Lee Smolin disproves his critics politely

Loop Quantum Gravity researcher Lee Smolin has answered 'critics' (mainly string 'theorists' who believe in unobservables) on Peter Woit's blog, LQG for Skeptics, http://www.math.columbia.edu/~woit/wordpress/?p=330. Lubos (Lumos) Motl of Harvard and some others rushed in with all sorts of 'arguments' trying to simply ridicule the spin foam vacuum approach to understanding quantum gravity (unifying general relativity and Feynman path integrals), when in fact they were just plain ignorant. Smolin then had to politely correct all their miscomprehensions:


Lee Smolin Says: January 20th, 2006 at 6:13 pm

Hi Peter, Thanks for mentioning this. After a quick look I can say that there are some statements they make that I agree with (such as about the difficiulties of relating the spin foam to the Hamiltonian constraint theory) and others with which I disagree, such as their statements about uv finiteness.

In particular, the point you quote, “the need to fix infinitely many couplings in the perturbative approach….” seems to disagree with old, well understood results. (Not to mention they don’t seem to make a detailed argument for their claim.) In fact, there is a well understood and detailed explanation for how the theory is cutoff. I won’t repeat the argument here (see hep-th/0408048) but the key points are that, as a result of the finitess of area and volume, one can show that the Planck length cannot suffer an infinite normalization if the theory is to reproduce the finiteness of black hole entropy,and the appearence of gravitons in perturbations around weave states. Thus, the theory is uv cutoff and the divergences do not have to cancel as they were never there in the first place. The key issue is then how is this finite cutoff length compatible with the symmetry of the ground state, which leads to the expectation that the symmetry is DSR.

But honest criticism based on detailed study is always welcome and I will read the paper carefully before seeing if I have any more substantial reponse to make.
In case anyone is interested, I am teaching a course on LQG, and video’s of lectures will be available as they are given at http://streamer.perimeterinstitute.ca:81/mediasite/viewer/FrontEnd/Front.aspx?&shouldResize=False

Thanks,
Lee

Lee Smolin Says: January 21st, 2006 at 9:51 am

On reading NP I am grateful for the hard work that they put in, but I end up feeling that they still miss the point, because they have prejudices about what a quantum theory of gravity should do coming from old expectations. They appear to evaluate LQG and spin foam models as if they were proposed as a unique theory which was a proposals for a final theory of everything. This is in my view a misunderstanding. One should understand these as a large set of models for studying background and diffeo invariant QFT’s. These are based on quantization of a set of classical field theories which are constrained topological field theories. There are three key claims: 1) these theories exist, rigorously. i.e. there are uv finite diffeo invariant QFT’s based on quantization of constrained TQFT’s. 2) there is a common mathematical and conceptual language and some calculational tools which are useful to study such models and 3) there are some common generic consequences of these models, which are relevant for physics.
Nothing NP say questions these key claims. Unfortunately, they do not mention key papers which support these key claims, such as the uniqueness theorems (gr-qc/0504147, math-ph/0407006) which show the necessity of the quantization LQG uses. And while they mention the non-seperability of the kinematical Hilbert space they fail to mention the seperability of the diffeomorphism invariant Hilbert space, (grqc/ 0403047). It is unfortunate that they omit reference to such key results which resolve issues they mention.

A second misunderstanding concerns uv divergences. NP do not discuss the results on black hole entropy, so they miss the point that the finiteness of the black hole entropy fixes the ratio of the bare and low energy planck length to be a finite number of order one. Calculations on a class of semiclassical states they do not discuss-the weave states-lead to the same conclusion (A. Ashtekar, C. Rovelli, L. Smolin, Weaving a classical metric with quantum threads,” Phys. Rev. Lett. 69 (1992) 237.). So there can be no infinite refinement of spin foams and no infinite renormalization. These theories are uv finite, period. This is one of the generic features I mentioned. Thus, their main claim, that the fact that there are many LQG or spin foam models is the same as the problem of uv divergent is just manifestly untrue. The freedom to specify spin foam amplitudes does not map onto the freedom to specify parameters of a perturbatively non-renormalizable theory. For one thing, few if any spin foam models are likely to have a low energy limit which is Poincare invariant, a property shared by all perturbative QFT’s, renormalizable or not, defined in Minkowski spacetime. In fact, we know from recent results that in 2+1 none do-the low energy limit of 2+1 gravity coupled to arbitrary matter is DSR. So their argument is false. They do get a number of things right. The following are open issues, much discussed in the literature: 1) whether there is any regularization of the Hamiltonian constraint that leads to exchange moves, 2) whether thus there are any links between the spin foam amplitudes and Hamiltonian evolution, 3) whether the sum over spin foam diagrams is convergent or, more likely, Borel resummmable (although they miss that this has been proven for 2+1 models, hep-th/0211026). I don’t agree with all the details of their discussion of these issues, but these certainly are open issues.

NP seem to argue as if one has to prove a QFT rigorously exists in order to do physics with it, by which standard we would believe no prediction from the standard model. They mention that there are no rigorous constructed, semiclassical states, which are exact solutions to the dynamics, but this is the case in most QFT’s. This does not prevent us from writing down and deriving predictions from heuristic semiclassical states (hep-th/ 0501091), or from constructing reduced models to describe black holes or cosmologies and likewise deriving predictions (astro-ph/0411124), Nor does it prevent Rovelli et al from computing the graviton propagator and getting the right answer, showing there are gravitons and Newtonian gravity in the theory (gr-qc/0502036).

