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.
“What is somewhat depressing is not that [Mentos] does not know the answer, but that he gave the impression that it is not worthwhile to know the answer…”
I am sorry if I gave that impression. It’s not that I don’t think the answer is interesting. It’s that I don’t understand the question.
As to the status of CQFT/AQFT as a “minority interest of a few individuals,” you seem to be arguing that, in some past golden age, that was not the case. The fact is that it was always a minority interest.
That’s not a criticism of AQFT. It’s simply a statement of reality, and important to repeat for those too young to remember the “golden age.”
“…they should not be used denigrate somebody who signs with his name and takes the responsibility for what he writes.”
Which is not my intention either.
“As to the status of CQFT/AQFT as a “minority interest of a few individuals,” you seem to be arguing that, in some past golden age, that was not the case. The fact is that it was always a minority interest.”
That is certainly true, but this was a democratic choice and if one made that choice and had some innovative ideas there was no problem, it was the quality on the level of the state of art of an area which determined careers. There was no need for a hegemonial control through citation indicees in which mathematical physics fares less well so AQFT also could profit from the “golden age”.
“That’s not a criticism of AQFT. It’s simply a statement of reality, and important to repeat for those too young to remember the “golden age.””
I meant “golden age” for particle physics not for AQFT, although as I said AQFT did not fare badly.
Now that we are in tune again, I could try once more to get to that question of intrinsicness (autonomy) with respect to string theory across. Let’s forget the vacuum polarization aspect and explore that intrinsicness in a more specific context of the free 10-dim. superstring (to avoid tachyons) in the covariant gauge (conformal formalism, BRSTetc.). We probably can rapidly agree that if one applies the free string field operator once to the vacuum (the “one-field state”) and descends via BRST cohomology to the physical subspace, one obtains a highly reducible unitary Poincare representation which describes a mass tower. Take it from me (we can argue about this separatly, this is where I use modular localization) that the two point function which is a function of center of mass X and internal dynamical variables is point-localized in X and hence the physical projection of that free string field inherits this localization. If that field would have been string-localized it would have shown up right here in a reduced spacelike (anti)commutativity where the geometry of the string would be plainly visible (if one string comes into the timelike causal shadow of the other). It does’t, and so you could get the impression that the situation is indistinguishable from a pointlike infinite component free field. But I am almost certain (I have not done the computation) that the result will have a much better spacelike commutativity than one can get in infinite component QFT (and in any QFT for that matter): depending on the excitations of the internal degrees of freedom the situation will be “supercausal” i.e. the (anti)commutator will continue to vanish up into the timelike region (inclusing lightlike distances) below a certain timelike distance which varies with the internal excitation state. This then may be considered as an intrinsic characterization of a free string versus an infinite component free field. I is certainly independent on all the words which went into its manufacturing (conformal QFT, BRST, reparametrization and gauge aspects etc.). In other words the question is which property distinguishes the string mass tower from a generic infinite component tower. I do not know the answer, but would you agree that this at least is a way for aiming at an intrinsic meaning?
No, let’s stick with vacuum polarization.
Maybe what we need is an example of the kind of explanation that would satisfy you.
Consider Lattice Gauge Theory. What “structural property” of Lattice Gauge Theory ensures that it has vacuum polarization?
Sorry this is off-topic, but I’m wondering what’s happening to Peter Woit’s book “Not Even Wrong”. I thought it should have been published in April (according to one listing in amazon), but apparently not. And another listing in amazon says it won’t be published till 9/30/06. Just want to get a more definite answer from the author. Thanks.
Unfortunatly nothing, you just do not get those nice monades which structurally encapsulate and bind together(modular) localization, vacuum polarization, thermal manifestation of localization in the vacuum etc.
I would not know how to rewrite my papers on localization entropy on the Goettingen AQFT server in terms of a lattice model.
It seems to me that the lattice is good for nonperturbative approximations but not for structural problems, in fact it is particularly efficient if you do not yet understand the conceptual structure of a problem. In the present case one really knows a lot about the QFT structure, and that analytic insight should not be vasted by returning to a lattice (I do not know how the lattice works for string theory).
