I started thinking about who are typical of the young crop of LQG people because of the Smolin essay
[published in June 2005 Physics Today, a monthly of the American Physical Society]
In case you don't have hardcopy of the Smolin essay, Motl provided this link to the text
http://waltf007.mindsay.com/
And then there was the discussion about the essay at Not Even Wrong,
http://www.math.columbia.edu/~woit/blog/archives/000204.html
http://www.math.columbia.edu/~woit/blog/archives/000206.html
and Smolin's clarifying post there, which selfAdjoint refers to
https://www.physicsforums.com/showthread.php?p=603973#post603973
...I agree Smolin comment at Peter's blog is good reading and has some valuable insights. Why not post it here, as sA suggests? So I will. It fits in more with this thread discussion of diversity/lack of diversity in US departments. Choices grad students have, what their options are here in US and abroad especially in Europe.
So I will fetch a copy and post it here.
Post #10 in this thread was a copy of Smolin's 14 June response on N.E.W. to comment made there on his essay.
Then there were further comments by others---if you want to see them follow the links to N.E.W.
then Smolin responded further. Just for completeness I will copy his 18 June and 21 June responses on Peter's blog.
----quote Smolin 18 June Woit's blog---
Thanks again for all the insightful comments. Perhaps I can add something to a few of the threads of discussion.
-On LQG and discrete structure. First, do we agree that even though electrons move in space the spectrum of the hydrogen atom being discrete means that quantum mechanics of the atom has discrete structure? In a very similar sense, since all the geometric observables including volume, area (and yes length) have discrete spectra, corresponding to a discrete basis (of diffeo classes of embeddings of labeled graphs) then the quantum geometry of space has become discrete. The key point is that the discreteness scale-roughly L_Planck, cannot be taken to zero, otherwise black hole entropy comes out wrong, and semiclassical states do not correspond to classical metrics.
-But it is true that if you derive a version of LQG from a strict quantization of GR, there is a fixed background, which is the bare differential manifold. There is no background metric but there is a background topology and differential structure, defining the diffeo classes of embeddings of the spin networks.
-Hence, Markopoulou followed by Freidel and others, proposed dropping the embedding and basing the theory just on combinatorial spin networks. These models are then discrete in a stronger sense. There are some advantages to this (reformulation in terms of a matrix model, cleaner relation to causal sets) but one can non longer claim the theory is a precise result of a quantization of GR. Both frameworks, with and without embeddings, continue to be studied.
-The discreteness of length was shown in T. Thiemann, gr-qc/9606092, J.Math.Phys. 39 (1998) 3372-3392. Angles also have disrete spectra: S. Major, Class.\ Quant.\ Grav.\ {\bf 16}, 3859 (1999) gr-qc/9905019; gr-qc/0101032.
-On spin foam models and discreteness. There are several different spin foam models under study. In all of them a history is a discrete labeled combinatorics structure (for example branched 2-complex.) In some of them the label sets are continuous because they come from the rep theory of Lorentz or Poincare and areas are not discrete. But these have not been shown to correspond to evolution amplitudes for canonical states. Others (Reisenberger, Markopoulou, etc) do give evolution amplitudes for spin networks and have discrete areas.
- M asks, is there a suitable correspondence principle where known physics can be recovered? The answer is yes. There are several results that show that excitations of certain LQG states reproduce, for momenta small in Planck units, the spectra of conventional QFT’s including gravitons, photons etc on flat space or de Sitter spacetime. Some are cited in section 4.4 of my review hep-th/0408048. See also hep-th/0501091. See recent papers by Freidel, Livine and others that show in full detail how standard Feynman perturbation theory emerges from a spin foam model for gravity coupled to matter in 2+1 when G_Newton goes to zero.
As to what people in non-string approaches to quantum gravity are doing, I agree, why not look at the conferences? Here are some recent ones, some with talks available.
http://www.cpt.univ-mrs.fr/~rovelli/program2.html
http://www.ws2004.ift.uni.wroc.pl/flash.html
(talks at: http://www.ws2004.ift.uni.wroc.pl/html.html )
http://www.perimeterinstitute.ca/activities/scientific/PI-WORK-2/
-Several of the comments ask, why quantize as in LQG? Why not quantize with another approach (such as one that uses anomalous reps?)
I do not see how there can be an apriori reason to prefer one quantization scheme over another one. Our job is to construct candidate quantum theories of gravity, compare their results and learn from them. In LQG there are existence and uniqueness theorems that prove that the approach exists, and theorems that guarantee uv finiteness. Thus, the approach leads to a structure that mathematically exists and within which computations can be done. Many computations have been done.
We are thus no longer at a stage where it is interesting to ask why do or why not do questions. There are now a different class of questions which include: Does the theory make predictions? How do they compare with experiment? What properties have been shown? What remains to be shown? There are certainly several key open issues to discuss, and we are not shy to discuss them.
No one is claiming that we know LQG is the right theory of nature. We are claiming that it is a well developed approach, that gives an apparently consistent answer to what we think is a necessary question, which is how to construct a diffeo invariant QFT in the absence of a fixed background metric. This gives a rich arena with many open problems and many things to do either to understand it better, make predictions, or as a jumping off point for the invention and study of new theories.
