This Week’s Non-Hype

Since I often post here complaints about articles produced by the press offices of various institutions that hype in a misleading way physicist’s theoretical work, I thought it a good idea to make up for this by noting a positive example of how it should be done. The SLAC press office this week has a Q and A with Lance Dixon, with the title SLAC Theorist Lance Dixon Explains Quantum Gravity which is quite good.

Dixon gives an informative explanation at a basic level of what the quantum gravity problem is. He includes an even-handed description of the string theory approach to the problem, and explains a little bit about the alternative that he and collaborators have been pursuing, one that has gotten much less attention than it deserves. This is a very technical subject, so there’s a limit to how much he can explain, but he gives the general idea, and includes a link to his most recent work in this area.

Many promotional efforts for string theory begin by making claims that quantum field theory cannot be used to understand quantum gravity, due to the divergences in the perturbation series. This has been repeated so often, for so many years, that it is an argument most people believe. The situation however is quite a bit more complicated than this, with one interesting aspect of the story the discovery in relatively recent times that long-held assumptions about divergences in perturbative quantum gravity calculations were just wrong. Such calculations turn out to have extra unexpected structure, and thus unexpected cancellations, making naive arguments about divergences incorrect. Continuing progress has come about as Dixon and others have developed new techniques for actually computing amplitudes, uncovering unexpected new symmetries and cancellations.

For a good summary of the current situation, see this talk by Zvi Bern, especially page 7, where Bern details how, going back to 1982, “So far, every prediction of divergences in pure supergravity has either been wrong or missed crucial details”. For N=8 supergravity, current arguments say that a divergence should show up if you could calculate 7 loop amplitudes, but Bern warns against betting on this. In that talk he also explains the recent work with Dixon and others that gets mentioned in the SLAC piece, about the surprising nature of the divergence in pure gravity at two-loops, making its physical significance and whether it really ruins the theory not so clear.

I was interested to read Dixon’s account of his thinking back in the mid-80s:

I began to be concerned that there may be actually too many options for string theory to ever be predictive, when I studied the subject as a graduate student at Princeton in the mid-1980s. About 10 years ago, the number of possible solutions was already on the order of 10500. For comparison, there are less than 1010 people on Earth and less than 1012 stars in the Milky Way. So how will we ever find the theory that accurately describes our universe?

Although this never made it into media stories, I think that by a couple years after the initial enthusiasm for string unification in 1984, many theorists had already started to notice that the idea likely had fundamental problems, with a serious danger that it would turn out to be an empty idea. This now has become clear, but the idea lives on, with “QFT must have divergences” the main argument for continuing to take it seriously. Now that argument isn’t looking so solid…

Update: A good explanation of the situation from 4 gravitons who, thankfully, is not overly worried that he might be giving succor to the Woits of the world…

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37 Responses to This Week’s Non-Hype

  1. Christopher Herzog says:

    I think it’s interesting that one of the main tools that Dixon et al. use to compute scattering amplitudes in gravity is a relation between gravity and gauge theory amplitudes that in my opinion is simplest to understand from a string theory perspective — the Kawai-Lewellyn-Tye relations (Nuclear Physics B, 269 (1986) p 1-23).

  2. Peter Woit says:

    Christopher Herzog,
    Sure, that’s one of several techniques they use. But if you look at Bern’s slides string theory doesn’t seem to be the source of the new phenomena that they’ve been discovering in recent years. It looks a lot more like they are uncovering new basic structures in perturbatively quantized gravity quantum field theories, and I don’t see evidence that string theory is the way to understand them.

  3. Umesh says:

    Perturbative divergences aren’t the only problem plaguing QFT-like treatments of gravity – this is a very retro, 80’s way of stating it, and it’s no fault of string theorists that it keeps getting reported/ repeated this way. The much more profound aspects of non-QFT like behaviour of gravity involve the area like scaling of entropy, for which there seems no sensible explanation from a local QFT point of view. The only known way is AdS/ CFT, which is string theory again (of course other examples of explicit calculations are Strominger/ Vafa etc, which involves string theory in a crucial way.). This isn’t to downplay any of the the above work on perturbative supergravity amplitudes, but to make use of the above to attack string theory by cherry picking one aspect of perturbative quantum gravity is wrong.

