Re: Errors in loop quantum gravity entropy calculations
From: Wolfgang Beirl (wbeirl_at_hotmail.com)
Date: 07/31/04
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Date: 31 Jul 2004 10:15:34 -0400
baez@galaxy.ucr.edu (John Baez) wrote in message news:<ce6317$9ts$1@glue.ucr.edu>...
> In article
> <Pine.LNX.4.31.0407200016280.25397-100000@einstein.physics.harvard.edu>,
> Lubos Motl <motl@feynman.harvard.edu> wrote:
>
> >Hi guys,
> >I've read the recent Polish papers
> >
> > http://www.arxiv.org/abs/gr-qc/0407051
> > http://www.arxiv.org/abs/gr-qc/0407052
> >
> >that try to claim that all previous calculations of the black hole entropy
> >in loop quantum gravity - despite the claims that they were independent -
> >had the same error in them. They explain that it is not true that the
> >entropy is dominated by the punctures of the smallest minimal spin. Their
> >resulting entropy therefore does not contain anything such as log(2) or
> >log(3) but rather log of a transcendent number in between.
> >
> >Do you have some comments about it? I am still not quite decided whether
> >the new papers are correct, at least in some sense.
>
> I see the error that Lewandowski spotted in the original calculation
> by Ashtekar, Corichi, Krasnov and myself - we had a long discussion with
> him about this before he came out with his paper. But, I still need to
> check the details to make sure Meissner's new calculation is correct.
> I have no particular reason to doubt it, so I went ahead and spoke about
> it in Dublin:
>
> http://math.ucr.edu/home/baez/lectures#lqg
>
> But, I'd like to think about it more; the new papers came out just
> while I was busy writing my talk!
>
> By the way, nobody claimed all the previous loop quantum gravity
> calculations were completely independent. They all boiled down to
> the same combinatorics problem in the end: counting lists of spins
> that satisfy certain conditions. It's this combinatorics problem
> that the new papers are claiming to straighten out.
>
> I'll say a bunch more about this in a while. I expect there to be
> still more interesting twists in this story.
I would like to ask a (stupid ?) question about area quantization, which
prevents me from really understanding the calculation of the entropy.
On one hand there is the result that areas are quantized as
area = sqrt( j*(j+1) ),
on the other hand the 4D Barrett-Crane model assigns each area a label
j = 0, 1/2, 1, 3/2, ...
How does this fit together ? I understand that the BC model is defined on
Riemann geometries, while black holes live in the Lorentz sector. But is
this the (mysterious) reason for the different area spectrum ?
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