# Help with the ABCK 1997 entropy/area paper

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There is an 8-page paper that does not look terribly hard that I would like to read with other interested people

Quantum Geometry and Black Hole Entropy
Ashtekar, Baez, Corichi, Krasnov (1997)
http://arxiv.org/gr-qc/9710007 [Broken]

The number 97-10-007 means 1997, October, 007-th paper of October.

There has been an interesting followup to this paper recently.
John Swain (May 2003) has proposed a form of the Pauli exclusion principle involving area
http://arxiv.org/gr-qc/0305073 [Broken]
Swain is an experimental high energy physicist who works
at CERN, does cosmic ray astrophysics, and teaches physics at Boston's Northeastern University.
At CERN he is on two LEP projects ("L3" and "CMS").
His PhD is U. Toronto 1990.
It intrigues me that such a hep experimentalist should be getting interested in Loop gravity and suggesting an extension of Pauli exclusion (or "spin-statistics" theorem) to area. I visited his
homepage to try to understand better
http://www.physics.neu.edu/faculty/swain.html [Broken]
Should we be expecting that in future we will hear about the
"Swain-Pauli exclusion principle"

Anyway the ABCK paper is seminal---it holds potential for further interesting development. And it is quite short---8 pages.
It derives the entropy/area formula for all black hole cases.
And seems to suggest that in the picture where states of geometry are "polymers"-----networks with astronomical numbers of segments which carry half-integer or integer spin---that the
integer spin (especially spin = 1) punctures of the area predominate!

So it answers one question (S = A/4, entropy is 1/4 times area) but raises another. Why should spin=1 predominate?
Swain says that this may happen "for much the same reason that photons lead to macroscopic classically observable fields while electrons do not." His paper is also short---just 7 pages.

I guess to put it in the most primitive terms, you can have a coherent flash of light where a bunch of photons are getting together and acting almost like one big photon and you can see this flash. But you can not have a coherent ball of electrons getting together and behaving like one big electron. They are
individualistic like Paris drivers as compared with LA traffic. They can be in a cloud but each one must have his own individual track or motion-state.

It is still too early to know what to make of Swain's 2003 paper.
Altho does seem interesting. I think the thing to do is try to
understand the basic paper ABCK 1997
or one of the other papers that repeat the main result if they
give more explanation and are easier to understand.

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Baez has just posted his latest TWF, Week 180, and it has his latest news about quantum foam. CUrrently things are interesting rather than simple. He links to three papers on the asymptotics of 10j symbols.

Gold Member
Dearly Missed
Baez has just posted his latest TWF, Week 180, and it has his latest news about quantum foam. CUrrently things are interesting rather than simple. He links to three papers on the asymptotics of 10j symbols.

thanks I will check it out next thing
IIRC 10j symbols are good research material for computer science
people---efficiency of algorithms---seems hard to compute
them rapidly. so a little man-computer drama gets into the gravity circus

Staff Emeritus
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I just read Swain's paper, at your link. Splendid! To get to "Swain-Pauli" he would have to prove his version (combinatorics and all) and preferably show that in the large length limit it goes over into the spin-statistics theorem.

BTW I didn't miss his experimentalist's dig at "so far as we can prove anything in quantum field theory".

I really like this whole issue of how to keep j=1/2 in there since on the one hand it has the feel of a problem to which a solution would really move things along and on the other it's simple enough - at least superficially - that you can have fun theorizing about it on your own.

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Originally posted by jeff
I really like this whole issue of how to keep j=1/2 in there since on the one hand it has the feel of a problem to which a solution would really move things along and on the other it's simple enough - at least superficially - that you can have fun theorizing about it on your own.

For the convenience of anyone who feels as Jeff does that this problem would be fun to think about, I will list in no particular order some papers that have been written on it (so far there are only a few short papers---it is a new problem that surfaced last year)

A 4-page commentary by John Baez in a newsletter circulated
to gravity researchers------page 12-15 of
http://arxiv.org/gr-qc/0303027 [Broken]
"Quantization of Area: the Plot Thickens"

A 3-page article by Alejandro Corichi
"On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry"
http://arxiv.org/gr-qc/0212126 [Broken]

A 2-page informal discussion by John Baez in Nature
13 February 2003 page 702-703 and copied at Baez homepage
"The Quantum of Area?"
http://math.ucr.edu/home/baez/q.html
Baez note has referenences to other articles by Lubos Motl and
and by Sahar Hod which bear on this question

An article by two Beijing physicists found recently by Jeff
http://xxx.lanl.gov/abs/gr-qc/0309018

The article by John Swain referred to by selfAdjoint and at the start of the thread
http://arxiv.org/gr-qc/0305073 [Broken]

"Quasinormal Modes, the Area Spectrum, and Black Hole Entropy"
by Olaf Dreyer
http://arxiv.org/gr-qc/0211076 [Broken]
a 4-page paper that initiated the discussion

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