has been very long, and whoever is interested in this hypothetical alternative to string theory may want to read it.
Jacques Distler has originally asked a simple, well-defined question, but he can't get any answers although he has probably deduced the right answers from the non-answers anyway if he did not know them already before the discussion. ;-)
He is asking which gauge theories and which matter spectrum can be coupled to loop quantum gravity, and how does the anomaly cancellation constraint appear in the formalism?
That's a very clear question. If you asked the same question in any completion of a gauge theory that works, you could get a clear answer. For example, if you ask this question about type I string theory, you can present the cancellation of worldsheet anomalies that makes the full scattering amplitudes finite and cutoff-independent, which also guarantees the cancellation of the spacetime gauge anomalies, although the required mathematics looks highly non-trivial and different. But formulae can show that the cancellation of the worldsheet anomalies does imply the cancellation of spacetime anomalies.
Incidentally, Jacques has described very clearly how Lee Smolin misunderstands the word "finite" in physics. In properly done physics, finiteness of a theory means that the results are cutoff-independent. Lee Smolin uses the adjective "finite" for a theory that has been given a cutoff, without requiring any independence on the cutoff and physics near this cutoff scale. Putting a cutoff is always possible and easy, but it is a very different thing from solving the actual UV problems of a physical theory.
These problems are only solved if the framework generates results independent of the possible choices of the cutoff and the terms at the cutoff scale. String theory achieves this independence completely and removes all parameters; effective field theory achieves this goal approximately because relevant and renormalizable interactions at low energies only depend on a finite number of parameters. Nonrenormalizable theories as well as loop quantum gravity fail to satisfy the finiteness constraint.
In other contexts of string theory, you could show that only anomaly-free effective field theories are generated. In various subsets, you could say that you only generate non-chiral theories where the anomalies are absent and there is no interesting question to ask and calculate. In the case of dimer models, you could translate the anomaly cancellation conditions to a geometric language. At any rate, if you understood your formalism at least infinitesimally, you could have provided Jacques with a clear and complete answer within 10 minutes.
Jacques is asking these questions because he knows very well that the theories of chiral fermions are very problematic in the approach via lattice regularizations. If LQG is compatible with very basic properties of the world and particle physics and gauge theories in its low-energy limit, it must be able to reproduce the same conditions of the gauge anomaly cancellation.
By now, all of us more or less know that loop quantum gravity has no features that would make it more physically acceptable than other latticizations. One could simply answer Jacques' question with this answer:
- At this moment, we don't seem to get any constraints on the UV physics, we don't know whether we get a correct low-energy limit, and we don't know how the anomaly constraints arise.
We would offer such an answer in new approaches to string theory whenever such an answer would be correct. Instead, Lee Smolin is offering answers that look like commercials addressed to a very undemanding audience. Everything great can be done, and if it has not been done, it will surely be done quickly, and so forth. Neither of these sentences has anything to do with the hard core of Jacques' question. It's just a meaningless jelly.
Sometimes, the answers of the loop quantum gravity advocates use technical language, and if you try to interpret their sentences as assertions about science, you will find out that they are plain wrong. There is a long subdebate about the simple connectedness of the configuration space of loop quantum gravity, and so forth.
Every time Jacques or someone else offers a no-go theorem with a proof showing that a certain mechanism simply can't work or is plagued by an error that can be sharply described, Lee Smolin argues that the methods can't be used because LQG is something different, it is more and transcends the arguments of mortal beings like Jacques. Using Jacques' words, Lee Smolin indeed seems to believe that he has co-invented a new kind of science. ;-)
This kind of jelly-fish nonsensical chatter makes no sense to me. If a theory can't reproduce even the very general features of low-energy physics that have been experimentally verified, such a theory is in a big trouble. There is certainly no reason to celebrate because the theory, if the word theory is appropriate for a structure that has infinitely many continuous unknowns, has no implications for physics.
Another loop quantum gravity advocate called "fh" honestly says that
- if you think that physics is about a description of interactions on Fock spaces, then LQG is not even wrong, utter failure, silent, and unable to say anything.
Jacques is being nice so he says that he does not think that this is what physics is all about. Your humble correspondent however thinks that all of natural science is about objects and their properties, and according to the cutting edge physics, objects are excitations of quantum fields and they have interactions that can be described by terms in an action. All of particle physics is about the spectrum of possible particles and quantification of terms that allow them to interact. Even string theory can be interpreted in this framework if you extend it appropriately (e.g. allow string fields in string field theory).
There are more diverse insights in physics than just talking about the spectrum of an operator and the values of the couplings, but even these diverse insights are indirectly insights about the spectrum and the couplings.
If a theory cannot say anything about the spectrum of objects and their interactions, then it cannot say anything about physics. A theory can claim that the fundamental objects are really different than quantum fields in spacetime - and various formalisms in string theory indeed tend to say that locality in spacetime is something emergent and not fundamental - but you must still be able to use your more fundamental building blocks to derive the known properties of physics as encoded in classical GR and the Standard Model, or at least qualitatively similar theories. If you can't do it, you just have nothing to say about physics.
Another line of Lee Smolin's argument is that no one likes canonical loop quantum gravity too much anyway because people are switching to spin foams. First of all, all major canonical LQG practitioners such as Thiemann or Ashtekar are continuing with the canonical LQG approach. Second of all, switching to spin foams makes no difference because no explanation of anomaly cancellation (or other mechanisms from real physics) exists in the spin foam framework either.
Lee also asks:
- Do you really believe that a lot of smart people have worked for 20 years on something and just fooled themselves?
No, I don't think so because of at least two reasons. First of all, it has been more than 20 years, and second of all, I doubt that the adjective before the word "people" is overly accurate. ;-)
The way how the loop quantum gravity jelly-fish debaters try to avoid any calculation, any answer, learning of any new understanding of physics that actually makes sense, or any inconvenient conclusion in this debate about anomalies in LQG indicates that they could fool themselves or comparably "smart" people not only for 20 years but for 1000 years if necessary. They just have not understood what hard science means, in which case 20 or 1000 years make no difference. The Earth has seen millions of years in which no significant progress in science was made by smart people. Sorry, I mean people. Sorry, I really mean apes. ;-)
The questions that they were trying to answer incorrectly for 20+ years can be answered correctly by a good high-energy physics student who just defended his or her PhD in 1 hour. That does not mean that the grad student is 200,000 times smarter than the loop quantum gravity community because the relation between the intelligence and the rate of making progress is nonlinear. ;-)