Over the last twenty years there has been an endless stream of hype about “tests of string theory”, pretty much all of it complete nonsense. For some examples just from the first few months of this year, see here, here, and here. Most of these examples seem to have been generated by confused PR people who misunderstood carefully worded comments by various physicists about the relation of their work to string theory. The average person just finds it hard to believe that it really could be true that there is no way to test a theory that has gotten so much attention for so long from so many prominent people.
Today there’s new nonsensical hype about testing string theory, but this time it’s due not to a clueless press relations person, but to several physicists, including the one who decides what gets into the hep-th arXiv and what doesn’t. The hype isn’t buried in the article somewhere, it’s in the title: Falsifying String Theory Through WW Scattering. In their abstract, the authors claim to derive a bound on coefficients of operators in the effective electroweak Lagrangian such that “a measured violation of the bound would falsify string theory.”
The first striking thing about this paper that purports to show that string theory is falsifiable is that there’s actually nothing about string theory in it. It’s only four pages long, and the first three pages consist of an introduction followed by some calculations in the non-linear sigma model one might want to use as an effective low-energy theory of pions. This is just a warm-up exercise for the real calculation that the authors want to make some claims about, which involves the low energy effective action for a non-linear sigma-model coupled to gauge fields. This is the model that one expects to describe the low-energy behavior of the Higgs field coupled to electroweak gauge fields, if one takes the Higgs mass to be very large.
The authors go on to just copy the terms in the relevant Lagrangian down from a 1993 paper by Appelquist and Wu, then stop and promise to actually calculate the relevant bounds in a forthcoming paper. Unless one wants to try and sit down and do oneself the calculation the authors haven’t done yet, it’s hard to know what these bounds will actually say and whether they will really be non-trivial. It’s also unclear to me exactly how all of this depends on the Higgs mass, which I guess is being assumed to very high, thus violating the known indirect experimental bounds from precision electroweak measurements (which assume the standard model). Very hard to tell about any of this, since it’s dealt with in a paragraph with no equations.
It turns out that the author’s proposal isn’t a proposal to falsify string theory at all, but a proposal to falsify the idea that physics satisfies Lorentz invariance, analyticity and unitarity at high energies. This would falsify our standard ideas about QFT, but it wouldn’t falsify current ideas about string theory. The authors don’t define what they mean by “string theory”, but presumably they mean some version of perturbative string theory. This involves a divergent series (even granting the conjecture that one can make sense of these amplitudes at more than two loops), so it’s unclear how one is going to “falsify” that. Standard ideology about non-perturbative string theory (“M-theory”) is that it will involve some new ideas about space and time, so I don’t see how one can assume that it won’t violate the analyticity and Lorentz invariance properties characteristic of QFT in flat space-time. I’m not convinced that the author’s proposal will falsify anything, but if it does, it will be QFT that is falsified, not string theory. After all, this paper is a QFT calculation (or, more accurately, a promise to do a QFT calculation), not a string theory calculation.
The authors note the problems of non-predictivity generated by the Landscape, and in the first version of the paper write:
Moreover, even if it is found to be difficult to generate the proper model from string theory, one would sooner accept the notion that it is the theorist’s imaginations which are insufficient than conclude that string theory has been falsified.
In the second version of the paper, they seem to realize that this attitude of “one” is kind of unscientific, and they change it to
Moreover, even if it is found to be difficult to generate the proper model from string theory, some would sooner accept the notion that it is the theorist’s imaginations which are insufficient than conclude that string theory has been falsified.
This new version leaves it unclear who this unscientific “some” is. In both versions they note correctly that:
This line of reasoning has resulted in sharp criticism of the theory.
This paper is motivated by the “swampland” program of trying to find effective field theories that can’t be the low energy limits of a string theory. I’ve written about the problems with this elsewhere, and blog postings by Distler have amply embodied what some of them are. In his first posting on the Swampland he gave as an example of a low energy effective theory that couldn’t come from string theory one with only one or two generations, only to be told by a commenter how to construct such things from string theory. He has a more recent blog posting called Avatars of Nonlocality? about the swampland work of Arkani-Hamed and collaborators that motivated this new paper. In a comment there, Arkani-Hamed takes him to task:
This post is a great illustration of what I dislike about blogs and more specifically trackbacks. As I explained to you when you were visiting Harvard last week, your first point about the RG running is standard effective field theory (with an abbreviated discussion in our paper because it is fairly common knowledge–read Georgi’s book). I of course don’t object to your writing a paper to clarify these points to yourself or others. But this is minor. More importantly, as I also explained to you both in email and in person, what you write about the DGP model is totally wrong…
Now, in general I don’t care about what is said on blogs, as I believe they largely fulfill the primate desire to look and see what the other monkeys are doing, and I think they are a big waste of time. But I do object to having a trackback, linked from my paper, to a post about it that claims that one of the central claims is wrong, when a 45 second computation, even done for the reader’s convenience in the paper itself, refutes the argument.
This whole subject really is a swamp, if you ask me, and has nothing at all to do with physics, including nothing to do with the supposed “falsifiability of string theory”. It will be interesting to see if a referee thinks otherwise.
Update: It has been pointed out to me that I’m being a bit unfair to the authors in characterizing the calculation in this paper as a “warm-up exercise”, since they claim that it is a correct first approximation to the actual calculation that they intend to do.
you can congratulate yourself. You have Distler made to write a paper with your blog.