In principle one should find an answer somewhere, but it is too much buried in details. Just as in QM, vacuum polarization is not structurally forced upon you. In QM and lattice theory you always have factorization between the Hilbert space of a region and its complement (and the cacuum factorizes trivially), whereas in QFT there is never a factorization between the subspace of localized states and that of states belonging to the spacelike disjoint region. In fact you can only create such a tensorproduct factorization if you allow for a “collar” region which separates a localization region from its causal disjoint; but even if you do this “splitting” you will not loose the thermal aspects of the vacuum (which are never there in QM and lattice theory unless you introduce a heatbath by hand).
With other words it would be a terrible mess if you were to describe the Hawking radiation phenomenon on a lattice. For this reason you have to be satisfied with my other more pedagogical example; try to look at it, it is not so bad for getting the structural point of “intrinsicness” across.
there is a logical point about testing scientific theories that in the long run is probably more important than some particular paper about a particular theory. it is illustrated by this post:
“…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 Analyticity, Unitarity, and Lorentz Invariance is false. It is up to the experimenters to determine which is the case.”
Something worries me about this. suppose the conclusion were
“(EITHER SST is false OR General Relativity is false)” And suppose the conclusion were “It is up to the experimenters to determine which is the case.”
This is not a possible way to falsify SST, because logically in order to do that one would have to prove that General Relativity is TRUE. but that is, in principle, impossible. One cannot show that a scientific theory is true one can only continue to test it.
One can not put up to experimenters the job of proving a theory true.
But in order to function as a falsification of SST one would have to do just that. therefore the logical scheme presented here UNSATISFACTORY as a proposed falsification. (this is not a Distler issue or a SST issue, it transcends the immediate circumstances and involves our understanding of how theories can be tested)
The scheme would only work marginally in a context where all educated people of good faith accept Gen Rel without question. As an unquestioned premise that is not felt to need experimental support.
But in our particular case here, “Analyticity, Unitarity, Lorentz Invariance” is very far from being such an unquestioned premise. I see indications of widespread skepticism that nature conforms to those three rules. As the poster indicated, we could NOT take it on faith but would have to hand over the job of verifying it to experimentalists. They, however, would be logically incapable of verifying these as features of nature, and could at best falsify them.
The Distler et al paper, it seems, could serve a textbook example of how NOT show the falsifiability of a theory (because it illustrates this simple, but easily overlooked logical point.)
“Unfortunatly nothing, you just do not get those nice monades which structurally encapsulate and bind together(modular) localization, vacuum polarization, thermal manifestation of localization in the vacuum etc.”
Well, if lattice gauge theory does not have the requisite “structural properties” that you require, then I am sure that nothing I can think of will either.
QCD, for you, is a nonexistent quantum field theory.
The problem lies not in string theory, but in all of the “quantum field theories” of moderm particle physics. Even the best of them is not defined in a fashion that satisfies your requirements.
““…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 Analyticity, Unitarity, and Lorentz Invariance is false.”
I don’t think that is what their paper says.
They argue that IF there is no light Higgs, AND the calculated bounds are found to be violated THEN one or more of Analyticity, Unitarity, and Lorentz Invariance is false. Since SST incorporates the properties of Analyticity, Unitarity, and Lorentz Invariance, then IT, TOO, must be false.
That’s quite different from the logical syllogism you propose. Perhaps it has its own flaws, but not the ones you claim.
thanks for the reaction Mentos. I am glad you have a different interpretation, this gives more of a chance for Distler et al work to exhibit genuine falsifiability.
I have three questions for you.
what does it mean to assert that “Analyticity is false” ?
what does it mean to assert that “Unitarity is false” ?
what does it mean to assert that “Lorentz invariance is false”?
Perhaps as you suggest, your version of the syllogism has its own flaws, such as the flaw that these statement are meaningless. What is your view?
Personally I cannot imagine attributing a meaning for these statements unless we venture into the realm of metaphysics and make normative statements restricting the mathematical content of physical models—i.e. stop judging theories on the basis of their performance.
Metaphysical statements such as (“mathematical functions used in modeling should be expandable in power series”) are not, I believe, empirically testable—-they concern human conventions and not the physical world. How does one falsify a metaphysical principle,
or a normative injunction about conventions?
