The relation between entropy and probability at quantum levelu

[mitchell porter]

I haven't decoded all of that yet. But it's interesting to see that http://arxiv.org/abs/hep-th/9912012" (computing the conformal anomaly using holographic RG flow) employs the Hamilton-Jacobi equations, because they also offer a path to the Bohmian approach to quantum mechanics. You may have seen news stories recently about the reconstruction of definite trajectories for photons in a double-slit experiment, using "weak-valued measurements"; those were "Bohmian trajectories". So, here we're close to something very basic about how quantum mechanics works.

 

[dhillonv10]

Just an update, I've been working on a related problem in the meantime however, today two very interesting papers came up, I am not sure if anyone mentioned those already or not.

1. dS/CFT Duality on the Brane with a Topological Twist: A C Petkou, G Siopsis (2001)

Abstract:

We consider a brane universe in an asymptotically de Sitter background spacetime of arbitrary dimensionality. In particular, the bulk spacetime is described by a ``topological de Sitter'' solution, which has recently been investigated by Cai, Myung and Zhang. In the current study, we begin by showing that the brane evolution is described by Friedmann-like equations for radiative matter. Next, on the basis of the dS/CFT correspondence, we identify the thermodynamic properties of the brane universe. We then demonstrate that many (if not all) of the holographic aspects of analogous AdS-bulk scenarios persist. These include a (generalized) Cardy-Verlinde form for the CFT entropy and various coincidences when the brane crosses the cosmological horizon.

This in some sense goes back to the idea bf being able to uplift AdS to dS and that may preserve some of the holographic dualities.

2. dS/CFT Correspondence in Two Dimensions: Scott Ness, George Siopsis (2002)

Abstract:

We discuss the quantization of a scalar particle moving in two-dimensional de Sitter space. We construct the conformal quantum mechanical model on the asymptotic boundary of de Sitter space in the infinite past. We obtain explicit expressions for the generators of the conformal group and calculate the eigenvalues of the Hamiltonian. We also show that two-point correlators are in agreement with the Green function one obtains from the wave equation in the bulk de Sitter space.

Restricted dimensionality however, if I understand this correctly, it has something to do with the wave function from the quantum mechanical model constructed at the boundary to the correlators in bulk.

 

[mitchell porter]

I finally got to see one of the http://pirsa.org/11060046/".

But the sense in which it's a holographic construction eludes me. Holography is mentioned in the first ten minutes, and then again in the very last minute. There are mappings, q and q_T (q transpose, the inverse of q), which are not bulk-to-boundary mappings but bulk-to-"screen" mappings, where a screen is a surface in the bulk of one less dimension. There is a remark at 34 minutes that space-time points become the lowest Landau level of something in one extra dimension. At 45 minutes the matrices q and q_T show up again, as noncommutative space-time coordinates for strings stretching between a stack of N D4-branes and a cloud of k D0-branes. Then all this gets uplifted to a six-dimensional space of the form S^4 x S^2 - the D4-brane become space-filling D6-branes and the D0-branes become D2-branes wrapping the S^2 - and this six-dimensional space happens to be twistor space! - 4-dimensional space with an extra "sphere" at each point, corresponding to directions in 3-dimensional space. Again, the strings between these branes implement a version of twistor string theory, with one part being equivalent to the self-dual part of N=4 Yang-Mills, and another part giving you the rest of N=4 Yang-Mills coupled to conformal supergravity. Verlinde (http://arxiv.org/abs/1104.2605" , because the classical continuum picture no longer applies at very short distances), and he says it's holographic too - but that's the part I don't understand - at the end he says there's a projection onto the "twistor line", but I thought that was equivalent to one of the "S^2"s, so if he's talking about the reduction from 6d perspective to 4d perspective, it just seems like Kaluza-Klein - approximating in a way that neglects the compact extra dimensions - and not the dramatic holographic elimination of one large dimension.

So I don't get it, but it's extremely interesting, and will hopefully make more sense to me in the near future.

 

[dhillonv10]

Thanks for the link to the talk, I was looking around for the talk on Simulating the universe as a quantum computer when i found the talks from the Holographic Cosmology 2.0. There was some talk on the Denef paper as well. Anyways the idea of using a screen is very interesting, it reminds me of the Grassimian representation that we talked about before, the fact that you would use a third theory that is more fundamental. You make the bulk dual to the screen and then the screen to the boundary, so the paper I mentioned before: dS/CFT Correspondence in Two Dimensions: Scott Ness, George Siopsis (2002) might actually work. I'll comment again with questions and such as I watch the talk.

update: There is also a talk on uplifting, titled: Uplifting AdS/CFT to Cosmology

 

[Fyzix]

I ressurrect this thread.

Could you outline your main thoughts in layman terms?
What is it you are thinking is going on in the horizon that gives us the illusion of randomness and nonlocality?

 

[dhillonv10]

Fyzix: this thread isn't dead yet, we are simply waiting, at Strings 2011, Herman et. al announced that they had worked out a complete example of dS/CFT and the paper will be out later this month. Once that's in, then we can do a lot more instead of making guesses as to what really happens because of the lack of an example.