  4. Peter Woit says:

    This isn’t an “attack on string theory”, just reporting the fact that one of the standard arguments used to claim qft cannot describe quantum gravity shows signs of being in the process of being shown to be wrong.

    As for entropy scaling with the area not being possible in qft, recall that Hawking radiation is a semi-classical qft calculation.

    Going on about how poorly understood relations to AdS/CFT are the only way to understand quantum gravity in 4d dS is just pure hype, and trying to claim that such arguments show qft can’t be used in this context is absurd.

  5. Umesh says:

    Hawking’s calculation is indeed an ‘semi-classical QFT computation’, but the entropy in question is of the black hole background – which needs a quantum theory of gravity to be understood. QFT, with it’s local degrees of freedom, can never produce an area extensive scaling. Of course effective QFT in a black hole background is sufficient to highlight this point, but the conclusion is about gravity (semi-classical in this case), not about QFT. To repeat, Hawking’s calculation doesn’t say anything about the QFT. Also, nowhere in my comment have I claimed that AdS/ CFT can be directly (or in any obvious way) used to understand dS quantum gravity. I have used it to highlight the conceptual issues about quantum gravity, the area scaling of entropy being one of them.

  6. Peter Woit says:

    The posting was about conventional claims that you could never get quantum gravity out of qft because of its perturbative short-distance behavior now looking like they may be wrong. I don’t think your claims about qft and area law behavior are any more solid. The history of qft contains a long list of claims that qft couldn’t reproduce X (see the history of the Higgs mechanism and QCD) which turned out to be nonsense. Often this was because of the subtleties of gauge invariance and gauge degrees of freedom. The subtleties of geometrical degrees of freedom and diffeomorphism invariance are even greater.

  7. Umesh says:

    It is true that QFT has overcome many issues claimed to be beyond its reach in surprising ways in the past. The claim that QFT cannot reproduce the area extensive entropy are much more solid and quantitative – references are numerous – contrary to what you claim. Of course one cannot predict anything about the future, but perturbative finiteness doesn’t mean non-perturbative consistency (which is where the trouble with quantum gravity lies, and the area extensive scaling is a hallmark of a non-perturbative effect in quantum gravity – leads to issues like loss of unitarity and so on). Barring some miracle (with local theories like QFT), it is in no way clear as to how to get an area law for something as universal as the entropy, at least in any obvious way. I’m also quite sure that nobody claimed ‘you could never get quantum gravity out of qft because of its perturbative short-distance behavior’ – it surely was one problem with making a conventional QFT of gravity for starters. If one thinks he/ she has an answer to that, there’s a huge list of issues waiting to be answered – area extensive entropy is next on that list.

  8. Peter Woit says:

    Sure, there are problems with any theory of quantum gravity that go beyond the heavily advertised perturbative short-distance problems. I’m just pointing out there’s a problem with the central heavily advertised claim here (do you deny this?).

    I personally don’t see any point to entering into ideological arguments of the “my non-existent supposedly consistent but inherently untestable non-perturbative theory of quantum gravity sucks less than your non-existent supposedly consistent but inherently untestable non-perturbative theory of quantum gravity” sort. It seems clear to me that the bottom line is we don’t yet know what the right fundamental degrees of freedom are to describe space-time geometry, or what the right way to go about quantization of these is. In such a situation, vague arguments about “entropy” and “locality” are no serious reason not to pursue any particular line of research.

  9. Noboru Nakanishi says:

    Two decades ago, I showed that the perturbative approach to quantum gravity is nonsense, because it is based on the wrong assumption that the zeroth-order approximation of the gravitational field is a c-number (see N. Nakanishi, Gen. Rel Grav. 27 (1995) 65). Quantum Einstein gravity can be formulated quite satisfactory and beautifully without using perturbation theory (see N. Nakanishi and I. Ojima, Covariant Operator Formalism of Gauge Theory and Quantum Gravity (World Scientific, 1990)). The method for solving qft in the Heisenberg picture is reviewed in N. Nakanishi, Prog. Theor. Phys. 111(2004), 301.