One might imagine how long he thought about the problem of falsifying string theory and how desperate some scientists are, when they begin to publish such nonsense.
It’s all very sad. I sometimes think that if these guys (many of whom are brilliant) took a break from string theory and started thinking about something else (perturbative QCD, collider physics, whatever), they may actually get inspired and find a way to revive strings.
The analogous constraints, in the simpler case where the Higgs exists and is light (as data indirectly suggest), had been studied in section 5 of http://arxiv.org/abs/hep-ph/0604111.
Dear Peter,
Isn’t this what you would want… papers at least attempting to falsify string theory, on general grounds?
Hmm I supposse this is a falsify argument both for string theory and QFT, but at least it aim to proof that the scenary where QFT is falsifyed and string theory remains is unlikely.
Justin,
This isn’t a paper that gives a plausible way to falsify string theory and get rid of it, it’s a paper trying to claim that string theory is in principle falsifiable.
The whole issue of whether string theory is falsifiable, and thus a part of conventional science, is an absolutely crucial one that people are now debating. As far as I can tell, all evidence at the moment is that it is not falsifiable. This paper makes a dramatic claim, in its title, that string theory actually is falsifiable by looking at relatively low energy WW scattering amplitudes. My posting explains why this claim is simply incorrect.
You said:
“It turns out that the author’s proposal isn’t a proposal to falsify string theory at all, but a proposal to falsify the idea that physics satisfies Lorentz invariance, analyticity and unitarity at high energies”
In my reading the paper says no such thing. Rather it says that IF there is no light Higgs, AND the calculated bounds are found to be violated THEN EITHER SST is false OR one or more of Analycity, Unitarity, and Lorentz Invariance is false. It is up to the experimenters to determine which is the case. Quoting one sentence out of context does not invalidate this conclusion.
I’m not a scientiest, but I think the argument that string theory is not science because it is not falsifiable is a red herring. String theorists don’t claim that they understand string theory, let alone that it is a full fledged scientific theory. If and when string theory develops into a full scientific fledged theory, it will no doubt make many predictions and some will be falsifiable. It seems to me that if you want to attack string theory, you need to argue that it is a dead end, and that there is little or no hope that it will ever develop into a full fledged scientific theory. If you can’t make that argument, you have nothing worthwhile to say.
Elliot,
I have been making pretty much that argument, here and elsewhere (at most length in my book).
I am honestly not a fan of blogs, but I cant help but just make a short comment about the paper. The paper just points out that there are bounds on gauge bosons scattering which, if violated, would mean that the underlying theory violates one of the assumptions stated in the paper. Namely, unitarity, analyticity and Lorentz invariance. If one assumes that string theory obeys these assumptions, then string theory, is falsifiable.
The most intriguing part of the paper is that we can perform a low energy experiment which probes the complete UV theory. This is what makes this test truly interesting. It also opens the possibility for other such tests which allow us in practice to test certain assumptions we make about the what lies beneath the standard model.
The title could have just as easily been, “Falsifying …….. using W Scattering”, where in the blank you could put in your favorite “theory of everything” which is suppose to obey these mathematical assumptions. Note that the blank could not have been filled with Loop Quantum Gravity, since (see Smolin)it has been conjectured to violate Lorentz invariance in the UV. So that just leaves string theory, defined with those above assumptions.
Now whether or not this is the “working def” of string theory should be discussed. Certainly perturbatively its true and its true non-perturbatively its true in AdS. So it seems reasonable to assume it true
in Minkowski. But…. I believe its fair to say that If the bound were violated it would certaintly mean that we would have to rethink string theory.
If I were a betting man, Id bet the bounds wont be violated but, as I said, the point of the paper was to point out that this kind of bound is
possible at all.
Elliot,
It is very late in the game to be allowing that “string theorists don’t claim that they understand string theory, let alone that it is a full fledged scientific theory, ” given much of the rhetoric that has surrounded the subject.
At this stage it seems quite likely that genuine understanding will require such a profound shift of perspective and approach that it will amount to a repudiation of much of string theory as a research program, and will be perceived as such by most string theorists, even if some important formal features of string theory are clearly related to elements of the new perspective. (The latter is almost guaranteed to be true; such is the nature of mathematics.) Vital physical ideas are missing, and it doesn’t seem likely that they will discovered by continuing to wallow in a vast morass of formalism.
The paper of Distler et al at hepph0604225 says:
“… Analyticity: the cuts lie on the real axis … with no singularities on the physical sheet off the real axis.
Unitarity: the discontinuity in the forward scattering amplitude across the cuts is given by the total cross section.
Lorentz invariance: the amplitude can only depend upon the three invariants.
Most importantly, these assumptions must be obeyed for arbitrarily short distances.
String theory, which is designed to be valid at all distance scales, is constructed to produce an S-matrix with precisely these properties. …”.
It seems that they are saying that, for example, obersvation of ANY Lorentz violation, no matter how small, would falsify conventional superstring theory.
Do other conventional superstring theorists agree ?
David Mattingly at UC Davis has written a review “Modern Tests of Lorentz Covariance” at http://relativity.livingreviews.org/Articles/lrr-2005-5/ in which he says:
“… Currently, we have no experimental evidence that Lorentz symmetry is not an exact symmetry in nature.
The only not fully understood experiments where Lorentz violation might play a role is in the (possible) absence of the GZK cutoff and the LSND anomaly.
