Ashtekar: deriving the covariant entropy bound from LQC

[marcus]

Here are some papers on the covariant entropy bound conjectured by Raphael Bousso

http://arxiv.org/abs/hep-th/9905177

http://arxiv.org/abs/hep-th/9908070

http://arxiv.org/abs/hep-th/0305149

It would be a significant development if the conjectured bound could be proven to hold in LQC.

It looks like Ashtekar et al have done this or are able to do it, with a bit more work. This was just posted:


http://arxiv.org/abs/0805.3511
The covariant entropy bound and loop quantum cosmology
Abhay Ashtekar, Edward Wilson-Ewing
15 pages, 3 figures
(Submitted on 22 May 2008)

"We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances."

 

[MTd2]

The very first paper from Bousso on the convariant entropy bound struck me right in the first year of my undergraduate course, and since then, I never ceased to feel amazed by it. Unfortunantely, I never seen it used directly as the axiom of a quantum gravity theory, or at least, an axiom inspired by this bound. Instead, people pretty much use it as a test.

Maybe ashtekar is trying to call Bousso to their side?

PS.: Just to clarify what I mean by never "seen". I looked for the hundreds of citation for those papers.

 

[marcus]

Maybe Ashtekar is trying to call Bousso to their side?

I would say that Bousso is less of a key person to watch than Marolf. If you want to watch for follow-on research reaction, see what Don Marolf does. If you look at two of the links I gave earlier
http://arxiv.org/abs/hep-th/9908070

http://arxiv.org/abs/hep-th/0305149
they are both papers by Don Marolf. Ashtekar cites them frequently in his paper, much more often than he refers to the original Bousso paper. they are his references [11] and [12]. I think they come the closest to proving Bousso's conjecture mathematically.

Here is Marolf's UC Santa Barbara page
http://www.physics.ucsb.edu/~marolf/
He got his PhD under Bryce DeWitt at UT Austin in 1992.

You can see in the acknowledgments of Ashtekar's paper that Marolf has already been discussing with Ashtekar about this Loop Quantum Cosmology proof of the covariant entropy bound. He might have something to say about it on his own later.

 

[marcus]

The very first paper from Bousso on the convariant entropy bound struck me right in the first year of my undergraduate course, and since then, I never ceased to feel amazed by it...

I spent much of today reading and thinking about
http://arxiv.org/abs/hep-th/9905177
which could be the one you mean.
Besides being a landmark paper it is clearly and beautifully written.
A Covariant Entropy Conjecture
Raphael Bousso (Stanford)
41 pages, 7 figures
(Submitted on 24 May 1999)

"We conjecture the following entropy bound to be valid in all space-times admitted by Einstein's equation: Let A be the area of any two-dimensional surface. Let L be a hypersurface generated by surface-orthogonal null geodesics with non-positive expansion. Let S be the entropy on L. Then S does not exceed A/4.
We present evidence that the bound can be saturated, but not exceeded, in cosmological solutions and in the interior of black holes. For systems with limited self-gravity it reduces to Bekenstein's bound. Because the conjecture is manifestly time reversal invariant, its origin cannot be thermodynamic, but must be statistical. Thus it places a fundamental limit on the number of degrees of freedom in nature."

 

[marcus]

To recall the main point of the thread, what Ashtekar and Wilson-Ewing are saying is that
1. even though Bousso conjecture is formulated in a General Relativity context and is supposed to hold in GR, it DOES NOT hold. It fails as you go back in time close to big bang.

2. Loop Quantum Cosmology SAVES the Bousso conjecture from failing at this point because it deviates from GR in a certain way as you approach the big bang.

So this seems to be a way in which LQC is superior to classical GR. LQC duplicates standard GR cosmology behavior except right around the big bang. From a brief instant before until a brief instant afterwards, it behaves differently. And it turns out that it behaves just right so that the Bousso conjecture holds.

http://arxiv.org/abs/0805.3511
The covariant entropy bound and loop quantum cosmology
Abhay Ashtekar, Edward Wilson-Ewing
15 pages, 3 figures
(Submitted on 22 May 2008)

"We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. [In classical GR,] the bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry which can supply the structure needed to test the bound. We find that [in Loop cosmology context] the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances."[/QUOTE]