And then if you DO falsify it, or at least contradict it, you get something like (“it is OK for mathematical functions to be expandable in power series but also OK if they are not, maybe they dont even all have to be differentiable, whatever works!”) And then how does that falsify SST?
It seems to me that “Analyticity is false” merely enlarges the range of theories that the maker of the statement is willing to consider and test. SST would still be required to make predictions and be judged on its merits, whatever be the field of competitors.
Something fishy about Distler et al claim to show falsifiability, I suspect. Can’t get a paraphrase of the argument that means anything. If you have one, I’d be very glad to hear it.
Saying that one of these properties is false is simply to say that the fundamental theory at very short distances does not possess this property. Perhaps, like LQG, the fundamental theory is not Lorentz-invariant at short distances. Or, perhaps one of the other properties does not hold.
Anyway, the dispersion-relation bounds of Distler et al are derived assuming that these properties hold to arbitrarily short distances in the fundamental underlying theory (whatever it is). If the bounds are found to fail experimentally, then these assumptions about the short distance theory must be false.
Perhaps, in that case, the true short distance theory is LQG. In any case (they say) it isn’t string theory.
To Who says,
I have the same problems with the paper. Analyticity is not a physical principle and Lorentz invariance may refer to the fact that string theory among other things permits also a Poincare-invariant solution. As it stands it implies a somewhat uninteded cabaret interpretation of the word “theory of everything”. Nevertheless it may indicate a deep desire to bring the discussion back to a more conceptual level. A characteristic aspect of the mentioned “golden age” is that it brought the conceptual dialogue to an art form and this has been lost and we probably must re-learn it.
Presently many works place calculations directly next to sophisticated mathematics without a mediating conceptual link. I am very suspicious when I see all that high powered and from a physical viewpoint amok-running mathematics (differential- and algebraic- geometry, Langlands etc) being juxtaposed to supersymmetry, e-m symmetry and other unfulfilled physical pleas to nature over and over again, although the D-J-R paper cannot be accused of duing that. But a first swallow does not yet make a spring and one has to wait and see whether this indicates a trend.
I’ve been finding your posts very interesting — and engagingly frank. My own interest is perhaps a very small subset of yours. I’m interested in the possibility of solving some of the interpretative/foundational problems with QM (not QFT) by looking more closely at the algebraic structure — in particular what happens when you couple systems together either in measurement situations or in EPR-type ensembles. It seems to me that some subtleties have been glossed over in traditional presentations: it is for example usually ignored that there are a very large number of tensor products that may describe a coupled system, and this range, in a sense, represents a physically determinable aspect of coupled systems that has not been looked at.
I’ve always thought that this aspect of QM (entanglement etc) must really get its fullest exposure in QFT and have always been quite dissapointed with what I’ve found. (Let alone what is in string theory.)
Is this an aspect of AQFT that you can comment upon? Particularly as many people think that AQFT ‘s local nature precludes it from saying anything about this from the outset.
If you’re not writing a textbook right now, could you outline a reading program? Let the starting point be a grad student who has had a first course in QFT.
Thanks in advance!
Concerning basic advanced structures in QM off hand I would recommend Claas Landsman’s homepage. I have seen a link in Peter’s homepage. The issue of entaglement etc. is a bit more demanding in QFT as a result of the ubiquitous vacuum polarization.
Also the second addition of Haag’s book on QFT has some nice material on the measurement which is presented in an interesting personal flair. More advanced topics on ERP and Bell in the context of QFT you find on Steve Summers homepage.
Very interesting and highly recommendable are also publications of the University of Pittsburgh Philosophy department. These people really know what they are talking about. I had many interesting email exchanges with Rob clifton and I was deeply saddened when I heard about his early death a couple of year ago. Hans Halverson, who is now in Princeton is a very worthy successor (he actually was his student). Apparently because of its rich conceptual structure AQFT has a very strong attraction to philosophers of science. Without knowing a little bit on the mathematical side one may feel lost in their articles, but I think they have also supplied some more pedagogical articles.