New experiments such as AUGER, a cosmic ray telescope, and MiniBooNE, a neutrino oscillation experiment specifically designed to test the LSND result, may resolve the experimental status of both systems and allow us to determine if Lorentz violation plays a role. …”.
Would all conventional superstring theorists agree to give up their virtual monopoly on USA high energy theory jobs and grants if Lorentz violation were observed by means described by Mattingly (for example, if the GZK cutoff is seen to be absent due to Lorentz violation) ?
Tony Smith
http://www.valdostamuseum.org/hamsmith/
PS – By associating conventional superstring theory with such well tested (at presently accessible energies) principles as analyticity, unitarity, and Lorentz invariance, Distler et al seem to be trying to make it appear to be a respectable physical theory.
If it really were respectable, then (after a generation of hard work by many smart people) it ought to be able to predict something like particle masses, force strengths, KM matrix parameters, etc, that are more easily tested than tiny (perhaps Planck-scale) violations of analyticity, unitarity, or Lorentz invariance.
In fact, Lubos Motl has said (reference frame 21 March 2006) “… particular string models predict the exact masses of all particles …”.
Such a spectrum of “exact masses of all particles” would be much easier to test expermentally.
Why don’t Motl, Distler, et al write a paper setting out such a spectrum, and saying that if such a spectrum disagrees with experiment, then they will consider conventional superstring theory to have been falsified ?
PPS – I am not asking them to do anything that I have not already done with my own physics model, so I think that it is, coming from me, a fair request.
The Distler et al paper is at hepph0604255,
not at hepph0604225 which is where my typo in a preceding comment put it.
Since it was a reference number, I am making this correction.
My apologies for all of my many typos, for most of which I just leave uncorrected hoping that people will understand that my fingers don’t always type what my mind thinks.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
With respect to the question of whether Lorentz violation would automatically falsify string theory, I would like to point out that the modern study of Lorentz violation began with the discovery that string theories might contain spontaneous breaking of Lorentz symmetry.
Of course, there are caveats. What was discovered was a Lorentz-violating local minimum of the potential in bosonic string field theory. This is not superstring theory, and, at least for the models studied, this does not appear to be the global minimum. The theories are actually unstable at tree level, and the true vacuum is only stabilized by quantum corrections. The fact that these quantum corrections are involved makes the question of whether the lowest-energy state is Lorentz invariant or not a (difficult) quantitative question, not an obvious qualitative one. I don’t know of any general feature of the theory that would ensure that the Lorentz-invariant minimum is the true vacuum; this can only be verified, so far, by computation.
In fact, there are a number of string theorists interested in possible Lorentz violations in the context of string theory, so it seems difficult to believe that the discovery of Lorentz violation would be followed by any repudiation of string theory.
Let’s if their forthcoming calculation fares better than the QM version of Feynman + Wheeler’s “action at a distance” model.
Wheeler JA, Feynman RP. 1945. Rev. Mod. Phys. 17:156
Where’s a guy like Pauli when he’s really needed.
It’s funny, in a pathetic way, reading all the theoretical pontifications about the Swampland and the nature of space and time on the Planck scale when theorists can’t even explain the structure and mass of the proton.
But then acual theories about the latter are subject to annoying and inconvenient experimental tests.
re: recent Happex results.
Brett says “… In fact, there are a number of string theorists interested in possible Lorentz violations in the context of string theory …”.
That is a clear contradiction to the statement of Distler et al hepph0604255:
“… Analyticity … Unitarity … Lorentz invariance …
Most importantly, these assumptions must be obeyed for arbitrarily short distances.
String theory, which is designed to be valid at all distance scales, is constructed to produce an S-matrix with precisely these properties. …”.
Such a contradiction shows that either:
1 – the attempt of Distler et al to associate conventional superstring theory with the principles of analyticity, unitarity, and Lorentz violation is incorrect (at best mistaken, at worst dishonest);
or
2 – the “number of string theorists” cited by Brett do not understand the fundamental basis of string theory (as described by Distler et al).
I would be interested in seeing some discussion between Brett and Distler et al about that.
Since I am not a conventional superstring theorist, I really don’t care who wins that argument.
With respect to unitarity (in particular, the Higgs unitarity bounds mentioned in the Distler et al paper), there is a lot of indirect Standard Model type evidence that the Higgs probably exists and is between 115 GeV (the upper limit of Fermilab’s search) and 200 GeV, so the chance of the LHC finding unitarity violation due to absence of such a light Higgs is probably very small.
My guess is that Distler et al are of the same opinion, and that the title of their paper “Falsifying String Theory Through WW Scattering” was a set-up for a sequel “LHC Confirms String Theory” when the LHC finds that there is no Higgs unitarity violation.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
My apologies for yet another bad typo. I typed “violation” when should have typed “invariance”.
What I should have written above was:
Such a contradiction shows that either:
1 – the attempt of Distler et al to associate conventional superstring theory with the principles of analyticity, unitarity, and Lorentz invariance is incorrect (at best mistaken, at worst dishonest);
or
2 – the “number of string theorists” cited by Brett do not understand the fundamental basis of string theory (as described by Distler et al).