  10. Ralph says:

    I’m confused about the emphasis on the very-large-number of discrete string theory vacua.

    With atoms, we tend to make continuous approximations for collections of millions or just thousands of atoms. Why are solutions to string theories different?

    With 1e500 string theory vacuosities, why should one count discrete solutions, rather than making continuous approximations to the set of solutions, and using less precise but more informative notions such as dimension and measure?

    E.g. 1e500 solutions would be no big deal if they were all spread along a single “line” characterized by a single parameter. One could treat the parameter as a continuous variable until/if we ever managed to constrain the parameter sufficiently to reduce to a smallish number of physically realistic solutions, and then when justified, switch to the more precise discrete picture?

  11. vmarko says:


    You should be careful to make a distinction between 10^500 solutions of a single theory and 10^500 different theories. The latter is the landscape problem in ST. It is the problem of 10^500 inequivalent ways to define one particular theory, before ever looking for any of its solutions.

    And no, you cannot parametrize those 10^500 theories with a single parameter (or any reasonable number of parameters), since there is no unique order relation between them (you cannot tell which vacuum would come “before” and which “later” as you increase the parameter). If such a technique were possible, people would be already using it. 🙂

  12. Umesh says:

    ‘..there’s a problem with the central heavily advertised claim here (do you deny this?).’
    This particular claim is more complicated according to me to be responded to in simple confirm/ deny (or agree/ disagree) terms (also my denial is of no value in these intensely technical matters). As far as specialists are concerned, I think it is true that highly supersymmetric theories of gravity (as in {\cal N} = 8 SUGRA in 4d) might be perturbatively finite to high orders. That said, to claim that the whole issue of short distance divergence of gravity (the ‘heavily advertised claim’, as you put it) has started to seem wrong is false. In my limited view of the subject, it is still reasonably accurate to say that most garden variety field theory versions of gravity (even with less SUSY) are divergent in the normal sense. I don’t know the full status of the field, but think it fair to claim that even experts would agree that the perturbative divergence issue in gravity as a field theory is far from settled. Again, let me emphasize the SUGRA community has done an amazing job with these intensely difficult calculations (not that my emphasis matters).

    “my non-existent supposedly consistent but inherently untestable non-perturbative theory of quantum gravity sucks less than your non-existent supposedly consistent but inherently untestable non-perturbative theory of quantum gravity”
    I cannot speak for you precisely, but I presume the aspect of the ‘ideological debate’ you refer to (in this case) is the case for gravity as a field theory (and its perturbative finiteness) vs. string theory as a quantum theory of gravity. As an aside, I should mention that there is a post somewhere on this blog that has a similar discussion, there the case has been about the ‘asymptotic safety’ scenarios for gravity (also to with gravity as a field theory) vs. string theory, and the same issues remain. Fundamental degrees of freedom describing spacetime geometry are well known in certain special geometries – again I’ve to refer you to many thousands of papers about the AdS/ CFT correspondence. Therefore, that we ‘don’t know the fundamental degrees of freedom of spacetime geometry’ is a blanket statement that is wrong. Further, you say, and I quote ‘..vague arguments about “entropy” and “locality”..’ . I must emphasize that the basic notions of ‘entropy’ and ‘locality’ in QFT and QFTs as applied to gravity are far from ‘vague’. Right from Hawking’s seminal paper full of quantitative calculations of entropy to other attempts at getting the area law and thousands of follow up papers (to Strominger/ Vafa’s calculation) are very much counter to your claim.

  13. Peter Woit says:

    This discussion shows exactly why I generally make it a policy to avoid debates about quantum gravity. It’s an extremely complex subject, with debates like this immediately degenerating into empty ideologically-driven sloganeering, with endless irrelevancies (“asymptotic safety”???) and dubious claims thrown in to make sure that no substantive question gets accurately addressed. This is just a complete waste of time.

