Talk:Holographic principle
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[edit] General comments
I just had an interesting thought that I think could help a person grasp the holographic principle. Try to visualize 3-space as a gigantic sierpinski sponge (for those who aren't familiar with it: http://mathworld.wolfram.com/Tetrix.html ). The object *looks* 3-dimensional, but if you calculate its dimensionality, it's 2-dimensional. Also, it's worth noting that the little pyramids a sierpinski sponge is made of have 4 sides...analogous to the way a bit of information is encoded on 4 planck areas. Maybe it's just a coincidence, but I'd love to hear a physicist's take on this. - Waylon Rowley
The holographic principle is rather unintuitive, but I think I can picture it, if denser mass makes space more hyperbolic. Mind you, I don't really understand curved space very well yet. But in hyperbolic space, I believe the center of a volume is supposed to be closer to it's surface than in euclidian space. So as the mass gets denser, the center aproaches the surface. When it reaches critical density, the center *reaches* the surface (VERY unintuitive), and it becomes a black hole. Is this at all logical? Does dense mass make space hyperbolic? I know mass is supposed to bend space, but I don't know which way, positive (ball) or negative (hyperbolic), or some combination.
- Some interesting thoughts, but I don't really understand what you're saying. I mean, space is not homogeneously curved in either direction, though you can approximate it as such depending on what your are talking about. I think you are perhaps speaking too generally? I mean, is the volume strictly hyperbolic, or are you dealing with some hyperbolic manifold embedded in some ambient space? I need some more orientation to understand the statement/question.
- Anyway, I have a question to posit here. Is this idea restricted to dimension 3? -- and if not, then what is the boundary like? Moreso, why does information inherently carry mass? So, in other words, what is the inherent principle here that suggests that information has density. For example, how much does an infinite collection of ~0 energy photons (~0 frequency radio waves) weigh? Just trying to understand. Also, if i may, does the holopgraphic principle rely upon the information entropy hypothesis, or can they be thought of (formulated) separately? 66.141.54.43 05:17, 20 July 2005 (UTC)
Is this idea restricted to dimension 3? No. It is concretely realized in the AdS/CFT correspondence which is actually a higher dimensional correspondence. It is a relation between gravity in D dimensions and field theory in D-1.
Why does information inherently carry mass? Nobody knows. If information would ever be proven not to carry mass, it would be a problem for the correspondence.
An infinite collection of zero energy photons weighs nothing. On the other hand, it doesn't carry any information, because they are not localized. If you think of photons in a box, the minimum wavelength of a photon is the length of the box (well, twice the length of the box), which means that the photon has a minimum energy. It turns out that photons in a box seem to conspire in just such a way to preserve the holographic principle, but nobody really knows a deep reason why.
I think the holographic principle can be formulated seperately from these entropy bounds, but they are logically connected, because you need the entropy bounds to remove degrees of freedom from the gravity theory: that's how you lose a dimension, because the vast majority of states in the field theory are not accessible, as they would form black holes.
This is an article I would really like to expand, but I don't have the time at present. The review article by Bousso is great, but technical. –Joke137 18:46, 20 July 2005 (UTC)
- Clearly I should probably just read the article, but a quick comment/question. So, in other words, we are relying fundamentally on the information entropy by this logic. For example, yes, nonlocal waves at ~0=E could carry information on the length scale of the universe, if you allow them to be out of phase with each other for example. Maybe impractical. I mean, I am trying to understand the base element construct. So clearly we are in some Boolean algebra over some profinite field? Forgive my ignorance, I tend to think in field extensions over Magmas too often I guess. Also, I do not understand this statement: "Is this idea restricted to dimension 3? No. It is concretely realized in the AdS/CFT correspondence which is actually a higher dimensional correspondence. It is a relation between gravity in D dimensions and field theory in D-1." I mean, dimension D<=26, I pressume? Which is fine. But then, what does the boundary look like on S^7, for example? 128.62.97.227 23:18, 20 July 2005 (UTC)
For the first question, I don't understand much of what you're saying about profinite fields, etc, but the basic argument is in the Bousso article, II.C.3. It turns out that for a gas of radiation, the so-called Bekenstein entropy bound is closer to being saturated for smaller boxes. The review says that the bound isn't particularly well defined, and proposes an alternate bound, called the covariant entropy bound. As for AdS/CFT, I think it is normally realized on 
(although the S5 could be any compact five dimensional manifold and really it could be 
), and the boundary looks like 
, where M is for Minkowski. If you object that anti-de Sitter space doesn't have a boundary, well, it's the conformal boundary. –Joke137 23:49, 20 July 2005 (UTC)
- I see. So sorry, I guess I should, more correctly, say profinite topology. Sorry about that. But no, so yeah this AdS/CFT correspondence is interesting, and I probably should go read it (I keep saying that ;)), but here, this is a gendanken for the idea. So even in S^5, if you think of the construction of the tesseract from a cube. You have to extend each vertex, but then maintain the 90 degree angle, which bends or twists out of the parameter 3-space. So, likewise, intuitively, S^5 is going to bend and twist (possibly back on S^2) from the point of view of the intuition contrived in 3-dimensions. So, the boundary may striate and wrap back on S^2. So I've heard of strings talked about in this way. But now, think of your room as S^2, but bounded in some way by S5. Well, then, the boundary is not strict in the same sense, no? So what about information packets acting (in the modular sense) as simple fibrations over S^2? Well then, your base elements are masked in the set X, and you can say that not only is your topology not profinite, but that in fact you are on an ultrafilter over X. No?
