## Thursday, July 14, 2011

### Those BS Mesons

A new CDF paper reports new $B$ physics, namely an excess of $B_s$ mesons. Good posts as usual by Tommaso and Resonaances (providing one ignores the stupid theory comments).

July Update: ATLAS does not see this anomaly.

1. I was just putting Verlinde and Bousso together at PF, and I have to say, vixra:1008.0015 makes a lot more sense to me now, e.g. statements like "Neutrino mixing is presumed to carry gravitational charge from
its generating (cosmological) horizon into the electroweak sector." Though in terms of dS/CFT as I now see it working, gravitational charge is generated just by using bulk variables at all (via the Verlinde mechanism of integrating out the off-diagonal degrees of freedom in a matrix model), and a cosmological horizon is just one possible holographic screen in the bulk. But I guess you want to make this work in terms of measurements, and the cosmological horizon, though observer-dependent, then has significance as a bound on possible measurements for that observer...

2. Missing 'not' spotted.

That's right, I am not thinking in terms of 'a bulk', but we must discuss our measurements as observers. And I do not view holography in terms of classical boundaries either. This is the frustration of a quantum information theorist, working with abstract spaces and resisting the temptation to attach them in some ad hoc manner to classical notions of casuality. There is far too much of this trash going on in Respectable (and now totally redundant) QG research. As you can see, Verlinde has latched onto the right ontology, but he is still confused about it.

You should not worry any more about traditional dS/CFT, unless you want to spend your life proving really boring theorems. Time is much better spent trying to understand the real theory, with its higher operads and motivic arithmetic and quantum cosmology and information theoretic black hole states.

3. Well, I'll make one more stringy comment.

Last sentence of vixra:1010.0029: "It is
therefore expected that General Relativity will be recovered via a higher categorical form of the twistor framework, using octonion matrix theory."

The twistor string was originally defined on a D1-D5 system, which is T-dual to D0-D4. The closest thing to a realization of Erik Verlinde's ideas within string theory (that I can find) is in a D0-D4 system - the gravitational precession experienced by a D0-brane is described by a quaternionic Berry phase arising from a Born-Oppenheimer approximation in which the D0-brane is heavy and the D4-branes are light. This is just one step short of what Verlinde wants to accomplish, which is to have the full gravitational force arise as a reaction force in such an approximation.

Meanwhile, in a brane system with even more supersymmetry, it should be possible to get an octonionic Berry phase.

So there may be some possibility of constructing within string theory, a twistorial realization of gauge fields, in which gravity also emerges a la Verlinde from an octonionic matrix model.

4. Yes, and kneemo already knows how to do it, using a $57$ ($= 54 + 3$ with bioctonions) dimensional (non linear) $E_8$ ternary $3 \times 3$ system, where the crucial complexification of the bioctonions (like Witten's complexification) is as briefly discussed in my latest draft. And then one can go further ...

5. So as in that nice paper you mention, we look at a Hopf map $S^{31} \rightarrow S^{16}$ where the $31$ is obviously associated to $248 = 31 \times 8$ (and then you should think of the $8$ in connection with a missing $H$ coefficient, but that is jumping ahead). Won't the mathematicians be happy?

To our readers: recall the magic of triality, in $C$, $H$, and $O$, and in $C.C$, $C.H$ and $C.O$, three ribbons to rule them all!

6. "Yes, and kneemo already knows how to do it"

I only just found the relevant paper, arXiv:math-ph/0503015, about "generalized twistor string theory" or "twistor matrix theory"; and his gr-qc/0505038, about Jordan algebra observables for LQG. That will all take a while to digest.

7. Mitchell

For context, you might like to read hep-th/0104050 and hep-th/0110106 first.

8. I read those yesterday! It all seems relatively clear now. The big remaining mystery for me - and here I return to my first comment - relates to your cosmological concept. If I was trying to implement Louise's idea, I would look for some component that was prominent in the FRW metric but not in the Schwarzschild metric, and then for a way to have light couple to that component so as to produce her equation. (This is a way to have light slowing down only on supergalactic scales, avoiding the problems with atomic physics if it's slowing down at subgalactic scales too.) I certainly don't see anything like that in your work, but then I don't see anything that would give rise to her equation, either. What am I missing?

9. Whoops, I didn't notice that the previous message was from Michael.

10. Mitchell, don't think of Louise's idea in the context of GR. We are deriving GR from a distinctive ontology based on measurement. Louise's equation $R = ct$ (cf. Kepler's law) is a statement of duality, contrasting nearby space, which, as observers, we think of as 'room', and far off space, which we observe in terms of cosmic 'time'. This is why a three time picture is useful, say in six dimensional theories, because one literally swaps Space and Time with dualities. And don't forget that special relativity is just a 1+1 theory, with symplectic topology suggesting the six dimensional extension.

Now remember that $\hbar$ appears in the commutation relation for $x$ and $p$. The finite dimensional analog is the MUB stuff, and $\hbar$ is like $\sqrt{n}$ for the dimension $n$ of a matrix. It varies so that $\hbar c$ is a constant in Louise's picture. These things simply cannot be done in string theory, which insists on ugly things like universal Planck scales.

11. You may find Banks' talk on holographic cosmology useful, if you can ignore all the stringy inflaton BS.

12. So in contrast to the loopy idea of an energy dependent $c$, for the energy of photons, we have an energy dependent $c$ where $E$ is associated not to the (locally Lorentz invariant) photon, but to the observer's environment.

13. "$\hbar$ is like $\sqrt{n}$"

From Combescure I learn that MUBs overlap like ${\frac{1}{\sqrt{n}}$, and there's a theorem about MUB-triplets in 6 dimensions... but does $\sqrt{n}$ show up in a commutator somewhere?

By the way, Anastasia Volovich has an old paper about a functorial quantization of de Sitter space which produces a spectrum of allowed values for $\hbar$.

14. Nice paper, thanks.

15. OK Mitchell, so if you're happy for $\hbar$ to vary in cosmic time, then why not allow $c$ to vary inversely? The pairing allows us to fix the constant $\alpha$, which is a reasonable approximation to what we observe (even if ends up having a small dipole).