    Dixon is doing the opposite, addressing a very specific, well-defined technical issue with the theory and making progress at better understanding it. Given his success at this and his background doing important work in string theory, his opinion that looking at alternatives to string theory as a theory of quantum gravity I think is well worth listening to.

  14. Umesh says:

    I don’t quite understand what sloganeering and dubious claims you’re referring to. I mentioned that there was a blog post here relating to the asymptotic safety scenarios for gravity as a field theory, and as similar discussion ensued. I’m sure Lance Dixon is a great physicist and has much important to say about string theory (surely more than me), but on the other hand, I could invoke equally competent authority to claim that ‘alternatives to string theory as quantum gravity’ are quite futile. That wouldn’t suit you, or help the discussion, would it? Just to repeat again, to make sure there is sufficient accuracy, here’s where I stand:

    The claim that gravity is finite in perturbation theory in no way makes the ‘non-renormalizability of gravity’ claims completely go away. It is true that highly SUSic theories of gravity are perturbatively finite. This by itself in no way dilutes the claim for string theory as correctly addressing the issues which remain once perturbation theory is accounted for.

    Also, said blog post relating to asymptotic safety:

  15. Peter Woit says:

    Following that link to my old blog posting, the only content there relevant to this discussion is a sentence from a commenter pointing to a long rant by Lubos Motl, and I see Lubos has a new equally long one today. I find it hard to think of any bigger waste of time than trying to engage with those.

  16. Umesh says:

    Sure, you’re free to decide whether or not to spend time on Lubos Motl’s blog. There’s more relevance than just the commenter’s pointing to Lubos Motl’s blog. Whether or not his post is driven by ideology is subjective and surely irrelevant. The only important thing is about the reference to black hole thermodynamics (surely independent of any ideology), which is discussed in the comment thread. I’m just pointing out the similarity to the discussion above. Let me copy-paste your reply to V_NO:


    What Weinberg is talking about is the standard claim for string theory that it is needed to deal with the perturbative renormalizability problems of quantum gravity. That may not be true, either because of asymptotic safety, or also because of possible perturbative finiteness of some supergravity theories.

    Non-perturbatively, you don’t really even know what string theory is, I don’t see how one can claim it’s the only possible way to deal with non-perturbative problems in quantum gravity. The problem is more complicated than just invoking black hole thermodynamics, which was originally discovered as a semi-classical phenomenon in QFT.

    If I understand your above reply correctly, you seem to be ambiguous regarding string theory being the only way to resolve non-perturbative issues of quantum gravity, one manifestation of which is black hole thermodynamics (please note similarity to above discussion, which is literally the same thing). If the problem is ‘more complicated than just invoking black hole thermodynamics’, then it stands to reason that one must solve that issue immediately if one thinks that he/ she has overcome the ‘renormalizability problem of gravity’ one way or other, before proceeding to ‘more complicated’ aspects you seem to refer to. If the same remains your stance pertaining to the above discussion, I’ve nothing more to say.

  17. Peter Woit says:

    If characterizing Motl as “driven by ideology” is “subjective”, so is everything… Sorry, I’ve wasted enough time on this.

  18. Umesh says:

    It just means that Lubos Motl’s blog posting is irrelevant to this this discussion. What is surely not ideology is black hole thermodynamics, and that’s the bulk of my last comment. The question of whether or not when one solves ‘perturbative issues in quantum gravity’ one can indeed solve issues related to black hole thermodynamics is a sharp physical question, independent of Lubos Motl’s (or yours, or mine or anyone else’s, for that matter) ideology. If you can concentrate on this aspect, we can make progress about the issue at hand.

  19. chris says:


    why is pointing out progress in a direction that progress has been thought to be impossible 10 years ago so offensive to you?

    Dixon&Bern have really done great work in the last decade. They picked up a task that ‘t Hooft gave up and made progress. Whether or not you like it, that does change the perspective on perturbative gravity for some of us.