Tony Smith
http://www.valdostamuseum.org/hamsmith/
A new critic of string theory thinks that string theory is not even wrong! Watch the press conference:
http://www.careerbuilder.com/monk-e-mail/?mid=8618821
A rebutal ?
http://www.careerbuilder.com/monk-e-mail/Default.aspx?mid=8628834&cbRecursionCnt=1&cbsid=a57e23071f7540b3bef38b62d7b9b45b-200020032-R9-1
Another rebuttal of Peter’s arguments from leading theorists:
http://www.careerbuilder.com/monk-e-mail/?mid=8630834
Based on what I know, I suspect that string theory is inconsistent with any explicity violations of Lorentz symmetry in the Lagrangian. However, spontaneous Lorentz violation is probably more interesting anyway. Off the top of my head, there are four ways that a general symmetry can be broken: explicitly, spontaneously, anomalously, and by boundard conditions. That Lorentz symmetry is anomalous is also possible in certain spacetime configurations, and we know that that boundary conditions of our universe break boost invariance quite strongly. For a theory of everything (especially one where the underlying equations of motion are not known explicitly), it may not be possible to disentangle violations of Lorentz invariance due to the fact that the universe is expanding from violations of other origins.
Man, this blog attracts some very, very bizarre things….
I think the Distler et. al. paper is clear enough, and one of the authors (Ira) emphasizes the point here, about what its technical claim really is. They are deriving bounds on electroweak scattering amplitudes based on assuming analyticity, Lorentz invariance and unitarity. It’s highly unlikely these bounds are violated in the real world, but certainly would be very interesting if they are.
These three properties are properties of Minkowski space perturbative string theory amplitudes, and that’s what the authors base their “falsifiability of string theory” claims on. I think this claim is unwise, for two reasons
1. These aren’t distinctive properties of perturbative string theory, they’re also shared by QFT itself.
2. They just refer to “string theory”, without defining what they mean by it. This leaves the implication that their results are relevant to the falsifiability of the general idea of string theory as a unified theory of gravity and particle physics, something which is not the case. Current hopes for connecting up string theory with real world particle physics involve branes and other aspects of a conjectural non-perturbative theory, and since no one knows exactly what this theory is, it is not at all certain that it has the three properties at issue.
Unitarity is something that one presumably won’t give up, but analyticity is not so clear.
Brett Altschul wrote in about the Lorentz invariance issue, but didn’t mention that he has a new paper today on the arXiv about this: http://www.arxiv.org/abs/hep-th/0605044
There’s also something on the topic from Cohen and Glashow: http://www.arxiv.org/abs/hep-ph/0605036
Thanks Peter for clarifying this. Just one last comment. I dont think anyone can rule out “string theory” given its enormous extent and the many forms it may take, many of which are not really understood. However, the canonical forms of the theory (even including non-perturbative objects such as branes) do have all the properties assumed in the paper. Thus, a violation of the bound would falsify this class/definition of string theory. As brett states the possbility of a Lorentz violating background has not been ruled out, though I am not sure if anyone has found such a solution. I believe it is fair to say that if a violation of the bound were found, then string theory would have to be reshaped in a highly non-trivial way.
Ira, how about the following way to falsify string theory as a theory of QG in 4D?
In section 6.1 hep-th/0501114, Nicolai, Peeters and Zamaklar point out that the free string is quantum gravity in 2D, and that the only non-trivial thing about this model is that the constraint algebra admits anomalies. Assuming that the only non-trivial thing about 2D gravity generalizes to 4D (why on earth would they bring it up otherwise?), the constraint algebra of 4D gravity must admit anomalies. However, there are no diff anomalies in 4D, neither in string theory nor in LQG. Hence both theories are wrong.
Ira,
The problem with “string theory” is it does not exist (there is not theory just a goulash of conjetures, hypotesis, and views). The problem is also that stringers use “string theory” in many ways including incompatible ones (probably because marketing purposes).
There are not “canonical forms of the theory” as you say, just historical development. Let me take the concept of “string theory” in a broad sense.
There are versions of string theories are unitary, and versions are not unitary. E.g. Nanopoulos non-critical string theory introduces a kind of local nonunitarity that he claims (is not true) can solve the measurement problem of quantum mechanics. There are some versions of D0-brane theory are not Lorentz invariant (it is not known is at what extension effects can be detected at low energies), etc.
After of near 40 years, the main postulate of string theory, that the theory is compatible with anything and the contrary of anything, continues being true. But that is not physics.
That I really find unethical of all this are the two main points “always” present in many stringers discourses:
1) Claims about next verification of string theory are not novel (are 20 years old). It is unethical to offer to non-expertises that kind of belief when expertises know what can or cannot be tested in that “theory”.
I can understand that after 40 years of continous failure to test the theory (or to fix main properties or even to check basic promises: e.g. quantization of gravity derivation of SM parameters…) stringers are more desesperate that when Glasgow wrote his critical paper decades ago. But forcing an unnatural survival of string theory between mass media and non-expertises via preprints as this.
2) During decades, violation of LI were studied in other theories as LQG. Then the only version of string theory was LI, therefore stringers rudely critized loop theorists. I heard many things including aberrations such as that loop theorists did not understand Einstein (however M-theory proves just the inverse) and that LQG was a kind of absurd ether theory violating all our knowledge about nature (stringers’ claim was more absurd still).
I heard that whereas string theory was a beatiful unification of SM with full relativity, LQG would be considered as a kind of ugly 19th century approach and, therefore, abandoned…
It is interesting to see how many string theorists agree on maybe LI is not exact now. History is fascinating.
Juan R.
Center for CANONICAL |SCIENCE)
Sorry by the typo Glashow!
