Something enters a black hole and all the quantum information is converted into gravity.
So the following example is not applicable...
An egg on the table has structure and pattern. Assuming all eggs are exactly alike, I can convey the structure of it to you with the term 'egg'. A broken egg on the floor cannot be conveyed as precisely. I might have to use words like this: "There is a fragment of a shell 1/4" in size over here, a splattering of yoke over there, and so on."
Each broken egg is different.
Particles as unique entities disappear. What was an electron/proton or what have you becomes gravity. So you can't go back and do "take that electron and put it back into this place". That electron is out of existence. So if you have a group of electrons that encode some information undergo a similar process. Where does the information go? (other than emerge on the internet by some mysterious process
)
Actually, the case of the broken egg *is* analogous. Imagine if we had a Super-Duper Universal Quantum Scanning Machine (SDUQSM) which could scan any specified region of space-time and store all quantum information it found there. Now let the egg roll off the table. Afterwards, we could take the information from our SDUQSM - how the egg rolled
just so, how
that spatter interacted
just so with
that molecule of gas, and then with
that atom of floor, and so on.... and so on....., well, we could reconstruct the egg just the way it was before. The information is perfectly preserved in the dynamic evolution of the system.
The problem with your scanner is that it is not physical.
You cannot learn every bit of information about a system without destroying it in the process.
And only classical information is preserved in the dynamic evolution of a system.
Part of the other information goes towards entropy and becomes irretreivable.
So you can only reconstruct the egg with information you cannot ever acquire!
In other words, you would have to approximate the egg because you cannot know fully how it was before.
Now let's point our SDUQSM at a black hole, and then throw an egg into it - into the black hole, that is, not into the SDUQSM, it's a very expensive and delicate machine :-)
Well, by knowing the initial quantum state of the black hole (I mean, all the information "written" on it's surface), and by observing how it behaves after the egg falls in - that is, by carefully recording all information given off as the black hole evaporates over a period of googillions of years, well, we could reconstruct the egg again.
You should read "George's secret key to the universe" by Hawking. It's a book written for children, but it does explore the possibility of reconstructing something that falls into a black hole. The point being, the information is NOT lost or destroyed. Merely, let's say, randomized, or encrypted in a certain sense.
Yes, but the information will be perfectly decorrelated if i'm not mistaken.
You would have no idea what bit of information that came out belongs to what information that went in.
You have no chance of even beginning a reconstruction!