# Black Hole Information Loss Question

If I understand correctly, Hawking Radiation is created when the anti-particle of a virtual particle pair falls into a black hole while the particle of the pair escapes. The anti-particle goes on to annihilate with a particle in the black hole. Is not the annihilated particle identical to the real particle that escaped the black hole?

Chalnoth
Either the anti-particle or the particle can escape. It doesn't matter.

As for what happens inside the black hole, we can't say. All that we do know is that the particle that escapes the black hole carries with it some of the mass of the black hole.

Either the anti-particle or the particle can escape. It doesn't matter.

As for what happens inside the black hole, we can't say. All that we do know is that the particle that escapes the black hole carries with it some of the mass of the black hole.

How does the escape of am anti-particle reduce the mass of a black hole? Such an event would have a particle falling into a black hole, thereby increasing the mass of the black hole and decreasing the mass of the rest of the universe.

If I understand correctly, Hawking Radiation is created when the anti-particle of a virtual particle pair falls into a black hole while the particle of the pair escapes.

That's one way of looking at Hawking radiation, there are others.

The anti-particle goes on to annihilate with a particle in the black hole. Is not the annihilated particle identical to the real particle that escaped the black hole?

That's not quite what happens. What happens is that the energy from the gravity creates a particle/antiparticle pair near the event horizon. The particle falls in. The anti-particle escapes. Because the pair gets created from the energy of the gravitational field, some of that mass/energy of the black hole leaves via the anti-particle.

Chalnoth
How does the escape of am anti-particle reduce the mass of a black hole? Such an event would have a particle falling into a black hole, thereby increasing the mass of the black hole and decreasing the mass of the rest of the universe.
Annihilation isn't the cause of the reduction of mass of the black hole. It can't be, because if you annihilate two particles within the event horizon, the photons that are produced in the annihilation will have the same energy, and those photons will just remain in the black hole with no change in the behavior.

Instead, the particle that ends up falling into the black hole turns out to have negative mass (this isn't a problem for short-lived particles).

Chronos
Gold Member
It really does not matter which particle falls into the black hole, all that matters is the one that escapes has positive energy. Call it a quantum entanglement thing if that makes it more palatable.

Annihilation isn't the cause of the reduction of mass of the black hole. It can't be, because if you annihilate two particles within the event horizon, the photons that are produced in the annihilation will have the same energy, and those photons will just remain in the black hole with no change in the behavior.

So why do they talk about quantum fluctuations springing into existence and then annihilating each other? Are you saying that photons spring up out of nothing every time there is a quantum fluctuation?

Instead, the particle that ends up falling into the black hole turns out to have negative mass (this isn't a problem for short-lived particles).

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.

bapowell
So why do they talk about quantum fluctuations springing into existence and then annihilating each other? Are you saying that photons spring up out of nothing every time there is a quantum fluctuation?
The actual picture of the Hawking effect in terms of virtual particles is actually rather murky. Hawking's original derivation made no mention of virtual particles slipping over event horizons; he instead examined the asymptotic transformation of a field fluctuation brought in from far away, past a black hole, and back out to very far away. If the initial field fluctuation far away was in its vacuum state, the final fluctuation far away generally is not (as a result of its gravitational interaction with the black hole). John Baez has a nice write up about this: http://www.weburbia.com/physics/hawking.html

The idea of the Hawking effect being the result of virtual particles popping into existence (and, yes, this could be e+/e- pairs popping out of the vacuum) near the event horizon, one falling in and one flying off, is more an illustration for the sake of popular science than an accurate description of the process, which admittedly, is hard to understand in terms of particles. After all, if there's any lesson we learn from playing with quantum fields in general relativity, the very concept of a particle has questionable significance in curved spacetime.

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.
If the black hole is in a particularly crowded part of the universe (like hungry black holes at the centers of some galaxies) they will gorge themselves on surrounding matter and increase in mass. Only when there is little left to eat will they begin to incur a net loss in mass due to Hawking evaporation.

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.

Bill I have seen a few of your posts and just want to clarify something in case you were unsure.

At a distance beyond the Event Horizon of the Black Hole the gravitational effects are the same as any other body of mass, Black Holes are not hoovers that suck everything in. As a thought experiment: if the Sun were to turn into a black hole of 1 solar mass then the Earth would continue to orbit in EXACTLY the same way (except maybe a little colder!)

You may already know this but it seems like you may have this common misconception and I am just trying to help

Chalnoth
So why do they talk about quantum fluctuations springing into existence and then annihilating each other? Are you saying that photons spring up out of nothing every time there is a quantum fluctuation?
Yeah, pretty much. Though they can't stay around for long or else they'll violate conservation of energy.

Also wouldn't you think that a black hole would be accumulating far far more stuff than it could ever evaporate? It should continue to grow until there was no more space/universe to feed it.
If a black hole absorbs a negative-mass particle, it reduces in mass, which means it drops in size.

Bill I have seen a few of your posts and just want to clarify something in case you were unsure.