Articles of Halverson you can also find on
Since I have my reservation about recent literatur on QFT, I still would recommend Haag (not so much as a textbook to learn tools of the trade, more to get a conceptual overview), also Streater-Wightman and Jost are still good in what they cover (and there are many important things they do not cover). For scattering theory, which is a cornerstone of AQFT, there is also a recent little book by Araki. For the tools of the trade Itzykson-Zuber is still good. With all those antidotes I think you can also get sum honey from Peskin-Schroeder since you can then easily spot the weak part where they allowed the string theoretical carricature of QFT to take over.
>With all those antidotes I think you can also get sum honey from Peskin-Schroeder since you can then easily spot the weak part where they allowed the string theoretical carricature of QFT to take over.
That must be the best 1-line book review ever!
Any choice words on other popular QFT texts (Weinberg, Srednicki, …)?
Bert, speaking of weakness, what do you think of Doplicher’s quantum area in the context of AQFT? Does it implies that the net of observable algebras contains a minimum algebra? Is it in contradiction with some fundamental issue of AQFT?
(and yep, I join in recommending the reading of Haag’s in paralell with P&S. I “stole” (xeroxcopied) Haag’s draft when in display at Leipzig IAMP meeting, and then I went straigh for the full book when it appeared at the bookstores).
“Bert, speaking of weakness, what do you think of Doplicher’s quantum area in the context of AQFT? Does it implies that the net of observable algebras contains a minimum algebra? Is it in contradiction with some fundamental issue of AQFT?”
If your question is what I think about Sergio Doplicher’s contributions to QFT, my answer is that I am impressed by them. The deepest work (in collaboration with John Roberts and in part Rudolf Haag) is the derivation of the structure of charge sectors, their statistics and the inner symmetry (in 4-dim. always a compact symmetry group) as well as the construction of the charge-carrying field algebra from basically the causality and spectrum structure of local observables. This is like Marc Kac’s “how to hear the shape of a drum” where the ear is the observable algebra and the shape of the drum is the field algebra i.e. the field algebra including its particle statistics and its inner symmetry is constructed from its observable shadow (the observable algebra), a marvelous conceptual achievment. You cannot do such things in the Lagrangian setting where the structure of the field algebra is assumed ab inicio.
Sergio (together with Roberts and Fredenhagen) also worked on “noncommutative QFT” with Quantum Gravity in mind (although what they actually do is noncommutative QFT in Minkowski spacetime). Despite their “good physical intentions” they arrive pretty much at those problems which other people many years afterwards also found with less good physical motivations (a L-invariance breaking “aether”, only partially solved problems with unitarity, no complete improvement of short-distance properties etc.)
In my view (AOP 319 (2005) 92) the most serious problems (in addition to unitarity) which the present generation of physicists are generally overlooking is the question of whether some sort of macro-causality (no timelike precursors, spacelike cluster properties) can be maintained. As I explained in my review, an earlier generation of physicists (in the 50-70ies) who studied the feasibility of nonlocal QFT really payed attention to this point and ended in failure (wrong in a sense which Pauli would have deeply appreciated!); this was at a time of honesty in particle physics when people did not published positive results and surpressed negative ones even though they came from the same assumptions.
I know that there is presently only one setting which fulfills all the assumptions (including cluster properties) the “direct particle interaction” of Coester and Polyzou, but the profound work of these nuclear physicists seem to remain unnoticed among particle physicists. When I mentioned this in a blog last month there came a very interesting reaction from Eugene Stefanovich pointing out that there are other attempts which use a more field theoretic presentation, but I did not yet find the time to look at them (they may very well also treat that macrocausality requirement correctly, but since this is a very delicate conceptual point, I prefer to look at this before I say something).
I have a question to all of you, can anybody provide me with a reference where the cluster factorization property of the string S-matrix was shown?
“I have a question to all of you, can anybody provide me with a reference where the cluster factorization property of the string S-matrix was shown?”
We went through the same problem with respect to vacuum polarization.
At the end of the day, you insisted that Lattice Gauge Theory (the only rigorous (some might say, not yet rigorous enough) definition of an interacting 4D field theory, that currently exists) does not have the requisite “structural properties” for vacuum polarization.
Can you point to a rigorous proof of cluster factorization in a 4D interacting field theory, as a model of a proof that you would consider satisfactory in the string case?
