I think you'll all enjoy this: http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=000073A5-C100-1F80-B57583414B7F0103 Cheers, Dimi
Greene and numbers Thanks Dimitri, What I find interesting is his reference to numbers: On my website: http://www.mu6.com/numbers.html I describe this as a property of restructured spacetime (postulating that spacetime is an unbreakable and almost infinite elastic membrane). The complexity of our 'reality' is just the macro and micro interacting spacetime layers which can push each other but also can couple and knot. If we could buy such 'membrane material' today in K-Mart or GB ...we could build such concept in REALITY, today. This is a real physics world concept ... not magic. ;-)
Thanks for the link, Dmitri. That was a very interesting conversation. I particularly liked the part when the interviewer brought up LQG. I appreciated that Greene, inspite of being an extreme supporter of SMT, still likes the idea that they could both be right (LQG and SMT)...they could be two different ways of looking at exactly the same thing. Of course, there's no obvious way to unite them now, but Greene's (and Smolin's) hope of unification is nonetheless possible...after all, the five different string theories were once thought to be distinct, and incapable of unification, but Witten changed that.
I've often wondered why people attribute to Lee Smolin such a "hope". Maybe it goes back to his earlier book "Three Roads..." I cant talk about that, not having read it. For a good recent survey by Smolin, outlining the differences between loop gravity and string/brane theories, have a look at his April 2003 paper "How Far Are We from the Quantum Theory of Gravity?" http://arxiv.org/hep-th/0303185 There is certainly the possibility that techniques from LQG (for background-independence) may be taken over by people in other fields. LQG is substantially closer to being testable experimentally and making definite predictions that may cause it to be disproved---that is, it is possible for the theory to be contradicted and that we will find this out sometime in the next decade by actual observations. I dont think anyone working on LQG "hopes" that the theory will fail experimental tests, but the possibility is explicitly recognized in their writings. Part of doing a competent job of building a theory is to build it so that it can be falsified by tests---otherwise the theory is scientifically meaningless. So various failure modes are cooly discussed by the theorists themselves and one possible outcome is in that event LQG techniques are taken over into string/brane to get background-independence. But I dont see Smolin or anybody else (in what Ive read) hoping for that, or any other, kind of "unification". Such hopes would be more Brian Greene's department, I should imagine. Not having read all the books and not having total recall I cant say for sure and I would certainly like to see a recent quote from Smolin, if anyone can supply one, expressing this "hope for unification". At this point Mentat you will probably be saying "But I only get an hour a day on the web!" and maybe someone else can supply a reference. Or do you have hard-copy "Three Roads...."---it is not exactly recent (a lot has happened since it was written!) but it might give some expression of this "unification-hope" that I have been unable to track down in his other writing.
I received the english version of the book TRTQG a pair of weeks ago, and here are a couple of excerpts of chapter 13: "It is then possible to entertain the following hypothesis: string theory and LQG are each part of a single theory. This new theory will have the same relationship to the existing ones as Newtonian mechanics has to Galileo's theory of falling bodies and Kepler's theory of planetary orbits.Each is correct, in the sense that it describes to a good approximation what is happening in a certain limited domain.Each solves part of the problem.But each also has limits which prevents it from forming the basis for a complete theory of nature. I believe that this the most likely way in which the theory of quantum gravity will be completed, given the present evidence" "While my hypothesis is certainly not proven,evidence has been accumulating that string theory and LQG may describe the same world.One piece of evidence,discussed in the last chapter, is that both theories point to some version of the holographic principle.Another is that the same mathematical ideas structures keep appearing in both sides. One example iof this is a structure called non-commutative geometry"
Hopf algebras again! Another reference to Alain Connes non-commutative geometry! Meteor thank you so much for finding that quote and taking the time to copy it in. It saved me a trip to either the bookstore or the library that I have been reluctant to make. It shows a shift, I think, in Smolin's thinking between the time he wrote what you quoted and Spring 2003 when he wrote "How far are we from the quantum theory of gravity". Now the program is more concretely aimed at completing Loop Gravity so it can be tested---always time later to explore other avenues. BTW non-commutative geometry/quantum groups stuff has been used in Loop Gravity for some years now, especially by Smolin. I must get some links. I think that particular "unification" goes back at least to 1996, but need to check to make sure.
I don't know very much about noncommutative geometry, but I know that is the basis of the matrix formulation of M-Theory
I think non-commutative geometry is the only logic approach since it includes the (historic) growth of hierachy. Connes is indeed important. He did a lot in founding string theory (strings = cordes in French).
Marcus, if you have the time ... what's your approach on holographic principles? To me it's a very simplistic view because it is a deny of spacetime dynamics. Chaos and randomness were first. What was able to stay ... was kept. The rest built on these first levels. I see a holographic approach as just copying or a repeating of identical structures. But maybe my view on holographic principles is to simple because it reminds me of holograms ?
whoah! this is primarily a string oriented thread. It started with Dmitri bringing up the Greene interview---then pela. mentioned the interest of non-commutative geometry in a string context. Meteor is modest but he admits he knows something about...M-theory using non-commutative geometry---which I dont! I bet that meteor is willing and able to explain some things. I only dropped in because Mentat mentioned Smolin and the hope of unification (I am doubtful that unification is on the agenda right now tho it might be later on) but those are side issues, so i will get out of the way. I see there is suddenly a cool "Aleph" symbol (for one of the uncountable infinities) among the smilies
As far as I know, the matrix formulation of M-theory predicts that space-time is discrete at short scales because the coordinates of a string are represented by matrices. These matrices, in the short scale don't commute(thus discrete spacetime).In the long scale, these matrices become progressively more diagonal, and diagonal matrices commute, thus the space-time seems a continuous manifold at larges scales. but this is perhaps a rough explanation, I'm still trying to learn!