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Smolin's reply to review in the New Scientist

  1. Oct 9, 2006 #1


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    Last edited: Oct 9, 2006
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  3. Oct 9, 2006 #2


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    text of comment by Lee Smolin on CV blog Oct 9th, 2006 at 10:24 am

    Dear Sean

    Thanks very much for an intelligent, perceptive review. If I may, then just a few words about the points where we disagree, because differences in judgment about these are at the heart of the issue.

    1) Background independence. You assert, “It’s unclear whether this is really such a big deal. Most approaches to string theory are indeed background-dependent…but that’s presumably because we don’t understand the theory very well. This is an argument about style; in particular, how we should set about inventing new theories.”

    No, this is not about style, it is about a necessary criteria a fundamental physical theory should satisfy. The argument for this goes back to Leibniz, and the literature is extensive. I won’t repeat what I said in the book and in papers such as hep-th/0507235. General relativity should, in the view of many experts have settled it on the side of background independence. For the many experts in physics and philosophy who are convinced of this, this is a non-negotiable criteria, which string theory so far does not satisfy. (For those who think it does, see below.) I believe the case for background independence is convincing and that many who are not convinced have simply not thought the issue through carefully enough.

    There is a style issue but it is not about background independence, it is about two communities, one of which is familiar with the history of thought about the nature of space and time, the other of which is more pragmatic and feels they can “wing it” , use the same kinds of techniques that work in background dependent QFT to evaluate a quantum theory of gravity, and do not feel the need to make a careful study of the literature on the physical interpretation of GR before attempting to go beyond it.

    As to whether the lack of background independence in string theory is, as you assert, “… because we don’t understand the theory very well,” this is a fond hope of mine, and it was the theme of my second book, Three Roads to Quantum Gravity. I spent many years trying to make a background independent approach to string theory-indeed LQG came out of this. So far it hasn’t convincingly worked, although I think that the direction I explored, which was a background independent membrane theory based on a matrix-Chern-Simons theory has promise. But being one of the few people to have tackled this problem, I should say it is not easy and I am worried that so few other people seem to be putting any effort into it.

    It is sometimes asserted that AdS/CFT is a background independent formulation of string theory. This cannot be correct, because the whole point of background independence, going back to Leibniz’s principle of the identity of the indiscernible, is that there can be no global symmetries in a fundamental theory. This is true of GR with compact boundary conditions, and certainly not true of AdS/CFT which has a large group of global symmetries, What AdS/CFT doers show us is that a global internal symmetry can be dual to a global spacetime symmetry, but this is not background independence.

    2) The need for rigorous mathematical foundations and proof for fundamental theories
    You say:, “Both the finiteness of stringy scattering and the equivalence of gauge theory and gravity under Maldacena’s duality are supported by extremely compelling evidence, to the point where it has become extremely hard to see how they could fail to be true.”

    Two issues are being confused here. First, there is not now a complete argument either for the finiteness of all orders string scattering or the strong form of the Maldacena conjecture, even at the theoretical physicists level of rigor. There are interesting developments in progress concerning finiteness, which is good, but nothing so far that is generally accepted at working to all orders. There is not even a closed form definition of “string theory on AdS^5 X S^5 backgrounds “ so there is not even a precise mathematical statement of the strong form of the Maldacena conjecture. And at no level of rigor is there a proposal for either the basic principles of string or M theory or the basic equations of the theory.

    Second, it is just not the case that we never prove things in physics. There is only one area where this is true-and then only partly-which is QFT. It is true that the standard model is very successful experimentally in spite of the fact that there is a lot of theoretical evidence it cannot have a rigorous formulation. But this is not a good model for a fundamental theory, for we accept this situation by casting the standard model as an effective field theory. It is certainly OK to work with an effective field theory which has no rigorous formulation, but that is precisely because we have good evidence that it is to be replaced by a more fundamental theory. Indeed, the expectation that the standard model has no rigorous underpinnings is one of the arguments for the need for a unification beyond the standard model.

    But a claim for a fundamental theory is something else, for it cannot-by definition-have a more fundamental underpinning. So it must stand up on its own. This means we must be able to formulate it cleanly and precisely and the important properties it enjoys should be theorems. It doesn’t mean physicists should all work at a rigorous level, but that rigorous framework must be there to refer to.

    This is not an unrealizable ideal. Classical Newtonian mechanics satisfies it. So does classical statistical mechanics, ordinary non-relativisitic quantum mechanics and general relativity. In each of these cases there is a body of rigorous results and a community of mathematical physicists who work on them.

