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If an object that enters a black hole has its information content frozen at the event horizon, in what sense is it frozen? The usual analogy is of a hologram encoded in 2d which can be decoded into a 3d representation. The same analogy is used in describing the 3d universe we see as a representation of the holographic information encoded on the 2d "surface" of the universe.

  1. What is meant by "information content"? Or have I stated this
    incorrectly?
  2. The analogy leads one to wonder if there is a way to
    recreate the objects that have entered a black hole in any sense. Is the information frozen on the event horizon of a black hole
    detectable or visible in any real sense from the outside? How is one to imagine this effect intuitively?

I understand that in thinking about the holographic analogy I may have been going completely astray so please don't snipe at the question, simply correct me.

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An excellent question but I doubt the answer will be very intuitive. You might want to read the book "The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics" by Leonard Susskind. My understanding is that the information is encoded in the outgoing Hawking radiation but that no one knows how it is encoded. Similarly when you burn a book, the information is still encoded in the smoke, ashes and gasses that are emitted, but no one knows how exactly. –  FrankH Nov 22 '11 at 19:48
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3 Answers

It is similar to complex, yet reversible phenomenon. If a wine glass is found shattered on the floor, by building a database of information(the density and thickness of the glass, the friction coefficient of the floor, the wind in the area, the viscosity, density and volume of the 'wine') You could, using an 'equation' or computer program, determine exactly the height, and orientation of the glass when it fell. This is what Hawking is referring to when he talks about conservation of information. a wine glass is a 3D shape, the shattered glass is slightly less 3d, almost 2D, as it is 'spread out' on the floor.
The black hole situation is much more complex, because the atoms and energies of the atoms are laid out on the surface of the black hole(not to mention the fact that the atoms no longer resemble atoms, because they have been 'squished' into a singularity), yet if we had a suitable database and equation or program, we could tell you what had fallen into the black hole, and presumably its orientation.

As for how this indicated that all of the universe is spread out in a 2-D fashion on some Altima-Sphere, I'm not sure.

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It isn't "frozen" on the event horizon, but smeared across it in a hot way, meaning in a way that is thermally very active. It is only "frozen" in a classical picture of objects approaching the horizon without any backreaction.

The hot motion of the horizon encodes the object before and after it crosses the event horizon in a complicated way. The encoding means that any physical property of the object can be extracted from knowing the quantum state only of the black hole, and this is true both after it crosses the horizon, and when it is sufficiently close to the horizon.

All this information may be extracted by doing scattering experiments on the black hole, shining light on it, and seeing the exact Hawking radiation that comes out. These experiments are hopeless away from an extremal limit, because the thermal nature of the black hole makes it just as difficult to know what comes out as to know what light will be emitted from a lump of coal after a laser heats it up.

In the extremal limit (when the black hole is charged as much as possible or rotating as fast as possible), then the near horizon geometry is AdS, and the physics is described precisely by AdS/CFT, meaning all near-horizon dynamics is described by a local quantum field theory on the AdS boundary. This map is the best hope of gaining more insight on how a black hole encodes information on the surface.

But even in certain examples of AdS/CFT, where we know the theories on both sides, we don't know exactly how the local gravitational physics emerges from the CFT. It is known that it does, but we wouldn't be able to describe a classical object moving around on the AdS gravity side very simply on the CFT side.

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Can you really extract the information by doing scattering experiments on the black hole? Isn't the Hawking radiation coming out completely independent of any new radiation going in? –  Peter Shor Apr 6 '12 at 18:11
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I believe that the reason why this "information content" thing is such an issue with black holes is that if a black hole truly has a singularity in the center, it would violate certain conservation laws. Here's why:

A singularity, by definition, is a point of infinity. All math goes out the window when you deal with infinity because infinity is not a number. Therefore, any charges, momenta, angular momenta, etc--all the things you read about that have conservation laws--cease to have any meaning and would not be conserved. This is a big problem.

This has lead many to believe that we don't fully understand what's going on in a black hole past the event horizon and that we need new laws of physics.

One attempt at salvaging our current laws is that whatever enters the black hole leaves its mark on the event horizon such that hawking radiation would conserve its properties when emitted (The emitted radiation would conserve the initial momentum, etc of the incoming particle).

As for re-creating the object that entered, the analogy FrankH gave would be correct, I think.

Please see: http://imperial.academia.edu/IshaKotecha/Papers/127918/The_black_hole_information_paradox_and_the_holographic_principle

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-1: This answer is incorrect. I am sorry to downvote, but a singularity is not a "point of infinity", but a point of infinite curvature, and even then, it is not so terrible by itself. The singularity is not the issue with this stuff, it is all exterior things that are the issue. –  Ron Maimon Apr 6 '12 at 5:09
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Sorry for downvoting, but I can't agree with the answer. In classical theories point particles also generate singular potentials, but all the conservation laws hold. In GR, if you have an asymptotically flat space (with a black hole) you can still comfortably enough introduce conservation laws. The real problem with information comes from the fact, that the objects can only enter, but not leave the event horizon. –  Alexey Bobrick Apr 6 '12 at 12:06
    
Oh, ok so if the data is permenantly stuck inside the event horizon, the it's considered "destroyed"? And "information" cannot be created or destroyed, right? Is that the idea? –  John Apr 6 '12 at 16:06
    
Yes, somewhat. If the bodies fall under the horizon, the information about them perturbs the horizon itself, and though outside observers cannot reach the bodies which have fallen under the horizon, they can still measure the properties of the perturbed horizon. –  Alexey Bobrick Apr 6 '12 at 16:36
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