    And about that area-entropy relation: all you have to do is cut a QFT at the stretched horizon. Or use Ashtekar variables. Yes, holography is an interesting feature – but how that motivates string theory is beyond me. and even how that relates to the topic discussed here other than a distraction from it is even less clear to me.

  20. Umesh says:

    As I’ve made clear in my comments, the work of Dixon-Bern is far from ‘offensive’ to me, as you claim. I’ve even made it clear that Dixon is a great physicist (and achieved string theorist as well). Therefore, I don’t understand why you feel the achievement of above physicists (which also I characterize as great, not that it matters) is ‘offensive’ to me. I should possibly be very clear that high order perturbation theory calculations in SUGRA are great. I have nothing against it, and am surely not advocating abandoning it or some such idiocy. Apart from that, because of my ignorance, I can’t quite comprehend your statements about black hole entropy, maybe some paper/ reference would help. I don’t think I’ve mentioned anything anywhere in my comments that imply ‘holography motivates string theory’. If you are saying that there’re other ways to get black hole entropy apart from strings, great, I don’t know of them. What I don’t quite follow is how impressive work on the finiteness of perturbative SUGRA (or asymptotic safety in gravity) would possibly imply that it is non-perturbatively consistent – without evidence coming from black hole thermodynamics and so on. Apart from that, lemme say again, tour de force work.

  21. vmarko says:


    I agree with you that advances in perturbative QG are not going to teach us much about nonperturbative problems such as the BH entropy.

    But I am quite perplexed by your statement “If you are saying that there’re other ways to get black hole entropy apart from strings, great, I don’t know of them.”. Wow, is it really possible that you haven’t heard of, say, loop quantum gravity? The calculation of BH entropy in LQG doesn’t involve AdS/CFT, doesn’t involve SUSY, doesn’t require 10 or 11 dimensions, doesn’t require string-anything, but certainly does get the entropy calculation right. And the calculation works for an ordinary Schwarzschild black hole, as opposed to the extreme Kerr black holes that are doable in ST. And you haven’t even heard about any of this?! Wow!

    If you honestly really didn’t know that there exists a LQG calculation of BH entropy, start for example here,

    and look up the LQG-related references cited in there.

    Best, 🙂

  22. Peter Woit says:

    Sorry folks, I’ll delete any more attempts to carry on this argument about black hole entropy calculations. It really has nothing to do with the Dixon article, and anyone who wants to read an LQG vs. string theory argument about these calculations can find it a hundred other places.

  23. Chris W. says:

    In reading the SLAC Q & A, which is obviously intended for non-specialists and the general public, it is apparent that Dixon avoids discussion of the dynamics of spacetime itself. That is, the focus is on how far one can get a conventional QFT for a field that has the characteristics expected of the gravitational interaction in flat spacetime with a fixed metric.

    The upshot is that one can get considerably farther than was initially thought after early attempts. This decouples two issues that seem normally to be conflated; (1) can perturbative finiteness of a quantum theory of the gravitational field be achieved, and (2) can gravity be understood as an interaction in flat spacetime, for which calculated effects normally thought of as indicative of spacetime curvature can be given an operational interpretation in flat 4-dimensional spacetime that works for most or all “practical” purposes.

    Notice that (2) assumes we can do calculations, i.e., that (1) has been answered in the affirmative. The question then becomes, what do we make of this? Does it fly in the face of the lessons we thought we had learned from general relativity? Does it make the program implied by (1) essentially pointless, even if it is successful on its own terms?

    One possible response—perhaps more or less what motivates workers in this area—is that the effort is far from pointless. It would give a well-defined quantum theory of gravity in which one can do sensible calculations with results that can be compared with observation. If those comparisons show disagreements (as one might expect), then the theory has problems, but they are empirical problems, not internal problems that render the theory inherently nonviable. One will have to consider where to go next, but an extremely important milestone will have been achieved, which contrasts sharply with the current predicament of string theory (and the putative M-theory).