Of course, the derivation of cluster properties as a structural consequence on the same conceptual level as TCP, spin&statistics is a consequence of the principles of local causality and positivity of energy. Have done this for the correlation functions the Haag-Ruelle scattering theory carries it to the S-matrix. Prooving it for a concrete model amounts to checking these two properties and this is extremely simple and in all models which have been constructed in any mathematical rogorous sense and in those models which only have a Lagrangian name but are not yet mathematically born it is guarantied by the fact that causal locality and positive energy-momentum spectrum are formal properties of the Larangian quantization setting which become rigorous as soon as you are able to fill this Lagrangian name with a mathematical content. It is of course true in every order of perturbation theory.
In string theory the conceptual position of the S-Matrix is totally different; instead of being the crown of an underlying theory it is the result of a yet mathematically (outside that genus perturbation theory) not secured cooking recipe which comes from a theoretical blue yonder attempt and therefore there is really something to prove here. But in my question I would be satisfied with an answer in lowest nontrivial order in fact I would already be satisfied if one can see that the 4-particle amplitude (the one which comes from that two tubes joining and splitting) goes to zero if you remove the center of wave packets to infinity in spacelike direction (but of course without any additional approximation of the amplitude). I am not so familiar with the analytical form of these amplitudes, otherwise I would have done it myself.
The important point is that whereas in QFT you get it for free (from other well-known properties), in string theory you have to prove something (asymptotic properties of presumably quite complicated function). I would find it very strange if this has not been done in G-S-W or Polchinski’s book.
Since I would except perturbation theory, there is no reason to take refuge to a lattice.
You may find the discussion in Polchinski’s book (for the bosonic string) satisfactory.
In general, there is an intricate mapping between properties of the 2-dimensional world sheet theory and analytic structure of the spacetime S-matrix.
(A word of caution, since in your question, you seem to blur the distinction between S-matrix elements and off-shell Green’s functions: conventional string perturbation theory does not attempt to produce expressions for the latter. Only S-matrix elements are defined, but the poles and cuts of the perturbative S-matrix do satisfy all the usual axioms – something that was not guaranteed in a quantum theory of gravity.)
Sorry for the several typos in my posting from yesterday, but since I think that they did not impede the understanding of the content.
Yesterday I left my cottage in Arraial do Cabo (160 km north of Rio de Janeiro, lovely micro climate caused by a passing cold Patagonian current) and went to the nearby Cabo Frio to interrupt my temporary self-chosen solitude. I went to a Chorinho Club. Chorinho is probably the result of the oldest musical encounter between African and European traditions. It is approximately of the same age as as ragtime and New Orleans jazz. The melodic lines (guitar, flute or clarinet) are rich and complex and they are all written down (like ragtime) and hard to improvise on. Everybody in the older generation knows them. The freedom of improvisation is mainly on the side of the rythm which is created by a pandeiro and a cavaquinho. There were many old couples and some “coroas”, widows or divorcees of African (probably the strongest ethnic component around Rio), Arabian and European descend. I did not know that Brazil received so many immigrants from the time when the Otoman empire fell apart. The coroas had extravagant very light clothes with a lot of gold rings around their arms, ornamental belts and impressive trappings around their neck. Their vibrant way of dancing encapsulated memories of past beauty and art de vivre. It reminded me of Wim Wenders social club.
I always have been attracted by the originality and richness of Brazilian popular music inasmuch as I liked jazz (when I was at Princeton in the early 60ies I went down to East Village several times to listen to Art Blakey and many other jazzists. While in Pittsburgh I once met a Brazilian au pair girl who aquainted me with the music of Chico Buarque de Hollanda, Gilberto Gil and other Brazilian composers. So when I finally went down there for the first time in 1968 at the invitation of Jorge Andre Swieca, I was not totally unprepared about Brazilean popular culture. The country was in the grip of a military dictatorship but the popular culture was flourishing. Several compositions of Chico were banned by the military and Gil and Caetano Veloso had to flee to London. The censureship was quite severe and many concert and theatre productions were forbidden. This often had the effect of refining the style (one had to avoid addressing problems directly) and significantly enhanced the artistic value (with all apologies to the aficionados of political correctness), an effect which my colleagues from the former Soviet Union probably also experienced. I perfectly understood why Feynman during his more than on year stay in Rio de Janeiro was so much taken in that he did not only become a honorary member in one of Rio’s famous Samba school, but he was an activel participant of the batucada section (he played the frigideira a small frying-pan-shaped piece of metal which requires a very high playing speed).
