What is the Holographic Principle and its relation to information and entropy?

In summary, the conversation discusses the relation between information and entropy in the context of Gerard 't Hoofd's holographic principle. It is mentioned that the maximum entropy of a volume V is given by the area of its boundary, and that according to Bekenstein, the maximum information in a given volume is also bounded by the area. The holographic principle in string theory, specifically in the AdS/CFT correspondence, is also examined and its usefulness is questioned. The connection between entropy and information is explained and the concept of degrees of freedom and their relation to entropy and information is discussed. The conversation also mentions Witten's generalization of the AdS/CFT correspondence and a Dutch article on the subject. In conclusion, the holog
  • #1
skowalcz
31
0
Hi there..

If was wondering about the relation between information and entropy, in the following context.
The way I understand Gerard 't Hoofd's holographic principle is this. We know that the entropy of a black hole is A/4. Now suppose that a volume V was found to have an excess in entropy of a black hole just big enough to fit inside V. By throwing in additional matter we could form such a black hole. But... this gives problems with the second law. The entropy decreases by this proces. Conclusion: the maximum entropy of a volume V is given by the area of it's boundary (in certain units).
In an article in the Scientific American (aug. 2003) Bekenstein says that the maximum information in a given volume is bounded by the area.
I don't see this relation between entropy and information clear. :confused:
 
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  • #2
I am trying to understand the holographic principle in string theory. More specific, in de AdS/CFT correspondence. The Anti-de Sitter spacetime is an empty space with a negative cosmologial constant, a contracting universe, right.
Then on the other side of this correspondence we have the conformal field theories on the boundary of this five dimensional AdS space. Maldacena showed these two to be indistinguishable. Or maybe what he did can be summarized better by saying that he made a 'dictionary' for translating words in the AdS 5D-world to the CFT 4D-world.
What then has this to do with string theory? Are these spaces curved or something? I heard people saying that this AdS/CFT correspondence is one of the most important results of string theory.. but what is so stringy about it..

Something else: What is the use of this correspondence? We don't live in an empty space with negative cosmological constant, do we.
 
  • #3
skowalcz said:
Something else: What is the use of this correspondence? We don't live in an empty space with negative cosmological constant, do we.

As far as I can tell, the "success" of the AdS/CFT correspondence is simply that it shows a clearly-defined relationship between two opposite (or distinct) physical formulations, one which is quantum and one which is cosmological.
While it isn't "realistic", the fact is that it can be done.

For me, the fascination of the HP is the intrinsic connection between geometry (area) and information.
 
  • #4
In the mean time I found out that since the invention of AdS/CFT it has been generalized, so that it works also in other spaces. Not only in empty space with negative lambda.
This was done by Witten and others, but what they showed exactly I can not tell. :confused:
 
  • #5
skowalcz said:
Conclusion: the maximum entropy of a volume V is given by the area of it's boundary (in certain units).
In an article in the Scientific American (aug. 2003) Bekenstein says that the maximum information in a given volume is bounded by the area.
I don't see this relation between entropy and information clear. :confused:

From http://arxiv.org/abs/hep-th/0203101,
the number of degrees of freedom = ln of the dimension of the Hilbert space = number of bits of information,
and if entropy = S, then [itex]e^S[/itex] = number of independent quantum states compatible with macroscopic parameters => entropy is a measure of our ignorance of the detailed microscopic state of a system.

Then, the number of degrees of freedom connected with information should be equal to the number of independent states compatible with mIcroscopic parameters, since information is negative entropy?
 
  • #6
I wrote an article on this, but ... :yuck: it's not in english.. :mad:

http://gene.science.uva.nl/~skowalcz/scoop_juni2004-18-20-holografie.pdf [Broken] (Scoop, 06-2004): voor als je nederlands verstaat :wink:

And if you don't speak dutch: check out my artist's impression of a black hole!
 
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What is the Holographic Principle?

The Holographic Principle is a theory in physics that suggests that all the information about a three-dimensional space can be encoded on a two-dimensional surface.

How does the Holographic Principle relate to black holes?

The Holographic Principle is often used in the study of black holes because it provides a way to understand the information paradox, which states that information cannot be destroyed in a black hole. According to the Holographic Principle, the information is actually encoded on the event horizon of the black hole.

What evidence supports the Holographic Principle?

There is not yet definitive evidence for the Holographic Principle, but there have been several studies and experiments that have provided support for it. These include the AdS/CFT correspondence, which relates a theory of gravity in a higher-dimensional space to a lower-dimensional field theory, and the study of entanglement entropy, which has shown that the amount of information in a region of space is related to the surface area of that region.

What are the potential implications of the Holographic Principle?

If the Holographic Principle is proven to be true, it could have significant implications for our understanding of the universe. It could provide a deeper understanding of gravity and the nature of space-time, and could potentially lead to new advances in fields such as quantum mechanics and cosmology.

Are there any criticisms of the Holographic Principle?

There are some criticisms of the Holographic Principle, as it is still a highly debated and unproven theory. Some critics argue that it relies on assumptions about the nature of space-time and the nature of information that have not yet been proven. Others argue that it may be incompatible with certain theories, such as the theory of relativity.

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