josh1 said:
As has been repeated many times in this forum, string theory appears to be based on a unique but as of yet undiscovered set of principles with different solutions describing different phenomenologies.
That is a nice idea. When the "unique but as of yet undiscovered" set of principles is discovered then there will actually be a string theory (not just a philosophy or ideology or intellectual framework). And THEN it may actually be possible to test the whole shebang and falsify it.
I like that prospect and hope you are right. Regretfully, so far it only "appears" to be based on some unknown but imagined set of principles, as you say.
I too use the term LQG this way. But I’m unaware of any serious LQG analog of the developments in string theory that suggest that these approaches are parts of the same theory...
There is Martin Reuter's QEG (asymptotic safe quantum gravity). There is Renate Loll CDT. There is Lee Smolin dynamical knotted graph combination of particles and geometry. There is Laurent Freidel combination of spinfoam and Feynman diagram (also putting matter and geometry in one format.) There is the approach pursued by Derek Wise and others (matter and geometry). Then there is the current attempt to merge Alain Connes NCG Standard Model with something like the conventional LQG setup.
Many of the approaches being actively pursued combine matter (e.g. the Standard Model basket of particles) with geometry. Some, like Reuter QEG do not. There is no easy way to see them all as related. Sometimes people point out analogies and generalize. Daniele Oriti has an approach which subsumes several different approaches.
But I would tend to agree with Josh that there is no one "LQG program" that one can describe. Also it seems to me that the different lines of research presented say at Loops '07 are exceedingly ambitious. Look at Garrett Lisi's work for example. Or Lee Smolin's.
So I would tend to disagree with Demy here---because he talks about a single "LQG program" and seems to think it does not involve the Standard Model. All these different people do not have a single program, I would say, but at least the majority clearly have a single GOAL.
That involves defining a quantum state of geometry-and-matter.
I cannot speak for the individual programs of course but personally I do think several of these current efforts would be destroyed if evidence were found of extra spatial dimensions. It would not be simply a matter of changing a few numbers and presto our theory applies to higher dimension.