  24. oneloop says:


    Please read this paper

    and this Wikipedia article

  25. vmarko says:

    While I admire the attempts of Dixon and others to push and see how far one can get with the idea of perturbative QG, and the quality of the SLAC Q&A being an exquisite example of non-hype (as Peter says), I have to say that I am somewhat skeptical regarding the whole program of QG as a spin-two field in flat Minkowski spacetime. Chris has put it in a form of a question:

    “can gravity be understood as an interaction in flat spacetime […] Does it fly in the face of the lessons we thought we had learned from general relativity?”

    My answers would be that gravity is (1) unlikely to be understood like that, and (2) it certainly does fly in the face of GR.

    Treating gravity as a spin-two field in flat spacetime is just like treating planet trajectories using epicycles — it can certainly be done, provided that you introduce enough free parameters, but it is unlikely to give you any real geometrical insight into what is going on, and it is ugly beyond anybody’s taste. One of the major points of GR was that spacetime itself is participating in physical events, as opposed to being a “box” in which physics happen. This is called “background independence“, and the approach to gravity as a spin-two field in flat spacetime (infamously endorsed and advocated by Feynman) simply ignores this lesson of GR. Besides, the background geometry is unobservable, so insisting on it is like insisting on aether in electrodynamics. You can have it, but to what purpose?

    Even if one accepts the background-dependent approach, the question is which background is better, Minkowski or de Sitter? Given that we observe a positive cosmological constant, one can argue that de Sitter background would be more “correct” than the Minkowski background, rendering void most of perturbative QG in flat spacetime.

    So while Dixon’s research is valiant in its technical ingenuity, skill and very nontrivial analysis, I somehow doubt that it can have any fundamental impact on the problem of quantum gravity.

    [attempt to discuss black hole entropy with oneloop edited out]

    Best, 🙂

  26. Peter Woit says:

    Perturbation theory isn’t analogous to epicycles in celestial mechanics, it’s analogous to, well, perturbation theory in celestial mechanics (where it has a very long history).

    It’s not unreasonable to expect that, for a weakly coupled theory, a perturbation expansion about flat spacetime based on gravitons might give an extremely good approximation, given that we live in a very nearly flat spacetime. If your perturbation expansion runs into trouble, you can argue that there’s a conceptual problem with the whole idea. One advantage the string theory quantum gravity program always had was that they had an argument that they didn’t run into this problem, but qft would (that argument now seems to have a hole).

    What I think is interesting about the Dixon et al. stuff is that they are unearthing new structure in these supergravity theories. Once this is better understood, it could be either not very interesting (a complicated mathematical artifact of the specific calculation), or very interesting (a deep new symmetry, one saying something about both fermionic and bosonic degrees of freedom).

    Dismissing what they are doing as useless because it’s not “background independent” or doesn’t reproduce an argument about black hole entropy, or isn’t holographic, or whatever seems to me foolish. Quantum gravity research programs that just study pure gravity, with whatever features you find attractive, are clearly missing a huge part of the fundamental structure of the world. Personally I’m extremely dubious that you can understand quantum gravity purely independently of matter degrees of freedom, and if you do, you’ll never know whether you’re right since you can’t test pure quantum gravity theories.

    And, please, endless arguments about “background independence” are even more stale and tedious than the black hole entropy ones. Just stop.

  27. vmarko says:


    “a perturbation expansion about flat spacetime based on gravitons might give an extremely good approximation, given that we live in a very nearly flat spacetime”

    As an approximation yes, I agree, but promoting perturbation expansion into a fundamental theory is a different ballgame. And we already know that there are high-curvature regions of spacetime (say, inside black holes) where the perturbative expansion around flat background just isn’t a reasonable thing to do. Promoting this approach to a fundamental theory of QG seems ill-conceived IMO.

    “a deep new symmetry, one saying something about both fermionic and bosonic degrees of freedom”

    I am not trying to dismiss Dixon’s work, and people should certainly be encouraged to keep studying it. But extraordinary claims require extraordinary evidence. If it really turns out that such a deep new symmetry is found and understood, I’ll probably become a believer. But until that happens, I’m simply very skeptical about the benefits of the whole perturbative approach.

