# What is the core problem of the information paradox?

Tags:
1. Nov 5, 2015

### Atla

Can you please explain what the core problem of the information paradox is?

Hi all!

I've read many articles about it, watched videos, argued with some physicists, and yet I can't grasp at all where the paradox lies.

For example, from the Wikipedia:

"An important difference between the black hole radiation as computed by Hawking and thermal radiation emitted from a black body is that the latter is statistical in nature, and only its average satisfies what is known as Planck's law of black body radiation, while the former fits the data better. Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole (the no-hair theorem). This leads to the black hole information paradox."

I don't understand this, where is the information lost? Do physicists actually think that virtual particles pop up randomly?
Is the "field" from which the virtual particles pop up not considered to be integral part of the universe? Why doesn't the information exchange with this field count?

I'm sure I'm missing something simple here.. thanks!

edit: oops.. too long thread name

2. Nov 5, 2015

### Demystifier

In a nutshell:

Information falls down into the black-hole interior, from which it cannot escape out. However, due to Hawking radiation the black hole eventually vanishes. After that, the information cannot be inside the black hole (because there is no longer black hole), but it also cannot be outside (because it cannot escape from the inside). It looks as if information was destroyed, but it also cannot be the case due to unitarity. This is the paradox. Some of the claims above must be wrong. Which one is wrong is a matter of debate and current research.

3. Nov 5, 2015

### Atla

But during the Hawking radiation, virtual particles are turned into real ones, meaning that there must be an information exchange between the black hole and the field from which the virtual particles got "ripped out" from. So isn't the missing information simply encoded into that field?

4. Nov 6, 2015

### Demystifier

That would mean that, all the time, all information is outside the hole. That's also a logical possibility, but it contradicts the semiclassical theory according to which information should fall into the hole.

5. Nov 6, 2015

### Atla

I don't see how. Only one of the particles escapes, the other one falls into the black hole, carrying information. So not all information is encoded outside of it.

6. Nov 6, 2015

### naima

I think that the paradox is due to opposite beliefs.
Quantum theorists believe that there is no collapse. before during and after being in a black hole
matter obey reversible law. So information is not loss (just reverse time).
You can also think that there is a singularity in the path which enable you to retrieve what happend before.

7. Nov 9, 2015

### Demystifier

Then I misunderstood you. So you are right, one of the particles falls into the hole, so information is inside. But there is a problem. Where is this inside information when the hole finally disappears? Or are you saying that the hole never disappears?

8. Nov 9, 2015

### Demystifier

In a sense, any paradox is due to opposite beliefs, almost by the definition of the word "paradox".

The issue is to determine which of the opposite beliefs is correct and which is not.

9. Nov 9, 2015

### Atla

I'm not sure whether I understand your questions correctly. Once the black hole has fully evaporated, then all the information that was previously "inside" the blackhole has been encoded into the escaping particles + the underlying field from which the virtual particle pairs get ripped out. Information that falls into a black hole gradually leaks out into the underlying field + through the escaping particles.
Hence I do not understand where the paradox is. I'm probably missing something very simple.

10. Nov 9, 2015

### Atla

Maybe the confusion is this: yes, the particle that falls into the black hole carries information as well, so while the black hole exists we must also take it into account. However, the "sum" of information inside the black hole decreases with every "instance" of Hawking radiation. The information carried by the particle falling into the hole is "less" than the (information carried by the particle escaping + the information carried by the underlying field).

So while the black hole shrinks, it's information content shrinks accordingly, until it eventually reaches zero.

11. Nov 9, 2015

### Staff: Mentor

The outgoing particles from the Hawking radiation are thermally distributed, so there's not enough information in them. If I compress ten kilograms of anything down below its Schwarzschild radius, the resulting tiny black hole will decay very quickly, so I'll get to see its entire lifecycle. But I'll get the same Hawking radiation (information content is "I'm coming from a ten kilogram black hole") out no matter what I started with.

12. Nov 9, 2015

### Atla

That's correct, but why are you ignoring the "rest" of the information that gets encoded into the underlying field, when the virtual pairs get turned into real one?

13. Nov 9, 2015

### Staff: Mentor

If it's "encoded in the field", then it's in the particles that leave via Hawking radiation, because once the black hole is gone they're all that's left.

You may be thinking in terms of the non-technical explanation of Hawking radiation being caused because a virtual particle pair forms at the horizon and the negative-energy member pf the pair falls into the hole while the positive-energy one escapes to infinity? That's a very incomplete description of the process (Hawking himself described it as "heuristic") so you may want to dig up a copy of Hawking's original paper.

14. Nov 9, 2015

### Atla

Say a virtual particle pair forms, there can be two outcomes. One, they annihilate each other two, they get turned into real ones.
To me, what you are saying is that there is no difference between these two outcomes. Isn't that a contradiction? Doesn't the difference between the two outcomes carry information?

15. Nov 9, 2015

### Demystifier

You are missing to answer the following question:
How can information gradually leak out from the black hole, from which nothing is supposed to leak out?

16. Nov 9, 2015

### Staff: Mentor

No, I am saying that if I dropped ten kilograms of stuff into a black hole, the same Hawking radiation will come out and the final post-evaporation state of the universe will be the same no matter what information is in the stuff that I dropped in.

I'm really not at all sure what virtual particles have to do with the black hole information paradox, which Demystifier summarized quite nicely in post #2 above. You can either use the real theory or you can use the oversimplified and somewhat misleading picture of Hawking radiation being produced by virtual particle pairs, but either way the information that went into the black hole with whatever object I dropped in never comes out again.

17. Nov 9, 2015

### naima

There is something i do not understand. Suppose someone watches a BH from a long distance. He never sees particles disappearing in it. Can he see the radiated particles by the BH while he is still seeing (weakly) them falling in it?

18. Nov 9, 2015

### Staff: Mentor

Hawking radiation is emitted from outside the event horizon so can reach an outside observer.

19. Nov 9, 2015

### Staff: Mentor

What definition of information are you using?

Leonard Susskind (in one of his video lectures) equated information to number of possible states. For example a spin 1/2 particle can have spin values up and down, two possible states. It can not evolve into a 1-state or 3-state system. For an N-state system to evolve into something with more or less than N-states would violate unitarity.

So, if number of possible states is the definition of information, then thermal distributions should be irrelevant, right?

20. Nov 9, 2015

### naima

The problem is that when N particles fall in the BH at the end he is at less 2N particles. N falling and more than N radiated!