P.S: Ginsparg, P; Glashow S. Desperately Seeking Superstrings. Phys. Today 1986, 86N5, 7-9
Juan R.
Center for CANONICAL |SCIENCE)
To Juan R.
One can be much more specific in criticizing string theory.
On the historical side the strongest criticism comes right from its confused start from the remnants of the S-matrix bootstrap program. It substituted the crossing property of on-shell quantities of QFT for the S-matrix and formfactors (for a recent review B. S, Ann. of Phys.319, (2005) 48 ), which is a deep (and admittedly somewhat mysterious) property up to this date, by what was later called duality, namely the saturation of crossing by infinite one-particle towers (the physical reading of the beta and gamme function properties used by Veneziano). This had no conceptual backing from QFT whatsoever (in QFT crossing is a delicate interplay between a finite number of one-particle states and their multi-particle cuts). It so happened that there was an extremely strong prodding for such a situation from phenomenologists of strong-interaction dispersion theory (especially from a Swiss phenomenologist named (?). Schmidt who was criticized by Res Jost). The phenomenologists really got what they wanted, but a short time later when the first results on high momentum transfer scattering came in, they got completely disillusioned with the duality idea. Without this support the idea was theoretical blue yonder in its purest form but it led to rich mathematical structures; we all know the rest of the story.
Physics would be more healthy if string theorists could be forced to compete on the same level as alternative ideas, but their hegemonial grip on power led to a sociological situation (physics/0603112) in which they are in firm economical control of the market (remember Marx: the existence preceeds consciousness which Brecht succeeded to put into a more popular form).
On the purely scientific side, particle physics incorporates two type of arguments: metaphorical ones and autonomous ones. QFT sometimes uses metaphorical arguments but as one can show in detail at least in the setting of QFT they can always be backed up by (often conceptually and mathematically more demanding) autonomous arguments. These words can be given an extraordinarily precise physical meaning (there is yet no reference, I am presently working on these ideas).
It turns out that string theory is totally metaphorical. Take for example the claim that QFT is originating from string theory in the low energy limit. Such scale-sliding arguments are only worthy if the structural relation between the two settings does not permit their application. The most important and characteristic property of QFT is vacuum polarization through localization. This is the reason why QFT goes significantly beyond quantum mechamics in producing thermal manifestations of localizations which go significantly beyond the uncertainty relations of QM (B.S. http://www.lqp.uni-goettingen.de/papers/06/04/). But string theory has no autonomously fluctuating quantum matter on its target space, its only knows quantum fluctuations which come from the (conformal) two-dimensional source space! Whereas autonomous vacuum polarization may get lost in “scale sliding” (see transition from QFT to nonrelativistic QM), it never can be created, i.e. Lambshift is not created through scale sliding, it has to be there before!
One can continue this list of autonomous versus metaphorical reality.
I do not know about you, but I often wondered why string theory appears so extraordinarily eerie and surreal, like a dreamworld. I finally found the answer in the total metaphorical nature of its arguments.
What is this “scale-sliding” that you refer to (and seem to very much dislike)?
The Renormalization Group?
Does Bert Schroer not believe in the Renormalization Group in QFT?
No, the RG, if it is correctly implemented, is done on the solution (quite a demanding task!) whereas scale sliding is that rapid kinematical argument (directly done on the Lagrangian/action) by which e.g. people convince themselves that nonrelativistic QM emerges from QFT for small energies (which I called metaphoric).
Since I do not have messianic expectations in particle physics, I would like to leave “beliefs” to people who like to find them there.
Bert,
Since no-one has signed up to my particular take on QFT I am in no position to pontificate here, but despite having been a researcher in QFT for a while I cannot say that I have understood much of your 09:13 post. I might add that it may well be possible that one of the reasons why the Feldverein remains a small and exclusive club is that a lot of the rest of the world does not know what you (= ihr, (would that English had a 2nd person plural)) are talking about. Of course, the same criticism can be levelled at Superstringers, but then they seem to be calling the shots at the moment, whereas you guys are not.
Or, to put it another way, your comment looked interesting, please expand/explain …
“No, the RG, if it is correctly implemented, is done on the solution (quite a demanding task!) whereas scale sliding is that rapid kinematical argument (directly done on the Lagrangian/action)”
What do those words mean?
Wilson’s renormalization group is a transformation on the action (in response to an infinitesimal change in the cutoff).
Are you saying there is something wrong with Wilson’s renormalization group?
Chris,
what I said this morning among other things is that Veneziano duality in contast to the crossing property of on-shell objects (S-matrix, formfactors) of QFT is a new postulate which without the phenomenological support from strong interaction, which however only had a shelf life of less than two years, would never have come into being; the mathematical content alone would not have been strong enough.
Do you not understand the logical content of this statement or are you worried of how to prove it? In the latter case I cannot help you in this blog (because of thematic restrictions), but I gave you a referemce which may be at least of some help.
Mentos
I told you what I meant by scale sliding, whereas you want me to enter the swampland of the renormalization group which I am perfectly prepared to do, but not in this blog, since it is not its topic and also since people don’t use this sort of argument when they say that QFT follows from string theory (the present knowledge of string theory is not sufficient to do something like this).
