Standard Logic of berkenstein bound?

[fredrik]

Does anyone know where I can find Berkensteins original reasoning/derivation for the entropy bound?

 

I think the papers is "Universal upper bound on the entropy-to-energy ratio for bounded systems" and it was published in Physical Review D 1981.

 

Is is available for free download somewhere? I'm sorry about the lame question, but I don't have access to those archives. But is the paper published elsewhere?

 

/Fredrik

[Martin]

It's not a dumb question by my standards at all. I don't know the answer though.

 

His name is Jacob Bekenstein and I think the original work may go back even farther like to around 1974. But I need to check about that because i'm not sure.

 

I expect you checked in Wikipedia. I will do that too

they are often helpful but not always

 

here's the link:

http://en.wikipedia.org/wiki/Bekenstein_bound

 

It looks like he had the idea about black holes around 1974, which is a special case and comes out to be the entropy being A/4

and then, just as you say in 1981 he published the generalization to any arbitrary region where the entropy cannot exceed a certain amount

proportional to the energy contained in the region.

 

I don't know how to prove either of these two results. Somebody here may, however, and also I might happen to see an explanation on the web.

there certainly should be something online because they are superfamous results.

 

when you call him Berkenstein it makes me think of those wholesome orthopedic German sandals called Birkenstocks

[fredrik]

I searched around and found some papers for sale but I figure it's weird that it's not available free download. OTOH I didn't search arXiv for copies or maybe never papers, I will do that. Good idea. I got the impression that there aren't much older papers there, so I didn't look there.

 

I'll report back here if I find it myself.

 

/Fredrik

[Martin]

I searched around and found some papers for sale but I figure it's weird that it's not available free download. OTOH I didn't search arXiv for copies or maybe never papers, I will do that.

...

 

IIRC arXiv was started in 1991-1992 but it sometimes pays to check for earlier stuff because I know of cases where a 1970s or 1980s paper was so much read and cited that somebody took the trouble to upload it on arXiv!

 

there is an ancient paper of Arnowitt Deser Misner which has been put on arXiv

 

also people will sometimes put modern TUTORIALS of ancient work on arXiv so you might find a nice clear explanation which would be easier to read than Bekenstein original work

 

I dont have any really good hints of how to proceed. Hope you find something

[fredrik]

I didn't find the paper I searched for but some other related papers from Bekenstein. I'll check them and see if I can get what I look for.

 

What I've after is that there are different kinds of entropy definitions and there are variations of the probabilistic approaches, depending on the thinking and I am curious what foundation/assumptions the bekenstein bound rests on. I've got a distinct feeling that similarly like background metrics are sneaked in, there are background priors assumed depending on the assumed information or knowledge concept.

 

/Fredrik

[swansont]

You might try this: http://adsabs.harvard.edu/abs/1981PhRvD..23..287B

 

And then use the search at the bottom, including the authors and limiting yourself to arXiv. It should give you similar papers that are available on arXiv

 

HTH

[ajb]

I found this on the Cern Document server, maybe it will help

http://doc.cern.ch//archive/electronic/quant-ph/0404/0404042.pdf

 

In fact, why don't you search the server yourself, Bekenstein has several papers on the topic.

 

http://cdsweb.cern.ch/

[fredrik]

Thanks everyone. I still didn't find the original paper, but OTOH I found sufficiently new ones that's sufficiently related.

 

Thanks!

 

/Fredrik

[fredrik]

when you call him Berkenstein it makes me think of those wholesome orthopedic German sandals called Birkenstocks

 

I missed this on first reading. The misspelling was completely unintentionally. I didn't mean to confuse him with the sandals

 

--

I haven't looked all over the place yet but I found several papers that refers back to Bekensteins 1981 paper (the one I fail to find for free download). Anyway, it seems from other comments that Bekenstein originally talks about the standard (absolute) shannon equivalent von neumann entropy, which imples the use of a background prior, which I have a little hard to accept as something possibly truly fundamental, so my initial suspect is that this bound either requires a restricted setting, or is a special case. But I may be wrong, that's why I wante to read the original paper to see the exact proof, and more importantly the assumptions going into it. I'll keeping looking.

 

/Fredrik

[fredrik]

I've scanned a few paper, and it seems clear that most papers take various semi-classical and IMO fuzzy approaches, meaning it's probably not that awfully interesting. Anyway, I decided to make an experiment. I am going to try a simple computer simulation and find the maximum relative entropy vs the parameters I would conjecture somewhat associated to "mass" or gravitating energy and and volume (event space volume). I might get back with my findings. The initial test for a specific prior distribution is that I seem to at least get the a*Volume^b shape on fitting with high correlation but I have yet to find out how a and b relates to mass/energy and the prior.

 

In the simulation I'm just usin a simple Rand statement. Anyone happens to know what model is behind the visual basid randomize routine?

 

/Fredrik

[fredrik]

My simple simulation did not seem to properly agree with the bekenstein bound. I'm going to get back to this later, but it's getting more clear what's going on. It seems that Bekenstein bound probably applies to special cases (I assume that's the whole point of the notion "bekenstein system" in the first place). The next step would be to interpret this special case in the big picture.

 

I suspect that a satisfactory understanding requires the information theoretic interpretation of

 

1) Entropy

2) Energy/Mass

3) Configuration/Phase space volume with an integrated a dynamics

 

These three concepts are clearly related. I think my first attempt failed because I failed to realize that the bekenstein bound isn't supposed to apply to a general case(only to bekenstein systems).

 

 

The intuitive associations I've made so far are

 

1) Entropy ~ an estimated measure of missing predictive power (missing information)

 

2) Energy/Mass ~ Thd confidence of any given data, can be associated with a "mass/energy", or "intertia". Defined as resistance to revision (change of opinon, as response to conflicting data).

 

3) The extension would be to define a generalized "phase space", which would most probably have a dynamical topology and dimensionality in the general case. This would contain a dynamical relatin between "volume" and "mass", but the explanation should be due to a fundamental relation between probabilistic "resolution" and "confidence".

 

The papers I've read mostly seem to not revise the whole notion of "entropy", I think that's needed. Also, semiclassical uses of mass and energy are freely mixed between GR and quantum notions. This is also quite disturbing.

 

Anyway, I think that this black hole / entropy thing, as well as the vaccum issue are the prime targets to test new ideas.

 

/Fredrik