Just a brain wave: I am not a physicist, so it is very probable that the following thoughts, about black holes, are partially or entirely flawed, but on this blog, nonsense is allowed, so let me get these thoughts out of my head.

The point is that I do not see what is paradoxical in the black hole paradox.

As far as I understand the black hole paradox, the problem is that there is a principle derived from quantum mechanics saying that information cannot be destroyed. On the other hand, when something is falling into a black hole, it looks like the information contained in it vanishes.

I have two thoughts about this:

- A black hole can actually store a tremendous amount of information. There is a theorem called the “no hair” theorem that states that black holes have no structure. They only have a small set of parameters: a mass, three values describing its place in space (with respect to some frame of reference, three values describing its movement through space (the direction and speed of the movement), three values describing its rotation (the direction of the axis of rotation and the speed of rotation). Moreover, they may have an electrical charge. These parameters are more or less analogous to those describing elementary particles.

However, having a small number of parameters does not mean a small amount of information. A single number can store an arbitrary amount of information. Think of the total amount of information contained in the internet. If you arrange all the computers or storage media in one sequence and read the dual digits stored in them as one sequence, you get a single number (with a very large number of digits). As you can see from this example, a single number (with very many digits, including those behind the decimal point) might store a gigantic amount of information. In this way, black holes are capable of storing very large amounts of information in a small number of parameters.

If a single particle with known properties falls into a black hole whose parameters are known exactly, the value of those parameters would change in a predictable way. This way, information stored in objects falling into the black hole can be preserved.

- However, what if two particles, say an electron and a positron, fall into a black hole from opposite sides. The mass changes by two electron masses, the charge remains constant. If you know the properties of the black hole before and after the event and you have not observed the particles before, the information about the direction from where the particles came seems to be lost. It cannot be reconstructed.

However, this loss of information only occurs if we look at the particles the way classical physics does. If we take them as quantum mechanical particles, we could say that they were in a superposition of states (since they had not been observed). This means that the information that seems to be lost simply did not exists, and therefore was not lost.

If an observer (i.e. a physical system interacting with the particle and storing information about it) did observe one of the particles, the information is not lost when the particles fall into the black hole. It is now stored inside that observer.

So the paradox only occurs if we look at things as if they are classical objects. If we look at them as quantum objects, there is no paradox.

If the observer observes the particle and then falls into the black hole himself before communicating this information anywhere (i.e. being observed by some other observer), no information is lost either: from the observer’s own point of view, no information is lost. It just passes through the event horizon. For any outside observer, no information is lost as well. If that second observer did not observe the first one, then the particle and the first observer where in a superposition of states and where entangled (through the first observer observing the particle), but from the second observer’s point of view no information is lost. The information gained by the first observer by observing the particle does not exist from the point of view of the second observer. If, on the other hand, the second observer did observe the first one and the information is transferred from the first to the second observer, then the second observer keeps that information and it is also not lost when the first observer falls into the black hole.

Lets call the second observer Alice, the first observer Bob and lets replace the particle by Caty S. (also known as Schrödinger’s cat). There seem to be three cases:

- Caty falls threw the event horizon. Caty does not lose any information in doing so. No information is lost from Caty’s point of view. From Bob’s amd Alice’s view, some of the information contained in Caty reappears in the form of changed values of the black holes parameters. If they had measured the black hole before and measure it after, they can infer the properties Caty had. Some properties of Caty cannot be inferred. From Bob’s and Alice’s View, these properties (e.g. if Caty was dead or alive) where in a superposition of states before Caty fell into the black hole. So this information did not exist from their point of view. So there is no observer from whose point of view any information is lost.
- Bob observes Caty before Caty falls into the black hole (e.g. Bob sees that poor Caty is already dead). Alice does not observe Bob, i.e. Bob does not pass this information to Alice. From Alices point of View, Bob and Caty are now entangled and they are in a superposition of states. So the information about Caty being alive or dead does not exist from Alice’s point of view. Caty falls into the black hole and then Bob falls into the black hole. For neither observer any information is lost.
- Bob sends the information about his observation of Caty to Alice before falling into the black hole, i.e. Alice observes Bob. The information is not lost since it is now stored in Alice. No information is lost from any observer’s point of view.

So I think the solution of the paradox lies in understanding that there is no absolute bird’s eye view from which information just exists. Information always exists only from the point of view of an observer. Making an observation means becoming entangled with the observed system. As long as a system is unobserved by another system, it remains in a superposition, i.e. its state is not determined and the information about its state does not exist. The principle that information cannot be lost means that it cannot be lost from the point of view of any observer, i.e. there is no observer for whom information will get lost. Note that observers are not necessarily humans or living things. An observer in this sense is any system interacting with another system and getting information about it (i.e. undergoing some change of its properties by being influenced by another system).

A funny aspect of this analysis is that the necessity of entanglement and perhaps of a multiple worlds interpretation of quantum mechanics seems to arise from the possibility of black holes. So the question I am asking is: is it possible to derive the rules (or at least some rules) of quantum mechanics from general relativity (which describes black holes, among other things) plus the rule that information cannot be lost. My knowledge of these theories and of the math involved is not sufficient to answer these questions and I do not have the time to get into these things any deeper.

I don’t know if these ideas are flawed. Let the physicist decide that.

Just some thoughts I had reading this post:

You write: “However, this loss of information only occurs if we look at the particles the way classical physics does. If we take them as quantum mechanical particles, we could say that they were in a superposition of states (since they had not been observed). This means that the information that seems to be lost simply did not exists, and therefore was not lost.”

A superposition is a wave function in the Hilbert space. You can have a mathematical formular of a superposition. You cannot predict the so called collapse of the wave function but you can have the formular for the whole wave function. So you really have information.

Also you seem to identifie information with knowledge. Even a exchange of subatomar particles is an information process in physics. So you don’t need a observer for information. So maybe some interesting links for you:

http://plato.stanford.edu/entries/information/

http://plato.stanford.edu/entries/qt-entangle/

http://plato.stanford.edu/entries/qt-epr/

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