Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Monday, August 21, 2006

In the beginning

...and the mind creates reality...

Consider a few examples. In Turok's universe there was no Big Bang and god's time runs through Brahmian cycles. Other people think the world was created only a few thousand years ago. Most physicists believe it sprung magically into being, spacetime and all, about 13 billion years ago, Earth time.

Einstein knew that all of these ideas were physically wrong. In a quantum universe, the passage of time and the meaning of mass are things that we measure. For example, when we look at an electron we find that its mass = 0.5109989 MeV. Now why is that?


Blogger kneemo said...

[Andrei] Linde said: "Turok and Steinhardt's model has many problems and the authors made quite a number of errors, which is why it is not very popular among cosmologists."

I'd expect that errors would be made, as the ekpyrotic scenario requires new math and physics. In short, the full M-theory is needed. Colliding 3-branes seems to involve some hardcore math. I'm not even sure people agree as to how to properly describe D-brane charge. Does one use K-theory or K-homology? I personally prefer the K-homology route, as it employs Fredholm modules, which are related to spectral triples in noncommutative geometry.

Urs talked about this on 07-26-2006, in the topic K-Theory for Dummies, II. The K-Matrix theory paper he cites by Asakawa is one I read back in 2004. They use Fredholm modules to describe D-brane configurations in 10D spacetime. Explicitly, the eigenvalues of the scalar fields Phi^{mu} (mu=0,1,...,9), are supposed to describe the positions of non-BPS instantons in R^10. So their spectral triples are of the form (A,H,T), where A=C(M) is a C*-algebra (algebra of scalar fields), and spec(A)=M describes the embedding of a higher dimensional D-brane worldvolume in R^10.

As the Phi^{mu} are Hermitian matrices belonging to the adjoint rep of U(N), I'm sure you can guess how primitive idempotents and ribbon graphs arise in K-Matrix theory. Even more, I'm sure you know what spec(A)=M looks like. ;)

August 22, 2006 5:08 PM  
Blogger Kea said...

At MOST06 I heard about
Brodzki et al on KK theory, and was struck by the increasingly categorical nature of the C* approach.

August 22, 2006 6:23 PM  
Blogger kneemo said...

This comment has been removed by a blog administrator.

August 22, 2006 8:13 PM  

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