At a distance beyond the Event Horizon of the Black Hole the gravitational effects are the same as any other body of mass, Black Holes are not hoovers that suck everything in. As a thought experiment: if the Sun were to turn into a black hole of 1 solar mass then the Earth would continue to orbit in EXACTLY the same way (except maybe a little colder!)

You may already know this but it seems like you may have this common misconception and I am just trying to help

Thank you, actually I did realize that. It would be the same as if a mass suddenly turned into a star, the gravity would not change as long as the mass stayed the same. What I was saying had to do with Hawking's evaporation theory. I believe through the effect of gravity that all massive bodies are fed continuously. Even after all the visible surrounding matter has been pushed into the black hole, space is still filled with particles and energy. As I said before there would be far more going into the black hole than could ever evaporate. As long as there was any SPACE/UNIVERSE left. Of course this is my opinion and I'm just looking for feedback.
Thanks again

Chalnoth
Thank you, actually I did realize that. It would be the same as if a mass suddenly turned into a star, the gravity would not change as long as the mass stayed the same. What I was saying had to do with Hawking's evaporation theory. I believe through the effect of gravity that all massive bodies are fed continuously. Even after all the visible surrounding matter has been pushed into the black hole, space is still filled with particles and energy. As I said before there would be far more going into the black hole than could ever evaporate. As long as there was any SPACE/UNIVERSE left. Of course this is my opinion and I'm just looking for feedback.
Thanks again
The black hole will only continue to feed as long as the temperature of its surroundings are higher than the black hole's temperature. If we imagine a situation where all of the normal matter is gone, and we only have black holes, then the temperature in question is the temperature of the CMB. So once the CMB temperature drops below the black hole temperature, it will start to evaporate in net.

The black hole will only continue to feed as long as the temperature of its surroundings are higher than the black hole's temperature. If we imagine a situation where all of the normal matter is gone, and we only have black holes, then the temperature in question is the temperature of the CMB. So once the CMB temperature drops below the black hole temperature, it will start to evaporate in net.

I agree and always have that black hole may evaporate and I can understand how this could happen. All I have been suggesting is that a black hole will continuosly be fed as long as there is space, given it hardly a chance to ever evaporate.

Chalnoth
I agree and always have that black hole may evaporate and I can understand how this could happen. All I have been suggesting is that a black hole will continuosly be fed as long as there is space, given it hardly a chance to ever evaporate.
Again, it has to do with temperature. If the temperature of the space is lower than that of the black hole, then the black hole will emit radiation more rapidly than it feeds.

martinbn
As already said the explanation with particle antiparticle is only an analogy. In the original paper Hawking writes:

"One might picture this negative energy flux in the following way. Just
outside the event horizon there will be virtual pairs of particles, one with negative
energy and one with positive energy. The negative particle is in a region which
is classically forbidden but it can tunnel through the event horizon to the region
inside the black hole where the Killing vector which represents time translations
is spacelike. In this region the particle can exist as a real particle with a timelike
momentum vector even though its energy relative to infinity as measured by the
time translation Killing vector is negative. The other particle of the pair, having
a positive energy, can escape to infinity where it constitutes a part of the thermal
emission described above. The probability of the negative energy particle tunnelling
through the horizon is governed by the surface gravity K since this quantity
measures the gradient of the magnitude of the Killing vector or, in other words,
how fast the Killing vector is becoming spacelike. Instead of thinking of negative
energy particles tunnelling through the horizon in the positive sense of time one
could regard them as positive energy particles crossing the horizon on pastdirected
world-lines and then being scattered on to future-directed world-lines by
the gravitational field. It should be emphasized that these pictures of the mechanism
responsible for the thermal emission and area decrease are heuristic only
and should not be taken too literally.
"

So Hawking's argument is that a black hole has a non-zero temperature and so radiates as a thermal black body. His justification is based in QM but with that caveat, "It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally," as posted by martinbn.

John Baez took up the argument, as linked by bapowell, beginning with, "In 1975 Hawking published a shocking result: if one takes quantum theory into account, it seems that black holes are not quite black! Instead, they should glow slightly with "Hawking radiation", consisting of photons, neutrinos, and to a lesser extent all sorts of massive particles."

And ending with, "Now in fact when you do a Bogoliubov transformation to the vacuum you get a state in which there are pairs of particles and antiparticles, so this is possibly the link between the math and the heuristic explanation."

This leads me back to the original question, which was (admittedly) understated. If Hawking radiation is more than simply thermal (i.e. comprised of "photons, neutrinos, and to a lesser extent all sorts of massive particles") then should not an observer at infinity be able to (at least in principle) measure the properties of all of the particles emitted by the black hole?

Yes sorry if this is just asking the same question again in a different way :uhh:...

I keep hearing that one of the big issues that is had with Hawking Radiation (or is it only a problem in relation to the Information Loss Paradox maybe??..) is that there is no mechanism for information to be transferred from the incoming B.H. food to the outgoing Hawking Radiated photons? I've heard it could be said that the two pass by one-another, but there's nothing suggestive of an interaction between them. Am I anywhere near on the right track so far?

