But there is one more comment that is pretty typical not only for Peter but also for others who have no factual arguments and who replace them by misleading ad hominem descriptions of the inconvenient thinkers:
- ...I’m curious to hear from experts what they think of this article...
As far as I can see, the previous paper about LQG by Nicolai, Peeters, and Zamaklar that we discussed here is by far the most cited LQG paper written in 2005. Is there some way to justify that these people are not experts? I don't think so. You may define experts as those who dogmatically insist on some Holy Scripture written by someone else in the past. But in this particular case, the Holy Scripture is known to be at least partially flawed and important analyses are missing in it altogether.
For example, LQG does not solve the UV problems with the infinite amount of undetermined higher-derivative terms; it just replaces them by an infinite number of unknown terms in the Hamiltonian constraint or parameters of the spin foam Feynman rules. Everyone who has a basic understanding of the physical concepts knows that the reason is quite clear and Peeters and Nicolai's arguments are robust. Peter tries to suggest that this particular serious flaw of LQG is analogous to string theory in some mysterious way. Of course it is not and only physics ignorants could buy such a statement. String theory does solve this problem and predicts a clear structure (and values) of all higher-derivative terms, including those in the gravitational sector. This is exactly what we mean by the well-established statement that string theory solves the UV problems of quantum gravity.
Similar observations hold for the ultralocality of LQG, a fatal flaw that makes the kinematical Hilbert space non-separable and prevents ordinary notions of continuity from appearing in the LQG framework. Of course that string theory does not suffer by any of these problems either. Its Hilbert space(s) is (are) always separable and continuity - in fact, the exact physics of GR and QFT - follows from string theory at low energies.
We could go on and on and on. String theory reproduces special relativity; LQG does not. String theory is consistent with the existence of other forces and fields (which moreover seem necessary not only according to the experiments but also because of internal consistency of quantum gravity) and it in fact predicts them; LQG does not. There is no "analogy" or "equality" and whoever thinks that for every argument against LQG, there must exist an argument against string theory (that's probably the ultimate approach of political correctness), is crazy.
Peter may criticize that string theorists investigate the "landscape" of solutions and he may dislike the large number of discrete solutions. But regardless whether we understand the landscape, its size and its interpretation correctly, string theory is the first theory we ever had (and the only theory we have as of 2006) that allows us to address the question about "possible Universes" at all. In all other "theories" (including LQG), the space of possibilities is only bounded by our imagination and the time we invest to write down new terms. The space of possibilities is an infinite-dimensional continuum. In string theory, the discrete set of possibilities is made out of solutions to rather well-defined rules and can be classified. This ability to discriminate what is possible and what is not is desirable; in fact it is necessary if we want to argue that we have mastered quantum gravity. It is because in quantum gravity, we can in principle get from any "phase" to any other "phase" (think about cosmology that has no superselection sectors) and a complete theory simply must know about all these "phases"; in the stringy jargon, I really mean the "backgrounds".
Should we really use the word "expert" exclusively for those who misunderstand these basic points? Do we really want to return to the Middle Ages when the quality of scholars and their teachings was determined by the degree of their dogmatic literal belief in the Bible (or Rovelli's book or what precisely plays the role of the Bible in this context)? Should we dismiss people as non-experts just because they know evolutionary biology or string theory - or they are sinners in yet another way? Sorry if you don't like to hear it but Nicolai and Peeters are among the leading LQG experts in the current world and your humble correspondent belongs to the group that follows after them.
I confirm that the paper not only covers the most essential material about LQG that we know but it also lists fully legitimate issues with LQG that would have to be resolved before LQG could be claimed to be a promising candidate theory of quantum gravity.
There is a significant asymmetry in the relation between string theory and LQG, of course. It is very likely that no "LQG specialist" would be able to write a meaningful review of string theory that others could cite. It's simply because LQG is, in comparison with string theory, a naive game for children. Quantum gravity is a pretty specialized field and it is just a wrong idea to try to isolate separate branches that should not talk to each other. People who are quantum gravity experts - such as Nicolai and Peeters - are just naturally interested in all these questions that LQG and other approaches try to answer. So am I. And they reach certain conclusions. It is not surprising that some people whose technical errors and oversimplified and flawed assumptions are revealed don't necessarily like these developments. But it is absolutely crucial for science to move on.
If there is any controversy, it is not really between string theory and LQG. It is between narrow-minded physicists who don't want to study the insights found by others and who want to be confined in prisons defined by hundreds of their mostly incorrect assumptions - especially the assumption that the world must be a version of LEGO and everyone who thinks otherwise must be wrong because the world surely can't be more complicated than LEGO; and those who do study physics without prejudices, who are able to change their opinions and ideas by looking at the evidence obtained by others, who are ready to eliminate conjectures that have been falsified, and who actually make some progress.
And that was the memo.