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http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=000073A5-C100-1F80-B57583414B7F0103

Cheers, Dimi

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- Thread starter Kalimaa23
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http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=000073A5-C100-1F80-B57583414B7F0103

Cheers, Dimi

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Thanks Dimitri,

What I find interesting is his reference to numbers:

SA: Can you describe noncommutative geometry?

BG: Since the time of Descartes, we've found it very powerful to label points by their coordinates, either on Earth by their latitude and longitude or in three-space by the three Cartesian coordinates, x,yand z, that you learn in high school. And we've always imagined that those numbers are like ordinary numbers, which have the property that, when you multiply them together--which is often an operation you need to do in physics--the answer doesn't depend on the order of operation: 3 times 5 is 5 times 3.

What we seem to be finding is that when you coordinatize space on very small scales, the numbers involved are not like 3's and 5's, which don't depend upon the order in which they're multiplied.

There's a new class of numbers that do depend on the order of multiplication.

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. ;-)

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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.

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MathematicalPhysicist

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and string theories are united in the form of the mysterious m theory.Originally posted by Mentat

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.

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marcus

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Originally posted by Mentat

Of course, there's no obvious way to unite them now, but Greene's (and Smolin's) hope of unification is nonetheless possible...

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 [Broken]

There is certainly the

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)

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.

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I received the english version of the book TRTQG a pair of weeks ago, and here are a couple of excerpts of chapter 13: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".

"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"

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marcus

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Originally posted by meteor

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.

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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 ?

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marcus

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Originally posted by pelastration

Marcus,

if you have the time ... what's your approach on holographic principles? ...

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

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but this is perhaps a rough explanation, I'm still trying to learn!

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