Let me comment on Lee Smolin's remarks about the paper by Nicolai and Peeters (NP):

- 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

The comment that the LQG papers share some general mathematical and conceptual language is a purely sociological assertion that essentially means that the LQG researchers have not had time to learn other portions of mathematics or other concepts and all of them seem to be confined by similar limitations. It is certainly not a good thing, and it does not suggest that LQG fits together. Narrow-mindedness of the mathematical methods is neither a necessary nor a sufficient condition for a physical theory to be logically consistent. These are completely different things.

- 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, (gr-qc/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,

We can write down non-renormalizable theories and non-renormalizable interactions, but unless we have a UV complete theory, these extra interactions cannot be predicted. They're purely a phenomenological description of the deviations from the "simpler" theory, and if we have infinitely many of such unknown interactions with coefficients of the same order, then it is equivalent to a complete ignorance. The theory is just about parameterizing our ignorance in a different way.

- 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.

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