    And regarding matter fields, I completely agree that studying only pure gravity won’t cut it. But the matter sector is also in a very poorly understood state. The Standard Model is complicated, reasons for particle families and symmetries unknown, and vast sectors not explored enough (dark matter, neutrinos…). It is questionable whether such a complicated structure can actually help in figuring out the properties of QG itself. IMO, QG should be studied together with matter fields, but only in a generic framework where the number and type of matter fields are not fixed in any way. Who knows what might come up next in LHC, or what dark matter is made of? One cannot really rely on any details of the matter sector when discussing QG — just generic properties and the type of coupling (equivalence principle, alternatives, etc…).

    Best, 🙂

  28. Peter Woit says:

    No one is claiming that a perturbative expansion is a fundamental theory. However, one might optimistically hope that if it succeeds, it will give evidence that one has identified a good set of fundamental fields and their symmetries. If one understands path integrals well enough (a big if..), one might then even be able to write down a fundamental theory.

    “the matter sector is also in a very poorly understood state”
    As opposed to the quantized geometry sector??? Here I disagree completely. The lesson of the last few decades in HEP is that we understand the matter + gauge fields sector depressingly well. And if your theory says nothing at all about this, and only deals with likely unobservable effects, you’ll have no way to convince others you have the right one, other than endlessly trying to claim yours is prettier than other people’s.

  29. Noboru Nakanishi says:

    As I stated above, the perturbative approach to quantum gravity has a conceptual difficulty. In order to set up the interaction picture, one has to choose not only a particular space-time structure such as flat but also a particular coordinate system such as Minkowski metric by hand (Indeed, if one adopts polar coordinate system, perturbation theory will become completely different from the conventional one.). This procedure explicitly violates general-coodinate invariance (more precisely speaking, BRS invariance) at the operator level, that is, pertubation theory explicitly violates BRS invariance in each order.
    The introduction of a particular c-number metric as the zeroth-order approximation of the quantum gravitational field is indeed wrong. The zeroth-order quantum gravitational field is a q-number; its explicit form was already given in terms of a complete set of Wightman functions.

  30. Peter Woit says:

    Noboru Nakanishi,
    I certainly don’t claim that I know how to set up such a perturbation expansion in a sensible way that properly handles local space-time symmetry via BRS. This is a question for Dixon et al. They have some calculational method which I believe they claim gives consistent, sensible results, and a lot of calculations of specific amplitudes to back this up. You’ll have to ask them how they handle the problem you identify.

  31. Dave Miller in Sacramento says:


    You said:
    >As I stated above, the perturbative approach to quantum gravity has a conceptual difficulty. In order to set up the interaction picture, one has to choose not only a particular space-time structure such as flat but also a particular coordinate system such as Minkowski metric by hand.

    You’re right, of course.

    However, when I was a doctoral student at SLAC back in the early ’80s, I did a bit of work on lattice theories: when I first heard about lattice theories, I objected that they violated Lorentz invariance in a *huge* way, and therefore could not be right.

    I trust that everyone here will agree that my initial impression was missing the point: i.e.,. working on lattice theories can be useful, and lattice theories can (sometimes) indeed recover Lorentz invariance in the limit that the lattice spacing goes to zero.

    Around the same time (circa 1980), I went to a seminar (I think it may have been by Dan Freedman, though I’m not sure — it has been a long time!) discussing early attempts at perturbative quantum gravity, and I made the same sort of objections that have been made here: the inability to deal with non-perturbative effects such as black holes, the breaking of general covariance, etc. The speaker tried to be polite, but clearly thought that I was an ignorant grad student who did not understand that you had to walk before you could run.

    Perhaps the speaker was right: I continue to be intrigued by the issues I tried to raise way back when, but, after all, neither I nor anyone else has solved those issues. Perhaps it is best to try to do something where one can actually calculate?


    P.S. Peter, I think discussion like this can help many of your readers think through these issues even if the discussion itself does not reach closure. After all, someday, some bright young physicist who is mulling over such conundrums may actually come up with something that will create a major breakthrough.