    Is this too much to hope for theories of quantum gravity. No! LQG has a rigorous foundation, given by Ashtekar, Isham, Lewandowski, Thiemann and others. The central result in the whole subject of LQG is a rigorous theorem, the LOST theorem (math-ph/0407006, gr-qc/0504147). It asserts that there is a unique quantization of a diffeo invariant gauge theory with 2 or more spatial dimensions, subject to some technical, but physically reasonable conditions.

    To respond directly to your quote above: given the apparent difficultly of proving the perturbative finiteness of superstring amplitudes, it is perfectly conceivable that it fails at some order. The delicate issues that make it hard to prove, such as those that concern the boundary of supermoduli space or the ambiguities of gauge fixing at arbitrary genus, are not to my knowledge addressed by power counting arguments that underlie our intuitions about when quantum field theories are perturbatively finite. My guess would be these problems can be overcome, but some mathematicians I now who have worked on these problems are not so sure. Even if it does, given how many QFT’s that are well behaved in perturbation theory fail to exist rigorously, and given that we have strong evidence that the string perturbation series is divergent, it is reasonable to worry that string perturbation theory, like the perturbation theory in QED, will not define a rigorous theory. And, as discuss in the detail in the book and in earlier papers (hep-th/0303185, hep-th/0106073), it is perfectly conceivable that a weaker form of the AdS/CFT conjecture is true, which does not rely on there being something rigorous corresponding to string theory on AdS/CFT.

    I think that the difference between people who are and are not convinced by the evidence in these cases comes down to the following: do you have at the back of your mind the belief that there is a mathematical structure corresponding to the exact formulation of string theory? If you reason assuming that the answer is yes, you tend to be convinced that the conjectures we have been discussing are true. But if you do not reason that way, and take the existence of a mathematical structure corresponding to exact string theory as an open conjecture, yet to be decided, you find it more plausible that many partial results could be true about a structure in perturbation theory or weak coupling, and yet, as in the case with many QFT’s, no rigorous theory exists that they approximate.

    3) LQG, You say that “general relativity is not well-behaved at short distances and high energies, where such new degrees of freedom are likely to play a crucial role” The LOST theorem just mentioned implies that GR, and indeed any diffeomorphism invariant gauge theory, is well defined at short distances. We understand in detail how spatial diffeomorphism invariance removes divergences from diffeo invariant quantum gauge field theories. We understand this in many different calculations, some rigorous, some not, some involving the behavior of operator products, some involving the behavior of path integrals. If you do not understand this you do not understand the basics of LQG. At this point the only thing to say is to ask you to please learn the basics of the subject before further commenting on it.

    4) On why string theory so strongly dominates over other approaches. You say, “String theorists have somehow managed to convince all of these people that their field is worthy of support; I personally take the uncynical view that they have done so through obtaining interesting results.” To some extent this is certainly true. But some of those results generated expectations that have since been disappointed, with regard to uniqueness and the ability to generate predictions, as well as with regard to the existence of M theory, which is still a conjecture.

    To some extent it may also be true that in the evaluation of the promise of string theory, departments took key conjectures as proven. As I describe in TTWP, some physicists I’ve spoken to in departments I’ve visited were unaware that perturbative finiteness, AdS/CFT and M theory were still open conjectures, without proof. Indeed, a few years ago, when I tried to find out what the precise situation was with regard to these conjectures, I had to ask many string theorists before finding someone who could give me the correct answer, so many experts were also confused and believed more was shown about these issues than has been.

    One example of what I mean is the following: in many presentations M theory is presented as if it were something that already exists, rather than its true status which is a theory that has yet to be constructed. I personally think it is misleading to show the usual star diagram and say this is M theory: we know the boundaries but we don’t know much about the interior, when the correct thing to say is that dualities satisfied by the theories on the boundary support belief in a conjecture that there is a theory that fills in the whole space, but we do not know if that conjecture is true because we do not have a satisfactory candidate for this theory. Indeed, perhaps as a result of talks which were no precise about this, some non-string theorist physicists I’ve spoken with had the impression that there really is a well formulated theory by the name of M theory.

    For what its worth, we in LQG were for the most part, very careful not to overclaim or exaggerate our results. If anything, the practice in non-string approaches to quantum gravity is to underclaim, as this is more the style in mathematics and in European science, where most workers come from. Indeed, I used to be sometimes an exception to this, and when I have on occasion over-claim my friends told me in harsh terms that it was harming the field.

    You claim I over-hype certain results in LQG, but in the book I make it very clear that these are early, preliminary results and that much remains to be done before we can see if their promise is realized.

