How does the Holographic Principle apply to different scenarios and dimensions?

[Nim]

I first came across this concept in a Scientific American magazine. At the time it was nigh impossible to find much more information on it. Even now I am having a hard time wrapping my head around it. So I have a few questions.

From what I understand, it basically says:

Every single bit of information in any volume of space can be encoded / written on its surface.

Scenario #1:

A volume of space, say a cube, could be completely described on its surface, which is 6 flat sides.

Scenario #2:

A book takes up a volume of space. So everything written in a book could be described on the surface of the book, which again, is 6 sided.

Scenario #3:

In any given room, everything in that room can be described on the walls of that room.

Moving on...

Usually when they talk about it, they talk about the universe as a whole or black holes. But it was stated that this idea applies to all space. If it applies to all space, that means it applies to any volume of space you choose, be it a volume of space that contains a book, room, planet or galaxy.

 

[craigi]

I first came across this concept in a Scientific American magazine. At the time it was nigh impossible to find much more information on it. Even now I am having a hard time wrapping my head around it. So I have a few questions.

From what I understand, it basically says:

Every single bit of information in any volume of space can be encoded / written on its surface.

Scenario #1:

A volume of space, say a cube, could be completely described on its surface, which is 6 flat sides.

Scenario #2:

A book takes up a volume of space. So everything written in a book could be described on the surface of the book, which again, is 6 sided.

Scenario #3:

In any given room, everything in that room can be described on the walls of that room.

Moving on...

Usually when they talk about it, they talk about the universe as a whole or black holes. But it was stated that this idea applies to all space. If it applies to all space, that means it applies to any volume of space you choose, be it a volume of space that contains a book, room, planet or galaxy.

What you describe is just a hologram, really.

The Holographic Principle relates to the fast that we expect the information content of a region of space in a theory of Quantum Gravity to be proportional to its surface area and not its volume as we might otherwise expect.

 

[phinds]

The fact that it is mathematically possible for the information to exist on the surface [according to people who know more than I do anyway] does not, I think, mean that it ever DOES exist on the surface, so use of the holographic principle to arrive at the conclusion, for example, that reality only actually exists as a set of 2D surfaces strikes me as total nonsense.

Personally, I find the whole concept impossible to believe, BUT ... I well know by now that the universe cares not at all what I believe or don't believe, and Susskind knows more physics and math than I will ever know, so I have to accept the concept, but the idea of its implementation just seems silly.

Oh, and just as an aside, your (Nim's) statement concerning the "universe as a whole" is likely incorrect. I think It is the OBSERVABLE universe that is the subject of such statements. Since the "universe as a whole" may well be infinite in extent and not have any surface, the holographic principle wouldn't apply to it. Again, this is my understanding and might not be mathematically correct.

EDIT: to go one step further in my object to the implementation of the holographic principle, consider the fact that a spherical volume of space, say the observable universe, is bounded by a mathematically defined sphere that has absolutely no physical existence, so there isn't anything on which to actually PUT all the information contained within this mathematically defined sphere.

 

[friend]

I wonder if the holographic principle is like Gauss' theorem in which a volume integral can be turned into a surface integral.

 

[nomadreid]

Interesting question, and I was hoping someone would answer it. I am posting this to bring the date of last posting a bit forward to see if this can attract any knowledgeable people.

 

[Nim]

The fact that it is mathematically possible for the information to exist on the surface [according to people who know more than I do anyway] does not, I think, mean that it ever DOES exist on the surface, so use of the holographic principle to arrive at the conclusion, for example, that reality only actually exists as a set of 2D surfaces strikes me as total nonsense.

If we do exist on a 2D surface, like a hologram, it does make sense of the idea that all information in a volume can fit onto its area, which is really bizarre. The whole thing sounds crazy to me, it's hard to envision an intuitive understanding of how such a thing is possible. Maybe I just need to learn more about holograms... or dedicate my life to physics.

Thinking of another scenario... imagine any stack of information, be it a stack of pages or a multilayered disc. When you add on another layer/page of information, the total amount of information is only increased by the thickness of its sides, since the front part is already calculated as part of the surface of the entire stack. It's really hard to imagine how that can be true, especially with really large and thin pieces of paper.

When I think of things like this, I start to wonder if I am just misunderstanding what the Holographic Principle actually states.

edit:

The fact that it is mathematically possible for the information to exist on the surface

I came across a somewhat decent research paper I wrote on the Holographic Principle for a introductory physics class over a year ago, and part of it really stood out. It came from this idea:

"The essence of the Holographic Principle is very simple. It is all about encoding information from a space in "n" dimensions into a space of "n-1" dimensions."

I wrote that:

"It may sound strange that this theory has been integrated with string theory, which posits 11 or more dimensions, but you can look at it another way: every n dimensions can be fully described by n-1 dimensions. So 2D can describe 3D, and 3D can describe 4D, and 4D can describe 5D, and so on."

I had references but I didn't put them inline with what I wrote. I did find this:

http://www.whillyard.com/science-pages/holographic.html

I attached the research paper I wrote. I can't say how accurate it is at this time, but it does have some usefull links and quotes.