renormalizable QFT. I didn’t say anything about the gauge invariance of such a QFT or claim that I have any idea how to do this.
Jackiw does claim to be able to do this (for the chiral Schwinger model) in 1+1d, maybe Srednicki should send him an e-mail about how ignorant about QFT he is.
“Sigh” Again, I can’t figure out what he is getting so excited about, since what he quotes is completely uncontroversial. I’m well aware that there is by now a long history of unsuccessful attempts by theorists to find a good alternative to using an elementary scalar field to break electroweak symmetry. Maybe an elementary scalar field is what is causing electroweak symmetry breaking, and one has to ultimately understand this field and its couplings as coming from fluxes in a Calabi-Yau or who knows what. But theorists should not be so arrogant. There’s a long history of experiments coming up with results that theorists had good reason to believe were not possible. In the late sixties theorists would have claimed that the strong interactions were such that scaling in deep inelastic scattering was impossible at high energies. And yet, that’s what was found, leading Gross et. al. to the discovery of asymptotic freedom. Let’s wait and see what the experimental results have to say about the dynamics of the Higgs sector before being so sure that all possibilities for what it can be are well-known.
I came to your web site because I was told that you are a critic of string theory, and I wanted to see what you had to say about it. What I find is appalling ignorance. You really ought to spend some time learning some physics before you attack it. I recommend starting with Weinberg’s three-volume text on quantum field theory.
I don’t have the time or the energy to explain *all* the errors on this web site, or even all the ones in this single comment. But I’ll tackle a few of them.
“The SU(2) gauge symmetry is supposed to be a purely internal symmetry, having nothing to do with space-time symmetries, but left and right-handed spinors are distinguished purely by their behavior under a space-time symmetry, Lorentz symmetry.”
Wrong, wrong, wrong! RH spinors are hermitian conjugates of LH spinors; you can’t have one without the other (in 3+1 dimensions; things are different in different numbers of dimensions). Parity swaps the LH and RH spinors (as does hermitian conjugation). The question is, in a particular theory, can we assign parity transformation rules to the scalar and vector fields (if any) so that parity is a symmetry of the action? If there are more than 3 LH spinors, and at least one scalar, then the answer is generically “no”, even if there are no gauge fields at all. (By “generically”, I mean you include all couplings allowed by gauge symmetries and renormalizability.) If there is some gauge symmetry, then the answer is also “no” if the LH spinors form a complex representation of the gauge group (with or without scalars). In no case is there any need for some mysterious intertwining of Lorentz and gauge symmetry.
“People mostly believe that theories with an anomalous gauge symmetry make no sense, but it perhaps more accurate to say that no one has yet found a unitrary, Lorentz-invariant, renormalizable way of quantizing them.”
Wrong, wrong, wrong! In the case of anomalous violation of a global symmetry, we know from experiment that the symmetry does not hold: this is proven by the decay rate of the neutral pion (for electromagnetic anomalies) and by the nonexistence of a ninth light pseudoscalar (for chromodynamic anomalies). Coupling a vector field to a non-conserved current violates gauge invariance. Of course, since *no* quantum field theory (in more than two dimensions) has been proven to exist (and gee, isn’t this one of the mighty criticisms you aim at string theory?), you are free to believe that something could be constructed that could be interpreted as an anomalous gauge theory. But it wouldn’t actually have any gauge symmetry.
“Why does the vacuum state break electroweak gauge symmetry?
If we could answer this question, we’d probably understand where masses of particles come from, as well as just about all of the undetermined parameters of the standard model (except for a couple ratios of the strengths of the gauge interactions). The exciting thing about this problem is that we have good reason to expect experiments to give us some new clues about it in 2008 when data from the LHC begins to come in.”
*Sigh*. Now we come to appalling ignorance of the history of ideas in particle physics. This sounds like it was written in 1979. A *huge* amount of effort went into exploring alternatives to the standard Higgs field in the 1980s. All these models died at the hands of the experimentalists, because they all kept predicting things that were not observed. We are left believing that the Higgs field is a fundamental scalar because there is no alternative that agrees with experiment, not because we are muddle-headed idiots who can’t think of the obvious.
I’m horrified that the ideas of someone as ignorant as you can be so widely circulated without serious rebuttal. You haven’t gotten serious rebuttal because the serious people have better things to do with their time. If you want to learn some physics first, fine. Unless and until you do, please stop trying to tell funding agencies (all staffed with people far more knowledgable than you are) how to best use their meager sums.
Professor of Physics
University of California
Santa Barbara, CA 93106
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