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).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.
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.
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.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 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".
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.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"
whoah! this is primarily a string oriented thread. It started withOriginally posted by pelastration
if you have the time ... what's your approach on holographic principles? ...