Let me again try by analogy try to get my point (about a structural comparison which has to precede scale-sliding) across. Suppose you would live in a 2+1 dimensional world where the locality principle allows for braid group statistics. Maintaining the approriate relation between spin and statistics in the process of energy becoming small compared with the mass, you would never recover quantum mechanics but always end up with a nonrelativistic QFT (vacuum polarization would be persistent). On the other hand in d=3+1 where plektons cannot exist, the Bosons/Fermions allow for a relativistic free field realization in which the one-field state contains no admixture of vacuum polarization. This makes the physical relevance of QM possible because now there is at least no structural obstacle against “scale sliding” or if you want the somewhat more sophisticated RG arguments (I think by now you know what I mean without having to enter any additional controvery). Conversely the nonexistence of autonomous vacuum polarization of quantum matter on target space (fluctuations only take place in the 2-dim conformal field theory which defines source=worldsheet space) in string theory makes it structurally impossible to recover anything like Lambshift. I know that you are willing to sacrifices a lot of things from the past in getting some messianic string ideas ideas going. But do you really want to sacrifice also Lambshift?
“I told you what I meant by scale sliding, whereas you want me to enter the swampland of the renormalization group…”
I didn’t understand what you meant by “scale sliding”, which is why I asked for clarification.
I take it, from your use of the word “swampland” to describe it, that you don’t like Wilson’s Renormalization Group very much.
“Conversely the nonexistence of autonomous vacuum polarization of quantum matter on target space …”
One-loop vacuum polarization computations in string theory look like fancy generalizations of the corresponding field theory computations (minus the UV divergences).
I don’t understand your comment about “sacrificing the Lambshift.”
My question to you: does quantum matter on string target space have vacuum polarization (on target space and not on the 2-dimensional worldsheet!)? I agree that some perturbative expression have a vague resemblence but this is a structural question! (and by the way QFT is not about taming ultraviolet infinities but rather about finding autonomous finite parametric subspaces in an apparently infinite parametric space of coupling strengths); either there is a target vacuum polarization (e.g. on the bondaries of localization of quantum matter on target space) or there is not. This is not a quantitative matter in the same vein as it is meaningless to take about “being a little bit pregnant”.
As far as my underlying philosophy of QFT goes it is Wilsonian and not TOEian. But Euclidean field theory is primarily statistical mechanics (following Osterwalder and Schrader, for a recent review see hep-th/0603118) and its use should be limited to structural arguments in (real time) QFT (because of the extremely subtle reflection positivity).
If you are so convinced to know what a cutoff is then please tell me what I have to do in any of those infinite families of two dimensional factorzing models (the Sine-Gordon/massive Thirring being the oldest one) in order to introduce a cutoff into their known formfactors or correlation functions; its not a retorical question, I honestly do not know how to do that. I of course know what a cutoff is in a Feynman integral but I am already lost if I should do something like this on a functional integral and even if I succeed how do I convince myself that I preserved the all-important reflection positivity which is my only assurance that I am still within quantum physics? I think if you ever seriously confront these question you will come to the conclusion that it is mathematically (and conceptually) easier to formulate and control local QFT than nonlocal (cutoff etc.) ones in which the nonlocality results from momentum space manipulations. Particle physics is not about attending holy cows; it is of pivotal importance to re-investigate old problems if there are new conceptual tools to do this.
“I agree that some perturbative expression have a vague resemblence but this is a structural question!”
I don’t understand your structural question, nor what you mean by the statement that the resemblance of the two perturbation expansions is only a “vague” one. Sure there are important differences, but none of them have anything to do with low-energy physics like the Lambshift.
“As far as my underlying philosophy of QFT goes it is Wilsonian…”
If your philosophy of QFT is Wilsonian, why do you call the Wilsonian Renormalization Group “the swampland”?
“If you are so convinced to know what a cutoff is …”
The presence of a cutoff is absolutely central to the Wilsonian approach to field theory. So your distrust of cutoffs is more than a little puzzling for someone whose underlying philosophy of QFT is “Wilsonian.”
How do you feel about a lattice cutoff?
Hi Bert,
No, I think I got the first bit.
So “autonomous” here just means “not metaphorical”?
What? The most important and characteristic property of QFT is that it is quantum mechanics wherein particles can be created and destroyed.
This is AQFT jargon that means nothing to me.
I expect that there are a whole swathe of papers I need to read before I can understand this (& I wonder whether any of them actually calculate cross sections).
A lattice cutoff would perfectly satisfy me but please tell me how you introduce any cutoff in a model whose rigorous construction principles are not following the Lagrangian quantization logic. You do not seem to be aware of the explicit existence of a large class of strictly local 2-dim. QFT which owe their existence to completely different ideas than those of Lagrangian actions and Wilsonian RGs. This is a class where not only the old bootstrap idea about the S-matrix works, but there exists in addition a QFT which is uniquely associated with this S-matrix (the formfactor part of the formfactor-bootstrap program). The point is that any introduction of a cutoff in any form would totally wreck this constructive approach by which they have been manufactured (I don’t think Lagrangian quantization will ever lead to such explicit constructions even in those case where the models may be baptized with a Lagrangian name). The cozy conceptual security in which you seem to live (and of course not only you personally) has been already seriously undermined apparently without you being aware to live in an undermined world. Of course you may want to execrate this reality by claiming that these models are irrelevant for TOE fans but it certainly will not go away but rather will grow stronger. It looks that this is just the first glimpse of a new way of entering QFT and a new way to look at QFT, and it is far away from the swampland entries.
So “autonomous” here just means “not metaphorical”?
