This approach shows how elegant and efficient some proofs of mathematical theorems may become in the future. You conjecture that an infinite sum or integral is miraculously equal to another sum or integral. You identify these objects as two different forms of a physical observable in string theory, and prove the required duality by finiteness of a moduli space which itself follows from the holographic principle. ;-) This kind of smart connection with complex calculus or even physics agrees with some of the sophisticated modern methods that were used in maths to prove various things.
These approaches are not incontroversial and several people asked their questions and expressed their opinion that it cannot lead to new insights about high-energy physics - maybe even "by construction". :-) I understand these comments. Everyone realizes that it is not guaranteed that new approaches to uncover the new wave of discoveries in theoretical physics will succeed. And most people realize that it is not easy today to find some really new and exciting stuff.
But whenever Cumrun or someone else says a sentence that is even partially wrong, someone immediately tries to correct him. We simply can't build and don't build on wrong assumptions and wrong statements. And if an assumption is uncertain, everyone acknowledges that it is uncertain. And if the assertion is ambiguous or incomprehensible, someone asks what it means. In summary, Cumrun and several colleagues try to identify the common patterns of the known vacua of string theory in order to learn some general lessons about quantum gravity; string theory is used as an experiment to study quantum gravity. These general lessons include
- finiteness of the volume of moduli spaces in string theory
- a special example of the previous point is the finiteness of the volume of the parameter space of CFTs with respect to the Zamolodchikov metric
- upper bounds on the numbers of species, possibly correlated with the cutoffs
- lower bounds on the numbers of species in various backgrounds
- bounds on the strength of various interactions (under construction)
When I looked at Robert Helling's description of Loops 2005
plus the related papers and so forth, my impression was completely different than the impression from Cumrun's visionary talk. Their conference seems as a continuous inflow of ideas that are wrong and ideas that are not even wrong. Also, it seems that I am kind of familiar with the work of nearly all the speakers, and know why each of them is kind of incorrect (except Robbert Dijkgraaf who is usually right but who did not make it to the conference at the end).
Carlo Rovelli tried to derive the graviton propagator. We discussed this paper already. First of all, a graviton propagator only makes sense once we expand the metric around a background, which is in contradiction with the very general goals of loop quantum gravity. Second of all, in loop quantum gravity, it is known from the articles of Baez and others that singular simplices dominate the path integral, while Rovelli (incorrectly) assumes that the nice simplices that look like flat space give the most important contributions.
Lee Smolin proposed a model how macroscopic causality emerges (the problem in LQG is, first of all, that there is ultralocality and signals can't propagate at all for simple choices of the Hamiltonian). After Lee constructed quarks from LEGO, he conjectured that this model was connected with the Pioneer anomaly and low-angular-momentum discrepancies at WMAP. Well, maybe... ;-)
John Barrett presented a well-defined new version of a spin-network-like model which admits a diagrammatic expansion. I am pretty sure that these things can't be related to gravity, but the talk, if we believe Robert Helling, made sense.
Stefan Theissen tried to explain basics of string theory as known in the 1980s to our LQG colleagues.
Fotini Markopoulou argued that quantum gravity is like a self-correcting algorithm of a quantum computer. I can't say anything intelligent about such conjectured connections because I couldn't distinguish them from tens of crackpots' ideas flowing to my mailbox every week. It is plausible that there is something interesting going on in this direction - and it is appealing - but it just makes no sense to me so far.
Olaf Dreyer, possibly inspired by Lee, proposes to solve the problems that have been solved by decoherence and conjectures that quantum mechanics is not linear and probabilistic but non-linear and deterministic.
Other talks discussed modest questions about thermodynamics of discrete systems analogous to the Ising model; speculative connections about temperature and time evolution. There are several other ideas around but eventually Robert Helling stopped his reports because there was nothing in the talks.
Thanks, Robert, anyway! And a message for Peter Woit: if you think that Cumrun's program is comparable to the weird ideas from Loops 2005 listed above, then I must say that you are [the rest of the message has been censored to preserve our usual highest standards of politeness].