When I came home I had to listen to some Brazilian form of hiphop because the young guys park their ghettoblaster cars near my living place. What a difference to what I had heard before and the high quality popular music which used to be deeply appreciated by all strata of Brazilean society (remember the maid in Pittsburgh I mentioned before)! Brazilian hiphop (at least the one I have heard) is primitive on the musical side and usually pornographic in its lyrics. How can such a rich popular culture fall into such gaping cultural hole within only two generations?
But isn’t the history of particle physics physics very similar? Did’t we hit the rock bottom in past years? Take a central issue as scattering theory. The S-matrix wasn’t the result of a prescription, but the proud crown resulting from underlying spacetime properties (the LSZ-Haag-Ruelle scattering theory). Because of this you did not have to worry about properties which you may have forgotten to impose. But look at what string theory made of this once proud object. If you want to know the counterpart of the Brazilian hiphop, well it is Kakuism, and I am not sure if even a car-dealer would like this kind of hiphop.
I really meant the on-shell S-matrix and not some off-shell extrapolation. It is precisely for that reason that LSZ and HR had to work on top of the (already at that time known) cluster properties of correlation functions.
Of course, that one can be much more specific in criticizing string theory, but in my personal opinion it is a waste of time, because most of stringers are so arrogant that do not even heard or read their colleagues. This is the main reason of failure ot string theory as working theory.
I find amazing the history of the subject, with almost all of past stringers’ claims recently proven to be false or considered today to be not so obvious.
From a historical point of view I find history of the variation of the number of dimension or the recent formulation of M(atrix) theory as a theory of pointlike particles two funny points. Maybe the biggest historical error is, in my opinion, the generalized belief between string theorists that a perturbative theory with a spin-two quantum field was a theory of quantum gravity. It was not, therein the need for the unknown M-theory.
Regarding your S-matrix question i never saw a full proof. In fact, would it exists?
The cluster decomposition principle is a hint of QFT (has anyone measured particles infinitely separated?) due to non-existence of full bounded states (only free fields are well-defined).
String theory borns from particle physics, therefore, it copies most of concepts and methods. However, string theory cannot ignore gravitatory effects (as QFT does) and in the large scale, you may include several effects as a cosmological event horizon or the dynamical expansion of universe. Standard string theory (e.g. bosonic version cited above) deals with a classical fixed predefined infinite background. In the generic case there is not factorization and the full string theory scattering perturbative approach breaks down.
Then what? A Hawking $-matrix like approach? I doubt.
The problem with QFT and string theory is that both admit S-matrix as the fundamental observable. Original criticism by Dirac or Landau whereas ignored by mainstream continues holding.
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Objection your honor, the S-matrix is not a fundamental (but extremely) object of QFT, rather it is the crown/roof of an edifice which is founded on localization and stability principles. The fact that with more recent insights (coming from modular localization theory) the S-matrix also reveals some information about wedge-localization does not really change its role as the honey glaze on top of the cake.
QFT also cannot deliver an intrinsic distinction between bound and elementary particle states; it rather implements full nuclear democracy being only moderated by a hierarchy between fundamental and fused superselected charges (and the cluster factorization property takes this nuclear democracy fully into account). A particular model may invite you to think of some particle state as being a bound version involving other ones, there is nothing wrong with this. But in many cases you find another description which shows that what you considered as elementary permits also a composite interpretation and there is nothing wrong with this either; this is just the consequence of the ubiquitious vacuum polarization. Only in QM such a distiction has an intrinsic meaning. Many of the things which appear intrinsic are not, e.g. the gauge theoretical setting to characterize a theory.
The S-matrix setting is valid precisely as long as the Wigner particle picture is relevant and of course in CST it is not applicable. For this reason Fredenhagen and Haag have based their derivation of Hawking radiation for a collapsing star on registration rates of radiation-counters (they define what this means) and not on Wigner particles (see also Walds comments in his reviews of this issue).