But, someone may ask, if LQG is the right general direction, shouldn’t there be a unique theory that is claimed to be the theory of nature? Certainly, but should the program be dismissed because no claim has yet been made that this theory has been found? To narrow in on the right theory there are further considerations, all under study:

-Not every spin foam model is ir finite.-Not every spin foam model is likely to have a good low energy limit.-The right theory should have the standard model of particle physics in it.
In addition it must be stressed that there can in physics be generic consequences of classes of theories, leading to experimental predictions. Here are some historical examples: light bending, weak vector bosons, confinement, principle of inertia, existence of black holes. All of these observable features of nature are predicted by large classes of theories, which can be as a whole confirmed or falsified, even in the absence of knowing which precise theory describes nature, and prior to proving the mathematical consistency of the theory. LQG predicts a number of such generic features: discreteness of quantum geometry, horizon entropy, removal of all spacelike singularities, and I believe will soon predict more including DSR, emergence of matter degrees of freedom.

One reason for this is of course that most of the parameters in such classes of such theories are irrelevant in the RG sense, and do not influence large scale predictions. Since we know the theory is uv finite this does not affect existence. The lack of a uv unique theory does not prevent us from testing predictions of QFT in detail, and it is likely to be the same for quantum gravity. The old idea that consistency would lead to a unique uv theory that would give unique low energy predictions was seductive, but given the landscape, it is an idea that is unsupported by the actual results. Having said all this, I hope that NP will put their hard won expertise to work, and perhaps get their hands dirty and do some research in the area.
Sorry to go on so long,

Thanks, Lee

Lee Smolin Says: January 21st, 2006 at 1:09 pm

To Zorq, I apologise that the one argument I gave is far from the whole story. I agree that to define a theory you have first to define a regulated theory and then study the limit as the regulator is removed and show that the expressions for observables that result have the symmetries and gauge invariances of the classical theory. The physical parameters are parameters of the resulting theory. But this was exactly what was done in the hamiltonian construction of LQG, the observables such as area and volume are constructed through a limit of regulated operators and then the limit is taken. The result is finite, diffeomorphism invariant observables. The parameters of the finite, diffeo inv. theory include the bare Newton’s and cosmological constant-not as coefficients in the dynamics but as coefficients in the algebra of observables. The diffeo invariance is proved restored in the limit. And don’t be confused, the bare planck scale was not the regulator, there was another regulator, that has already been taken to zero. Please study the details of the construction.

So what you ask for has been done-the logic is not circular and the theory is finite. I was addressing the proposal to still take a limit of the parameters vanishing, even after the limit of the regulator to zero is taken. This would be non-standard, and it leads to results in disagreement with the semiclassical theory.

To quantoken: obviously it would be better to have precise predictions than generic ones. But generic ones can still distinguish between classes of theories. If GLAST sees an energy dependent, polarization independent speed of light, thus confirming that the symmetry of the vacuum is DSR, this obviouosly kills theories that predicted either broken or naive Poincare invariance and supports the plausibility of theories that predict-even generically DSR.
I can’t agree with your equivalanece of LQG and string theory just because of the vast imbalence in how much work has been put into each. For each point about string theory there are dozens of papers, so the ins and outs of each issue have been often thoroughly explored. Key facts about LQG still rest, in many cases on one or a few papers. There are many obvious things to do that have not been tried for lack of people. So there is a lot still do to, for example to turn generic predictions into precise predictions.

And I don’t “believe” nature is discrete, we showed this is a generic property of a large class of diffeo invariant QFT’s.

I’ll reply to the rest later,
Lee

Lee Smolin Says: January 22nd, 2006 at 8:58 am

Zorq, the distinction between a finite theory and a uv fixed point is the following: a lattice QFT or condensed matter physics model with a fixed lattice spacing is a finite theory. You can still apply the RG to study the infrared behavior. The point in LQG is that AFTER carrying out the regularization procedure and defining the diffeo invariant states and operators from the limit of the regulator removed, there remains a theory with a fixed, but spatially diffeo invariant cutoff. So it is like a lattice theory in being intrinsically finite, except that all the states are spatially diffeo invariant. So the physical theory has a fixed cutoff. One place this is explained in detail is Rovelli’s book, pages 280-282, another is my review hep-th/0408048. To see how this is done rigorously see Thiemann’s gr-qc/0110034 or Ashtekar-Lewandowski GR-QC 0404018.

Lubos, the finiteness is achieved kinematically, once the procedure just described is done the theory is uv finite WHATEVER the dynanmics, again just as in a lattice QFT with fixed lattice spaceing. But, to continue with my example of 2+1, which you misunderstood, is that the symmetry of the groundstate is not put in, it is determined dynamically. In 2+1 it turns out to be kappa-Poincare. This cannot agree with perturbation theory carried out as an expansion around Minkowski spacetime, which order by order assumes ordinary Poincare invariance.
I agree there is an issue in the Hamiltonian theory with full spacetime diffeo invariance, which is one of several reasons I always discuss dynamics in the spin foam picture.

Thomas and Aaron, this has been discussed before. For QFT the harmonic oscillator kind of quantization leads to Fock space. The inner product of Fock space depends on the background metric, hence this quantization will never arise in a background independent formalism. So we do not avoid it because we are stupid, it is simply not an option. The question is then to find an inner product for states which are functionals of a connection mod spatial diffeos. The only known way to do this is to first construct a kinematical Hilbert spaced that carries an exact non-anomalous rep of the spatial diffeos and then use that unitary rep to mod out by the diffeos .

The uniqueness theorems tell us the result is unique. If you don’t like this please at least acknowledge the argument just described and either accept it or propose an alternative background independent quantization and do the work to show it is consistent.

Anonomous: See my talk at the loops 05 conference, details are in a paper under preparation.