So the attitude is rather different from other approaches. Some string theorists admit they do not know what string theory is, but they nevertheless are sure it is right. In LQG we study well defined theories, which have many good properties, but most of us feel no need to “believe in them” pending experimental confirmation.
So our attitude is if someone like Thomas Larsson has a different approach that’s great. We know what its like to be starting something new other people don’t understand or support, and we will support you, so long as you don’t waste your and our time attacking us on a priori grounds. We suggest you should try to develop your ideas to at least the point where we can compare the results.
For example, someone asks, “What's wrong with anomalies? Sure, it turns first class constraints into second class constraints, but Dirac showed us how to deal with that.” Fine, we only insist that this is not the only way. The LQG results and theorems show that you can find diffeomorphism invariant states through a different procedure, involving only first class constraints, which is
a. Construct a kinematical Hilbert space, which is a rep of a Poisson algebra that coordinatizes the phase space, which carries a unitary and non-anomalous rep of the spatial diffeo’s.
b. Use that non-anomalous unitary rep to construct explicitly another Hilbert space, which is the space of diffeomorphism invariant states.
c. Compute many observables of interest representing diffeo invariant classical quantities as finite operators on this space, leading to predictions of physical interest, an ultraviolet finite theory etc.
There are by now so many rigorous results supporting this construction that the burden of proof is on the other side: given that this procedure works and leads to a well defined finite physical theory, why not explore its consequences as a possible quantum theory of gravity?
So when Urs says, “It seems to me that the reason to drop weak continuity in the quantization of gravity in 3+1 dimensions is that it makes an otherwise intractable problem tractable - but possibly at the cost of having oversimplified a hard problem,” fine, but let's discuss the results. Does this lead to a space of states with enough physical states and with a well defined dynamics? YES. Are some states interpretable as semiclassical states? YES. Does that dynamics have all the properties we require for a quantum theory of gravity? YES to some questions such as uv finiteness, other questions are still open, such as a proof that the ground state is semiclassical.
-Aaron says, “It is, in fact, a radically different approach to quantization that, when applied to current theories, gives experimentally incorrect answers.” Thomas Larsson argues that “I find it very disturbing that LQG methods yield the wrong result for the harmonic oscillator.” I don’t understand the logic of their arguments at all. Yes, it is a different quantization, i.e. one based on representations of the algebra of Wilson loops and electric flux’s rather than local field operators. Yes, it is unitarily inequivalent to Fock space. That is good, as Fock space knows about a particular fixed background metric. If a background independent Hilbert space, which quantizes the whole space of metrics, were unitarily equivalent to a Fock space based on a single fixed metric, something would be wrong.
The claim is precisely that this is a new class of QFT’s which is available to quantize diffeo invariant gauge theories in 2+1 dimensions and above, and which has novel features and leads to novel results. So long as the resulting theory is well defined, I don’t see the force of an argument from a priori grounds. that experience shows Fock type quantizations must be right in all cases because they only work when there is a fixed background metric, while the whole point of the new quantization is that it provides an answer to the question of how to construct a well defined QFT in the absence of any background metric.
-If you still want to have an argument on a priori grounds as to why representations of non-canonical algebras will be required to have a background independent quantum theory of gravity, please go back to the papers of Chris Isham from the late 70’s and 80’s where he made a detailed and convincing case for this. These papers, together with the work of Polyakov, Wilson, Midgal etc on formulating quantum gauge theories directly in terms of Wislon loops were the major motivation for LQG. What we did was construct the non-canonical algebras Isham called for from Wilson loops. Also, please note that lattice gauge theory is not based on Fock space.
-Finally, I am not a director of PI, just one of the scientists, so PI is very far from “Smolin’s institute”. Also, when I am defending LQG I try to discuss the whole research program, not my own personal work, which departs in some papers quite a bit from that of many of my friends.
Posted by: Lee Smolin at June 18, 2005 07:35 AM
---end quote---
---quote Smolin 21 June Woit's blog---
Re the last comment, on recovering ordinary QFT from LQG, let me stress again that there are explicit known semiclassical states, and ordinary QFT is recovered at long wavelengths by studying excitations of them. Hence, we know that the physics of flat, or DeSitter spacetime is in the theory.
The problem is to go beyond these results to
i) show that the ground state, subject to some appropriate boundary or asymptotic conditions, is such a state, ii) show whether classical spacetime emerges from a generic physical state and iii) show whether lorentz invariance is preserved, broken or deformed by Planck scale corrections in the ground state, and hence predict what should be seen in AUGER, GLAST, ICECUBE and other upcoming experiments.
In recent papers, Freidel et al show how deformed Poincare invariance arises as the limit of LQG coupled to matter in 2+1. See also hep-th/0501091 for an admittedly heuristic argument that this is true also in 3+1.
For these see sections 4.4 and 5 of hep-th/0408048 and the references provided there.
As to whether it might be easier to obtain certain results in a different formulation with anomalous reps of the spatial diffeo's, perhaps, and this could be worth trying, but only if one does not put in what is to be shown, which would be the case if those reps are constructed with reference to a background metric.
Posted by: Lee Smolin at June 21, 2005 10:37 AM
---end quote---