What I have gathered from the conversation so far is that autonomous means standing on its own, not needing a reference to something else.
Sorry, I give up. Please don’t think that I am arrogant and I want to put you down. In reality am sad about this situation. The schism in particle physics generated by more than 30 years of string-induced metaphorical (as opposite to autonomous) thinking (string theory is only the culmination of something which already started before) has led to a situation where a genuine dialog is estremely difficult. I agree with Smolin that the physics discourse is on the verge of breaking down, but not only between string theory and LQG but also between advanced QFT and attempts at TOEs.
I don’t think it is my ignorance because I have followed the development of string theory form its cradle and I have a certain sympathy for the more conservative aim of LQG (which unfortunetly gets into a false recent competition with ST which forces it to occupy territories which are outside its conceptual range). But the fact that I understand what other people are doing is of little help here if it remains one-sided.
Chris, I am disappointed that you ask that abominable question. Of course I can calculate cross section and they would be the same as everybody else’s. Pointlike fields are singular generators of algebras and perturbative interactions are formulated by polynomial invariant couplings of free fields. Of the infinitely many forms for (m,s) free fields (see Weinberg) you can use any you want in doing causal perturbation theory. In case you have a Lagrange-Euler description which generically is the exception rather than the rule (for low spin fields such free field representations are known) you can also use the functional integral approach but why should I put this restriction on myself? Local quantum physics is an extension and not a narrowing down and if you define QFT through functional integrals you are narrowing it. Renormalized causal perturbation theory is the most general framework based on pointlike free fields and it is totally mathematically rigorous (in the sense of formal power series just as the formal algebraist like Drinfeld treat Kac-Moody representations or vertex algebras)but of course not in the sense of convergent sums which are formally representing the would be operators in Hilbert space.
Let us never come back an loose time on re-hashing such questions over and over again.
To Arun
Autonomous means that it contains its interpretation i.e. there is no freedom to add anything from outside, and the terminology metaphorical is used if the interpretation has to be added from the outside. Observe that metaphorical does not mean wrong, of course you make sure that you do not add something which creates an inconsistency (it is similar to Goedels situation in the theory of logic).
In QFT one often uses metaphorical arguments but thanks to vacuum polarization which distinguishes QFT significantly from any kind of relativistic QM matephorical arguments in QFT can always be replaced by (generally more deep and demanding) autonomous ones. I discuss such situations in connection with thermal manifestations of localization in QFT (for example the entropy problem) in
http://www.lqp.uni-goettingen.de/papers/06/04/
although I did not yet use this terminology in those papers. The usual thermodynamic limit approach in thermal QFT is metaphorical but there exists an open system formulation based on the so-called “split property” (which makes essential use of vacuum polarization) which converts the sequence of finite systems into a sequence of genuine inclusions which are all subsystems of an open system. In Haag’s book it is referred to as the statistical mechanics of open quantum systems. Without quantum matter which reacts to the process of localizing it by producing vacuum fluctuations on the causal horizon you cannot get to the autonomous formulation of open systems. QM and string theory do not have that vacuum polarization you need. Wheras this lack of autonomy does no harm to QM, it makes string theory (because it is supposed to contain autonomous QFT) look very eerie, more like a surreal painting of Dali than a realistic theory of quantum matter.
“You do not seem to be aware of the explicit existence of a large class of strictly local 2-dim. QFT which owe their existence to completely different ideas than those of Lagrangian actions and Wilsonian RGs.”
Almost all nontrivial 2D CFTs are non-Lagrangian. Most of the known integrable 2D QFTs are constructed as relevant deformations of a 2D CFT, and so are non-Lagrangian as well.
The same is true in higher dimensions. Nontrivial interacting fixed points generically have no useful Lagrangian formulation. (Sometimes such theories can be realized as the IR limits of a weakly-coupled Lagrangian field theory. Sometimes they can be realized as the limit of a family of Lagrangian field theories.)
There are even (thanks to string theory constructions) examples of nontrivial interacting QFTs in 5 and 6 dimensions. These, of course, are also non-Lagrangian.
“QM and string theory do not have that vacuum polarization you need.”
In the case of QM, you are, of course correct. In the case of string theory, you seem to have gotten a wrong impression somewhere along the line …
No, I think we are living in different conceptual realms. When you say you can construct you mean that you can make a mental picture but not anything which a mathematician or a mathematical physicist would call a construction or a proof of existence. There is not a single construction or existence prove in higher dimensional QFT with or without the RG, not to mention string theory. In string theory, unlike QFT one does nor even know any intrinsic characterization one only has some recipes. If the word construction would still have a mandatory engaging meaning which it used to have before the new barbarians appeared on the scene, we would never enter such futile arguments.
And finally: why do you think there are these trillions of vacua which do not communicate; in a theory with vacuum fluctuations caused by local quantum matter this would not happen, they would all communicate and not live separate lives as in a classical theory.
If somebody would have frozen me at a time when particle physics was still healthy and woken me up in the present, I would feel like in one of Kafka’s short stories: eerie and surreal.
“There is not a single construction or existence prove in higher dimensional QFT with or without the RG, not to mention string theory.”
That’s right.
By your criterion, QCD does not exist.
“If somebody would have frozen me at a time when particle physics was still healthy and woken me up in the present, I would feel like in one of Kafka’s short stories: eerie and surreal.”
Nonsense.