  32. vmarko says:


    “No one is claiming that a perturbative expansion is a fundamental theory.”

    Wait, are you saying that Dixon is not trying to construct a fundamental theory of QG? So he is talking about the prospects of quantization and renormalization of GR that will in the end be an approximate theory of some other fundamental QG model? Given that quantization is a nonunique process, why would you even expect that two different quantization schemes (the perturbative one and the “fundamental” one) would be compatible in any way at all? If Dixon is not trying to construct a fundamental QG model, then in what way is his work relevant for QG at all?

    Again, if he discovers some unexpected structure that can be used to construct a fundamental QG model, that’s great, and I’ll gladly change my opinion. Otherwise, I just don’t see what is the benefit of his approach, aside from developing mathematical techniques to perform complicated multi-loop calculations.

    ““the matter sector is also in a very poorly understood state”
    As opposed to the quantized geometry sector??? Here I disagree completely.”

    I said that the matter sector is also in a very poorly understood state. Namely, not as opposed to QG, but rather just like QG.

    “The lesson of the last few decades in HEP is that we understand the matter + gauge fields sector depressingly well.”

    Really? Why do we have three families of particles? Are neutrinos of Dirac or Majorana type? What principle fixes the choice of SU(3)xSU(2)xU(1) gauge group? Can you be certain that in the future LHC will not find the fifth interaction, extending the gauge group by an additional SU(4) term, for example? What is dark matter made of? What is the cause of matter/antimatter symmetry violation? I’d say that our understanding of these things is not depressingly good, but depressingly bad.

    The existence of the dark matter is a proof that the SM must be incomplete. So if we already know that, we have to expect that various properties of the SM are likely to change in the future (just look at what happened to the neutrino sector). It is a transitory theory, one that will keep being improved/substituted with various BSM models, as we learn new facts about matter fields from experiments.

    So when discussing properties of QG, one cannot rely on the details of the SM, simply because they are likely to be modified as we collect more data about matter in the UV and IR regimes.

    Best, 🙂

  33. Peter Woit says:

    One could hope that the relation between perturbative QG and fundamental QG might be much the same as for other QFTs one understands (e.g. QCD). Arguing that it’s not worth investigating the perturbative version is kind of like telling Feynman and Schwinger back in the late 40s “why are you wasting your time on those approximate calculations? Everyone knows the full QED theory is completely different, has a Landau pole, and that’s the real problem that needs to be solved”.

    I don’t know what to say about the claim that the state of QG is just like the state of the SM. Maybe there really are alternate universes and we’re in different ones…

  34. vmarko says:


    “Arguing that it’s not worth investigating the perturbative version is kind of like telling Feynman and Schwinger back in the late 40s “why are you wasting your time on those approximate calculations? Everyone knows the full QED theory is completely different, has a Landau pole, and that’s the real problem that needs to be solved”.”

    Well, the difference is that in QED we have access to experimental data that is described by the approximations that Feynman and Schwinger were developing, so they were obviously useful. But conceptually, this hypothetical criticism of Feynman and Schwinger is actually entirely valid — both QED and SM are effective field theories (i.e. approximations at a given scale), while the fundamental theory cannot be a QFT, precisely because of things like the Landau pole and such.

    In case of QED, perturbative calculations make sense because we can perform experiments, and compare the “true” experimental result to the approximate theory. When we see agreement, we use it as a confirmation that the approximation scheme is good enough, whatever the fundamental theory may be.

    In the case of gravity, however, we have no experiments, and there is no way to test if perturbative QG is anywhere near being a valid approximation to reality. So it’s a bit of an academic exercise. Putting one’s faith into it, then, is ideologically as biased as believing in the “truth” of string theory, LQG, or {insert your favorite QG model}.

    Again, I am not saying that perturbative approach is worthless or a waste of time. But if people are to take it seriously, its proponents must make a strong convincing case why they think that nonperturbative effects can be ignored in the quantization procedure. In QED you have strong agreement with experiment to make that case. In QG you don’t.

    Best, 🙂

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