    Does this difference in styles have anything to do with the relative success in gaining positions, funding etc in the US? I don’t know, but I think it is a question worth asking. In fact there has been much substantial progress in non-string quantum gravity and quantum gravity phenomenology over the last ten years. If you are right, should we be starting to see some interest in hiring the people responsible for them?

    5) On the connections with experiment. Of course evidence for extra dimensions or supersymmetry would provide moral support for string theory, but they would not provide confirmation for string theory itself. Neither do they contradict LQG, which can accommodate them. But the key point here is that the Planck scale is accessible through astrophysical measurements and those experiments are ongoing. The question that is experimentally accessible is whether Poincare invariance is broken or deformed at the Planck scale, if it is experiment will over the next few years detect this. This is important to stress because so many of us-including me-used to argue that the Planck scale is inaccessible. Consequently, there is a growing activity of Planck scale phenomenology, which is so far not very appreciated in the US.

    Finally, I am glad we agree about the need to do things to encourage more intellectual independence within US Science. But then you say “ In the real world, it’s difficult to see what to do about the problem.” No, there are a number of things we can do and I have made some obvious suggestions in my book and in my Physics Today essay. The first step is to talk with people like venture capitalists and investment fund managers about how they succeed in diversifying investments in a climate of scarce resources. Some of the obvious proposals I discussed were already implemented by the founders of PI such as making sure to hire people working on more than one approach to a fundamental problem. Others have been implemented by the FQXi foundation, which is to target people whose work takes big professional risks to attack foundational problems and fund them. More could be done both by departments and by foundations such as NSF, by simply changing the questions asked during peer review so as to give more advantage to people inventing and carrying out their own research programs and disadvantaging people doing unimaginative and unambitious “me-too” science.

    But let me close by again thanking you for a perceptive review.

  4. Oct 13, 2006 #3


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    Smolin at CV continued:
    Lee Smolin on Oct 13th, 2006 at 9:58 am

    Dear Sean, Jacques and others,

    It seems to me we have answered Georgi’s objection over and over again. I’ll try it again. First, is this the complete statement of it (from http://golem.ph.utexas.edu/~distler/blog/archives/000639.html): [Broken] “The point is that there’s no decoupling regime in which quantum “pure gravity” effects are important, while other particle interactions can be neglected. “Universality” in field theory — usually our friend — is, here, our enemy. Unless we know all particle physics interactions all the way from accessible energy up to the Planck scale, we can never hope to extract any quantitative predictions about quantum gravitational effects.”

    This is true unless there is a universal mechanism that cuts off quantum gravitational fluctuations and the fluctuations of anything else, because as a consequence of this mechanism there are simply no degrees of freedom with wavelength smaller than the Planck length. In fact, there is a such a mechanism, and it is understood, as I said, both heuristically and rigorously. To understand it heuristically you have to think carefully about how imposing spatial diffeomorphism invariance limits what can come out of an operator product, regulated through a point splitting procedure.

    This is clearly described in the literature now for more than 10 years, please read the literature at whatever of rigor you are happy with. Then come back and either indicate you agree or indicate that there is a technical error somewhere in the proofs of this.

    This implies that the uv problem does not suffice to fix the matter couplings. This however does not imply that the theory can make no predictions. An example is 2+1 gravity with matter as solved by Freidel and Livine. A universal effect is a deformation of the Poincare symmetry governed by a single computable parameter. If this turns out to be true also in 3+1, as indicated by semiclassical calculations, it implies predictions for GLAST.

    Please tell me why this does not answer Georgi’s objection.

    Also, to Sean, “whether the theory recovers GR (or some close relative thereof) in the classical limit, is not a minor technicality. It’s basically the whole point…” Certainly, and therefore you should be celebrating with us the results of Rovelli et al that show that the graviton propagator emerges from a spin foam path integral with the correct low energy behavior, demonstrating that the theory has gravitons and also a Newtonian gravitational force. You should also be celebrating with us the Freidel-Livine results I just mentioned as they show that in this interacting, perturbatively non-renormalizable model (2+1 gravity coupled to matter fields) the low energy limit emerges and it is QFT in a background spacetime, but on a non-commutative manifold.

    These are important developments, but they were not the first indications that LQG has a good low energy limit.
    There were also various results showing that there are semiclassical states which approximate classical metrics and that QFT on background manifolds emerges as an approximation when one studies excitations of those states.

    And while I agree with your sentiment, it didn’t have to turn out that the quantization of GR does give a rigorously defined hilbert space and observables algebra, but it did. Shouldn’t this be a clue? The fact that we now have good evidence that the low energy limit has gravitons is then I would think compelling.


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