Sorry in the previous post it should read: extremely useful, and in one of my earlier posts the incomplete phrase
“but since I think that they did not impede the understanding of the content”
should be completed by: I did not bother to correct them.
I know experimental success of field theory and also some of attempts to provide a more solid foundation to the whole issue.
I was saying is that QFT (and standard string theory) assumes that S-matrix is a fundamental observable. This cannot be true and reason for improvement from several schools and authors.
The theorems on localization, stability et cetera are not convincing when one checks mathematical details. This is reason that people as Dirac, Landau, Wheeler, or Feynman (I am citing only great past guys) knew of those limitations and took QFT as a first step in the formulation of a complete and consistent relativistic quantum theory.
They failed in their respective attempts but at least recognized the problem. Usual QFT textbooks simply ignore the difficulties with QFT, with others -such as recent Weinberg manual- going beyond and attempting to present us the discipline in an “axiomatic way” as if QFT were a well-founded subject!
Most of supposed rigor of QFT breaks down when one studies details of the formalism. For example, it is not difficult prove that a quantum field does not fit inside a pure Hilbert space structure and one may go beyond usual framework, for example via a Rigged structure [Phys. Rev. A 1996, 53(6), 4075]. This is especially true when one try to obtain rigorous descriptions of instable particles, or of non-equilibrium thermal states between others. Another example is thermal phenomena. The irrelevant attempts to study thermal phenomena using QFT showed the lack of a rigorous and full foundation for standard thermal QFT and finalized in a new approach TFD from the particle physics community and alternative (more solid still) approaches from the statistical mechanics community (there are some attempts to improve TFD from ideas developed in the latter). Maybe I would remember here that already the original TFD is based in at least 5 new postulates modifying the most basic of QFT: Hilbert space, state vectors, Hamiltonian, operators, etc.
Another difficulty with the S-matrix approach is that derivation of master formulae is not mathematical or physically founded. I wrote a paper just on this topic has been submitted and accepted. The fundamental idea is that if Hamiltonian unitarity is true, then there is not possibility for a rigorous one-to-one mapping to experimental data (master formula) and if you map to experimental data then unitarity is not true. For illustration, I checked “derivation” of S-matrix in Weinberg manual (1st volume) and showed it contains at least three mathematical errors and two external assumptions (of course Weinberg received a draft copy of manuscript ;-). Van Kampen called “mathematical funambulism” to derivations of that kind! That is true.
When remarking QFT is a free field theory I (as others) did mean that exists not full satisfactory relativistic theory for bounded states. That is the reason that only asymptotic states can be rigorously studied with no possibility for studying intermediate states [Phys. Rev. A 1996, 53(6), 4075].
You can -at least formally- write a Schrodinger-like equations for a single electron but you cannot write a full equation for a two electron system and people use partial mixed approaches such as a double Dirac equation with non-field 16 component spinors and interaction potentials derived from QED but complemented with ad hoc procedures before implementation in bound states (continuum dissolution problem, and rest of trouble)…
It is true that QFT lets us to study some properties of bound states via formal scattering processes |12> —> |1>|2> but that is very different from deriving properties for the real bound state |12>. Dirac was very clear in the incompatibility of QFT with QM in his last works.
The vacuum polarization is just a mathematical artifact arising in QFT when one does *certain assumptions*. Already Feynman explained in his book on statistical mechanics why the usual methodology in QFT and atomic/nuclear QM was not rigorous and one would see what happens when one reintroduces the effects of taking the response of the rest of universe in the model. The picture is then very different (see his famous article with Wheeler on the so-called Universe response theory).
One of the interesting point you are missing is that one can obtain same kind of effects usually ascribed to a “vacuum polarization” in field theory without vacuum. Advantages of this new approach are a more solid foundation and that one can also compute another things cannot be computed from a field-theoretic approach [Rev. Mod. Phys. 1995, 67(1), 113].
And all those without including well-known inconsistencies of CED are not solved by QED. In fact, modern textbooks carefully avoid the topic.
Wald and others’ thoughts regarding particles in curved spacetimes are not concluding (and some thoughts are simply wrong). See above reference for remarks on a theory of particles in curved spacetimes and how it has been applied to description of cosmological models without initial singularities.
There is more interesting stuff to be discussed here, but sincerely I have no time.
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