I'm having trouble reconciling a pair of statements. The author starts the paragraph with: "Black holes become more disordered as they absorb matter." Then the author ends the paragraph with "Black holes are thus the most disordered objects in the Universe." These two statements seem to contradict each-other.--Paul 21:30, September 11, 2005 (UTC)
- The total entropy increases when the black hole expands by absorbing matter. It's not an addition of entropies. --Pjacobi 07:39, September 12, 2005 (UTC)
I think references [1], ... in article don't work, is that correct?
- The relationship to the Sierpinski Sponge is misleading. Consider the Menger Sponge, a similar construction using a cubic geometry that has dimension of about 2.7. Unless I'm missing something entirely, the fractal dimension of the Sierpinski Sponge has nothing at the moment to do with this concept (though I concede that there is research connecting the two--consider [1]) SamuelRiv (talk) 07:58, 21 November 2007 (UTC)
[edit] Article needs more on the AdS/CFT correspondence
Currently the article is almost entirely about black holes and the Bekenstein bound, but the essence of what physicists mean by the "holographic principle" goes beyond this, and says that the dynamics inside any volume should be understandable in terms of the boundary of that region or some corresponding region in a space with a different number of dimensions. As I understand it, the key piece of evidence for this is the finding in string theory that there is an exact equivalence between the dynamics predicted by string theory in a region of 5D anti-deSitter spacetime, and the dynamics predicted by ordinary quantum field theory on the 4D boundary of this region (the CFT stands for 'conformal field theory', which I gather is a specific class of quantum field theory). For a good layman's explanation of this stuff, see the Scientific American article by Bekenstein that I added to the external links section.
Without this sort of generalization, it seems like the holographic principle would be nothing more than a synonym for the Bekenstein bound, and most of the article at present is just duplicating stuff already seen in the Bekenstein bound article. If nothing else, the article at least needs to make it clear that the holographic principle is a hypothesis which goes beyond just talking about the boundaries of black holes. Hypnosifl 20:34, 2 December 2006 (UTC)
[edit] Note about Scientific American Article
That link has a crackpot article about LSD research, past lives, and psychic claims that was just slapped on the end without notice of any kind. It would seem that a supporter of this latter essay used the credibility of Scientific American parasitically. The link I put in its place lacks a few sentences at the beginning, but seems to have all the rest. Scientific American article [New York] 12:40, August 13, 2007]
[edit] Bekenstein Bound
I removed a statement saying that the bound of entropy in space is Bek. Bound. The Bekenstein bound - which is a bit controversial - is something else, a bound on the entropy of an obect of a given size AND energy. S<A/4 is now part of the Covariant Entropy Bound (aka Bousso Bound).PhysPhD 22:33, 17 April 2007 (UTC)
[edit] Error found (bits and nats)
"One bit equals 2 nats" is false and must be fixed.
- Done --Michael C. Price talk 00:31, 1 July 2007 (UTC)
[edit] Feedback
This reads as a great science article and as a lay person with some grasp of physics, it makes no sense to me. I would encourage knowledgable people to re-write it so that it as encyclopedia article- accesible to everyone. Sethie 16:45, 13 August 2007 (UTC)
- Agreed...I think the SciAm article (as stated above) is a good layman's reference, was written by Wheeler's student Bekenstein, and I will take a stab at paraphrasing in attempt not to re-write, but to add Beckenstein quotes here and there explain. riverguy42 aka WNDL42 (talk) 16:57, 30 January 2008 (UTC)
