Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Monday, March 05, 2007

Monday Motives

Somehow we have returned to Motives! According to the illustrious wikipedia: in terms of category theory, [the theory of Motives] was intended to have a definition via splitting idempotents in a category of algebraic correspondences. Oh, yes, we were wondering about those, weren't we? Unfortunately, when I google twistor, motive and n-category, I find almost no hits. Hmm. Maybe that's the fault of the hyphen. But when I throw in Riemann hypothesis and MHV for good measure ...

Anyway, I must rush off and prepare to teach some eager young minds some good old Newtonian mechanics. It is a stunning day outside. At 7am there was a thick fog laying only a few centimetres over the ground, and the Waimakariri dust clouds have subsided.

3 Comments:

Anonymous kneemo said...

Hi Kea

It seems Utrecht's Jan Stienstra shares your belief that the 'M' in M-theory really stands for Motive. Check out her talk on the possible string-motive connection.

March 06, 2007 9:02 AM  
Blogger Kea said...

Thanks, kneemo. That's a nice talk.

March 06, 2007 9:17 AM  
Blogger nige said...

Motive-theory! A double entendre. Both a mathematical recurring pattern, and a theory which is motivating!

I thought the M stood for the membrane that 10 dimensional superstring forms on 11 dimensional supergravity, just like the surface of a cell is an N-1 = 2 dimensional surface on the N = 3 dimensional bulk of the cell.

However, Professor Woit suggests a list of other possibilities in Not Even Wrong, including some which reflect the fact that the M-theory is a bit of a speculative fantasy, connecting speculative spin-2 gravitons and speculative near Planck scale unification with speculative strings, speculative Calabi-Yau manifolds, speculative branes, etc., by way of the speculative theory of supersymmetry in speculative extra dimensions. No way is this theory dealing with any physical fact at all. It's not even a theory of gravity until someone discovers a spin-2 graviton. It's a theory explaining one set of speculative, unproved, non-falsifiable theories using a lot of other speculations.

At least LQG minimises the amount of speculation, connecting general relativity to quantum field theory simply without extra dimensions. (It is still incomplete, but then again, so is string theory.)

March 06, 2007 11:31 AM  

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