No one believed that the limited class of field theories, constructible by the techniques of Constructive Quantum Field Theory, were the only things that existed back then either.
Essentially all progress back then came from what you call a “different conceptual realm.” And that continues to be true to this day.
If anything, the set of rigorous results in 2D (the only dimension where CQFT/AQFT ever had any traction anyway) coming from other approaches is vastly greater now than it was then.
As to dimensions above 2 (like, for instance, 4 dimensions, where we happen to live), life goes on, despite the utter lack of progress from Constructive/Algebraic Quantum Field Theory approaches.
If you want to spend your time working on rigorous approaches to 2D QFTs, that’s fine. But don’t pretend to be surprised at other people’s lack of fascination in your progress.
Only in your fevered imagining is that a sign of the sickness of high energy theoretical physics. The center of attention has always been elsewhere and, for intellectually-sound reasons, remains elsewhere today.
Just this once:
The cross section calculation in 3+1 dimensions you refer to is I assume based on the Epstein/Glaser causal perturbation theory as outlined in (e.g.) Scharf’s Finite Quantum Electrodynamics. I bought a copy of the latter a while back and have a made a mental note of going through the arguments it in detail, but have not done so yet for the following reason: it just looks like good old renormalizing Feynman-Dyson perturbation theory in elegant clothes. Cutoffs are a crude way of “dealing with” theories that give unwanted infinite results, but not the only one. One may also introduce other kinds of spurious degrees degrees of freedom and take spurious limits and although I will grant that what is done here is better than cutoffs or dimensional regularization it still seems to amount to the same thing.
Yes Chris, everything of a systematic nature which you can do with functional integrals you can also do within the causal perturbation setting and much more (the perturbation theory in CST can only be done in cp and the resulting local covariance principle of Hollands, Wald, Brunetti, Fredenhagen and Verch is truely something which shows the vibrancy of modern QFT and there are several other startling results outside of the radar screen of string theory; but fortunately the relevance of some discovery for physics is not determined by Gallup polls among string theorists).
Bert,
Have you thought about writing your own textbook on quantum field theory, emphasizing the aspects which you feel are being neglected in modern textbooks treatments (ie. Peskin & Schroder, Zee, etc …)?
Peter’s opponents apparently in a more conciliatory mood:
http://www.careerbuilder.com/monk-e-mail/?mid=8823799
JC,
yes I have, but there are certain problems which I want to see solved before. I probably would not do this on my own because it is not enough to have new ideas (including of course new ideas on old open problems), one also needs a critical counterpart. Presently advanced QFT is too much in an upheaval, maybe in two years from now some of the dust will have settled. There are very astonishing structures in QFT which could not have been noticed with the old conceptual apparatus. The local operator algebras in QFT are all of one kind, i.e. if you have seen one, you know them all (just like points in geometry) and the richness of QFT, including its inner symmetries and its (noncompact) spacetime symmetries, is all contained in the relative position of a finite number of copies of this “monade” (explicitly: hyperfinite Type III_1 von Neumann algebras, Ed Witten may pardon me) which are placed in terms of modular algebraic concepts with geometry being the result and not the input (note the difference to Atiyah-Witten). The setting resembles that of Vaughn Jones’s inclusion theory but the monades used here lead to modular inclusions and they lead to spacetime, whereas the Jones inclusions are limited to only notice a left-right distiction (braid groups, topological field theory). The concepts and mathematics are clear and rigorous, what is completely open is the range of physical content.
I do not complain that the small dedicated group of people who are engaged in this project do not get enough attention, since I am convinced that real progress will not result from those globalized monocultures: there seems to be a critical size just as in the theory of traffic collapses. But of course on the other hand I am afraid that we will be left with near zero new blood at a time when it would be really important because the ball of local quantum physics seems to be rolling again. My polemic article was not written for the sake of polemics but mainly to let those many physicists who have doubts about how particle physics is administrated by string theorists know that there is another world. We are in a situation in particle physics which never was confronted before and which definitely cannot be explained without taking sociological aspects into consideration.
I think Arun makes a serious mistake if he thinks that this eerie and surreal appearance of string theory is my personal problem; he would be surprized how many particle theorists have a similar impression; in fact hep-th/ has in the eyes of most particle physicists become a site of messianic TOE expectations.
My question to Arun about the structural status of vacuum polarization was carefully chosen because the very nature of those above mentioned monade algebras already incorporates the vacuum polarization and thermal properties in their algebraic structure (these algebras have no pure states at all!). They are the heart of local quantum physics (much more basic than the use of particular field coordinatizations) and it would be interesting and important to know what string theory puts in their place. What is somewhat depressing is not that Arun does not know the answer, but that he gave the impression that it is not worthwhile to know the answer; for him it is only a minority interest of some isolated individuals who do their little thing and are detached from the great design of a final TOE. Although I live in a completely different conceptual realm than Peter or Lee Smolin (whose worries about a falling apart basis of communication within particle physics I however share) I never have the impression that they are dismissive about different views or that they have hegemonic ambitions.
With all appologies to Arun, I mean Mentos.
These pseudonyms add an impersonal flair. I think their original purpose is to further the course of democracy so that somebody, who wants to discuss with a bigshot, does not have to be inhibited or afraid of his reactions; but on the other hand they should not be used denigrate somebody who signs with his name and takes the responsibility for what he writes. Up to now I did not have the impression that such an abuse occurred with respect to my contribution.