What is the core problem of the information paradox?

[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

 

[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.

 

[Atla]

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.

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?

 

[Demystifier]

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?

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.

 

[Atla]

That would mean that, all the time, all information is outside the hole.

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.

 

[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 happened before.

 

[Demystifier]

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.

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?

 

[Demystifier]

I think that the paradox is due to opposite beliefs.

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.

 

[Atla]

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?

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 black hole 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.

 

[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.

 

[Nugatory]

Once the black hole has fully evaporated, then all the information that was previously "inside" the black hole 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.

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.

 

[Atla]

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.

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?

 

[Nugatory]

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?

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.

 

[Atla]

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.

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?

 

[Demystifier]

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 black hole 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.

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?

 

[Nugatory]

To me, what you are saying is that there is no difference between these two outcomes.

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.

Say a virtual particle pair forms, there can be two outcomes. One, they annihilate each other two, they get turned into real ones.

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.

 

[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?

 

[Nugatory]

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?

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

 

[anorlunda]

The outgoing particles from the Hawking radiation are thermally distributed, so there's not enough information in them.

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?

 

[naima]

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

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!

 

[Nugatory]

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!

How is that a problem? There's no more reason to expect the number of particles coming out to be related to the number of particles going in than there is to expect the number of soot particles coming from a fire to be related to the number of pieces of coal we threw onto the fire.

 

[naima]

I can tell it in another way.
The observer begins to observe a BH with a mass M. He sees later 10M infalling particles. and he never sees them disappearing inside it. this flow stops and he sees the evaporation of the BH. Each radiated particle is created outside of it, no problem with him). But the particles are supposed to be created by pairs and one of them have to annihilate a corresponding particle inside. Ok for M supposed to be inside when he began to observe but what about the other 10M?
A solution for him could be that when the radiated particles increase the number of the infallind particles he is still observing diminish.

 

[gjonesy]

The commonsense "core problem" is difference of opinion. Who's theory best fits. And the definitive answer is...drum roll...There isn't one. First you have to decide which of the several existing theories you want to subscribe to. Second you have to weigh the solution to the paradox down to what makes the most sense to you from your perspective and understanding. Third and most important (simply wait and see.) This day and age new discoveries are made every day, verification via experimentation in different fields could lead to changes in the standard model that could take us in the opposite direction.

 

[Nugatory]

But the particles are supposed to be created by pairs and one of them have to annihilate a corresponding particle inside.

That's a common popular description of what causes Hawking radiation, but it's not an accurate description of what's really going on and it can be very misleading. Try to forget that you ever heard it.

For a better layman-friendly explanation, you can try http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html but (as with all physics) there's no substitute for the real thing: https://projecteuclid.org/euclid.cmp/1103899181.

 

[Atla]

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?

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.

I'll try to put my question another way then: do you think that vacuum fluctuations (or however we want to conceptualize it) are random? By random I mean that it's not integral with everything else going on in the universe.

 

[Atla]

"The usual computation involves Bogoliubov transformations. The idea is that when you quantize (say) the electromagnetic field you take solutions of the classical equations (Maxwell's equations) and write them as a linear combination of positive-frequency and negative-frequency parts. Roughly speaking, one gives you particles and the other gives you antiparticles. More subtly, this splitting is implicit in the very definition of the vacuum of the quantum version of the theory! In other words, if you do the splitting one way, and I do the splitting another way, our notion of which state is the vacuum may disagree!"

Or we can take this definition for example - do you think that the very act of splitting into a positive-frequency part and a negative-frequency part carries the same amount of information (zero) as not having done a split? That idea is a contradiction. Maybe the mistake physicists are making is not ralizing that they need to keep track of several abstraction layers in their own thinking / in their own descriptions about the universe. They believe to be using one abstraction layer but here there are at least two - the second one means extra information.

 

[Demystifier]

I'll try to put my question another way then: do you think that vacuum fluctuations (or however we want to conceptualize it) are random? By random I mean that it's not integral with everything else going on in the universe.

What do you mean by "not integral"? Do you mean not correlated? If this is what you mean, then vacuum fluctuations (just as any other quantum fluctuations) are "not random" in this sense. They are correlated with other fluctuations.

In the case of black hole, one has two mutually correlated fluctuations, one outside the hole and another inside. The problem (or paradox) is that the inside fluctuation seems to eventually disappear, so that, at the end, the outside fluctuation has nothing to be correlated with. In your terminology, the outside fluctuation was initially created as a "non-random" one, but eventually turned into a "random" one. Such a transition from "non-random" to "random" is incompatible with unitarity.

 

[Atla]

In the case of black hole, one has two mutually correlated fluctuations, one outside the hole and another inside. The problem (or paradox) is that the inside fluctuation seems to eventually disappear, so that, at the end, the outside fluctuation has nothing to be correlated with.

There is no such thing as an "inside" and an "outside", in the sense that you are using the terms, that is merely a misconceptualization. There are no separate things in the universe.

 

[Demystifier]

There is no such thing as an "inside" and an "outside", in the sense that you are using the terms, that is merely a misconceptualization. There are no separate things in the universe.

If space is a 3-dimensional manifold, then a closed 2-dimensional sub-manifold splits the space into two regions, which may be called "inside" and "outside". This is a topological fact. Are you saying that, in reality, physical space is topologically not a manifold? It certainly is according to classical general relativity, so are you invoking quantum gravity effects? If so, how can you be so certain that your theory of quantum gravity is correct?

And more to the point, can your theory of quantum gravity (whatever it is) be approximated by classical general relativity at large distances? If it can, then there is a black-hole information paradox. If it cannot, then it is a very nontrivial property which requires an additional explanation.

Or perhaps you meant something else? In that case you need to explain what do you mean by "there are no separate things in the universe".

 

[Jazzdude]

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.

I think this argument is very misleading. It is true that you cannot macroscopically distinguish thermal radiation if it has the same temperature. But that has nothing to do with the information that is conserved in unitary evolution. The thermal radiation has a microstate that contains an incredible amount of information. Each different microstate must also have been caused by a different initial black hole state if you assume unitary evolution.

The problem arises only classically, if you try to take the no-hair theorem to quantum theory. This massively reduces the information that can possibly be stored in a black hole state. But as we know today, quantum descriptions of black holes strongly suggest that microstate information can be stored on the surface of the event horizon and that the classical parameters only belong to a macroscopic description.

Cheers,

Jazz