Understanding Black hole information paradox?

Question

I am not a physicist, I am a enthusiast trying to understand thinking behind "Holographic Principle" by Leonard Susskind. Recently I saw program on DS Through the wormhole - The riddle of the black hole, there was one analogy about Bob and Alice near black hole.

1) First they were in the space ship near black hole and Alice jumps in. Bob sees her getting closer to black hole but slowing down and frozen near event horizon. But from Alice's point of view she falls in the black hole passes event horizon with no traces at all.

2) Second time they each have an aeroplane with String theory propeller. Alice flies through the black hole and meets the same horrible faith. She could only see central hub of her propeller. But when Bob approaches black hole he could see increasing number of propeller.

I have few questions about above analogy

1) In the first analogy: Bob sees Alice frozen at the event horizon, If this is true why don't we see stars revolving around black hole slowing down when they approach black hole at the center of our galaxy? (I am talking about observations that indicate Black Hole at the center of our galaxy with stars revolving around it, which show stars speed up while they approach black hole)

2) In the second analogy: Does the propeller indicate vibrations of atom? If so why Alice does not see more propellers as she approaches event horizon but the Bob sees it ? Also can the plane without air in the space or it was just to imagine atom to propeller ?

Links:

Here is the video on the you tube

http://www.youtube.com/watch?v=1dwM_0kxYp8

Answer 1

"Through the wormhole - The riddle of the black hole" was a great show! Although, they left one thing out -- not only would gravitational time dialation make Alice appear to freeze at the event horizon, gravitational redshift would make her disappear to the naked eye. As light rays are red shifted, the wavelengths get longer. This means purple would become indigo, then blue, then green... down to red -- then down to infrared, then radio waves... Theoretically, at the event horizon, all light rays would be pretty much infinitely red shifted, so Bob couldn't actually see Alice at the event horizon, even the ship's instruments would lose the ability to detect her (see Kip Thorne "Black Holes & Time Warps: Einstein's Outrageous Legacy") --- but theoretically the ultra-long wavelength electromagnetic waves are still there, and indeed, could persist long enough to effect the Hawking radiation, thereby preventing the total loss of information. The ultra-long wavelength electromagnetic waves exist at the event horizon where time dialation is pretty much infinite, so they could exist as long as the black hole exists. But from the reference frame of Alice & the singularity, her mass has been crushed into the singuarity along with whatever asteroids, stars, etc the black hole has eaten.

One other thing is that the TV graphics made it look like a black hole assorbs matter & then immediately gives off a bunch of Hawking radiation. In fact black holes asorb matter really fast & give off Hawking radiation increadibly slowly & "evaporate" over trillions of years.

Answer 2

The point that Susskind is making is that the interior description and the exterior description are related by something similar to the quantum mechanical uncertainty principle. It's as if the exterior observer can see the momentum of a particle, and Alice can see the position. There is a transformation which takes one to the other, but you can't measure both simultaneously. The actual variables are not position and momentum of course.

The propeller business is not a very good way of describing it. The objects that fall into the black hole are just stuck on the surface from the point of view of someone outside, they never fall through, it's not as if the propellor turns in the interior are somehow directly talking to the exterior, the two classical pictures, like particle and wave, are only valid in different domains. One classical description for Alice, another for Bob.

The slowing down of time near a black hole, or near the surface of the Earth for that matter, is well known--- it is called the gravitational redshift. This is the dominant effect of General Relativity--- it's the one that is important for GPS purposes for example, all other effects are extraordinarily tiny. The gravitational redshift near a black hole is just the same as any other gravitating object, it is small, until you approach the horizon. Then it diverges to infinity. The infinite redshift relative to a distant observer is the reason for the freezing of objects on the horizon.

Susskind discovered that in string theory the strings also spread out over the surface as they approach it, in addition to slowing down. The spreading out he identified with thermalization to Hawking radiation.