## Monday, January 31, 2011

### Twistor Revolution

Mottle tells us about a new talk (which I cannot view at present) by Arkani-Hamed about the latest results from the twistor vanguard. Apparently Arkani-Hamed (who is a very eloquent chap, and taken seriously as a physicist) has decided to rename the Theory of Quantum Gravity in a fashion that pays less respect to stringy jargon. It is now officially about an ultratwistoholographic T theory triality!

Hmm, so that must be why no one has read my 2006 work on twistor triality. I wasn't using big enough words!

1. So how long before they start looking at $3 \times 3$ matrices and Koide rules for particle masses? A week? A year?

2. Someone at Physics StackExchange asked me about the relationship between twistors and Koide masses and I'm linking in this post. It might be nice to add a link to your best paper on the subject. I'm not sure I've seen all of your recent work.

Physics Stack Exchange seems to be a useful place to discuss these sorts of things. It's possible to ask questions that lead the readers (especially those who take time to answer) to a higher understanding. Of course, in dealing with physicists, things work best when one leads them to believe that they're the one doing the teaching.

3. Well, letting them think they are doing the teaching only works up to a certain point, Carl. Try telling someone about the antineutrino mass to CMB correspondence, for instance. Cognitive dissonance sets in pretty fast ...

4. As for Koide matrices ... it's simple enough. An ordinary number is like a $1 \times 1$ matrix. As a set of quantum numbers, it represents the unique outcome of a certain (classical) experiment. But as we all know, spin is an example of a two outcome experiment, which is why we use $2 \times 2$ Pauli matrices to describe spin measurements. A three outcome experiment should be described by $3 \times 3$ matrices.

The twistor connection is mathematically deep. It means interpreting the matrices in a very specific way (to do with Motives, as kneemo has just noted). Basically, though, the $2 \times 2$ matrices occur as basic elements of ordinary twistor geometry. We just need to extend that to the $3 \times 3$ case. This started way back in the 1980s as a search for a certain non Abelian cohomology theory ... since ordinary twistor theory uses sheaf cohomology. Getting the details right has been a tricky business. Most mathematicians have gone in for studying a certain class of (derived) categories, but they are completely ignoring the physics. This one simply cannot do, because the new mathematical foundations ARE about the new physics. (I had an audience member once (a prominent mathematician working on cohomology problems) tell me that he knew no physics ... and all I could think to do was raise my eyebrows).

Anyway, the Koide matrices do have an interpretation in terms of a universal motivic n-mology theory.

5. The tongue-twister is Lubos's expression, not Arkani-Hamed's.

6. Ah, thanks, Mitchell. But you get the idea?

7. Maybe I do, even if I prefer the concreteness of the stringy conception of mass (VEVs of geometric moduli). Mass in the twistor picture involves higher cohomology, and Duff has his black hole / qubit correspondence, so maybe it does all hang together.

8. Oh yes, it does. Stay tuned.

9. You can see it as pdf
http://pirsa.org/pdf/files/418223e8-4fae-4ebc-8de4-458f84364e3c.pdf

Note: Only a member of this blog may post a comment.