And I guess if that's truly the question, anyone around here who might be capable of recounting the popular possible solutions would be great. I've seen that holographic theories may allow the intricacies of a B.H.'s event horizon's shape to preserve the information? Something like the shape of the (entire) horizon changes simultaneously with any incoming matter, and therefore exactly how the B.H. contacts the adjoining space around it (creating the vacuum gradient or whatever [you can probably tell how over my head I am here by now heh] that generates the radiation) can be effected by something seems unconnected. (And the key being the singular, integral nature of the B.H. I take it?)

Are there other ideas for a mechanism? Or just giving up on the problematic quantum information tenant?

Thanks

Chalnoth
Yes sorry if this is just asking the same question again in a different way :uhh:...

I keep hearing that one of the big issues that is had with Hawking Radiation (or is it only a problem in relation to the Information Loss Paradox maybe??..) is that there is no mechanism for information to be transferred from the incoming B.H. food to the outgoing Hawking Radiated photons? I've heard it could be said that the two pass by one-another, but there's nothing suggestive of an interaction between them. Am I anywhere near on the right track so far?
Well, no, the information of what enters a black hole is necessarily encoded in the Hawking radiation that leaves it. It's just that that information is so exceedingly garbled that it is in practice impossible to determine from the outgoing radiation what fell into the black hole.

Well, no, the information of what enters a black hole is necessarily encoded in the Hawking radiation that leaves it. It's just that that information is so exceedingly garbled that it is in practice impossible to determine from the outgoing radiation what fell into the black hole.

Ugh...So the paradox was that, before the idea of Hawking Radiation, it seemed like the quantum information of the ingoing matter was disappearing forever, but Hawking's discovery (if true) shows how it can reemerge, thereby satisfying the universal bookkeepers?

I've actually read (e.g.) the wikipedia entry on this, etc., but it's still confusing to me.

Chalnoth
Ugh...So the paradox was that, before the idea of Hawking Radiation, it seemed like the quantum information of the ingoing matter was disappearing forever, but Hawking's discovery (if true) shows how it can reemerge, thereby satisfying the universal bookkeepers?

I've actually read (e.g.) the wikipedia entry on this, etc., but it's still confusing to me.
Well, Hawking radiation is on very firm footing, and can be derived in a large number of different ways. Hawking radiation has also been observed in analog systems where we produce sound horizons (as opposed to the light horizon of a black hole). So basically, if black holes exist at all (which is nearly certain), they produce Hawking radiation.

With that aside, the picture you paint is largely accurate. The main issue, however, is that it was a long time between the discovery of Hawking radiation and the solution of the black hole information paradox. Early on, it was largely believed that Hawking radiation could not contain any information about what went into the black hole. This has since been proven false.

martinbn
With that aside, the picture you paint is largely accurate. The main issue, however, is that it was a long time between the discovery of Hawking radiation and the solution of the black hole information paradox. Early on, it was largely believed that Hawking radiation could not contain any information about what went into the black hole. This has since been proven false.

Where exactly has this been proven?

So Hawking's argument is that a black hole has a non-zero temperature and so radiates as a thermal black body.

That's one argument. There are others. Some of them boil down to "if Hawking radiation didn't exist, then black holes would have zero temperature, and that causes problems with thermodynamics."

This leads me back to the original question, which was (admittedly) understated. If Hawking radiation is more than simply thermal (i.e. comprised of "photons, neutrinos, and to a lesser extent all sorts of massive particles") then should not an observer at infinity be able to (at least in principle) measure the properties of all of the particles emitted by the black hole?

Yes.

Early on, it was largely believed that Hawking radiation could not contain any information about what went into the black hole. This has since been proven false.

Also what has been proven is that Hawking radiation *could* contain information about what went into the black hole. Whether it does or not is another question, but it's one of those cool things in which "either way something weird happens."

There is a weird consequence to Hawking's solution. If you have information-preserving Hawking radiation with black holes, then you should have information-preserving Hawking radiation at the "cosmological event horizon." If that happens then the total information content of the universe stays constant which means that if you wait long enough everything nearly repeats. (i.e. in 10^10^120 years, we'll be having this conversation again and 10^10^120 years ago, we had almost the same conversation.)

http://arxiv.org/abs/hep-th/0208013

It's a paper called "Disturbing Implications of a Cosmological Constant"

martinbn

Basically it comes down to this proof by Hawking announced in 2004:
http://math.ucr.edu/home/baez/week207.html

I looked at the wiki page but says it nothing about a proof. Only lists verious proposals, all of which have some problems, so they can hardly be considered a proof. I haven't read Hawkings paper, hopefully later today, but the wikipedia page says that it uses AdS/CFT correspondence. I thought that that is still a conjecture. Even if it is proven, and I just didn't know about it, it would imply something about black holes in AdS spacetime. How does that resolve the paradox in general.

Chalnoth
I looked at the wiki page but says it nothing about a proof. Only lists verious proposals, all of which have some problems, so they can hardly be considered a proof. I haven't read Hawkings paper, hopefully later today, but the wikipedia page says that it uses AdS/CFT correspondence. I thought that that is still a conjecture. Even if it is proven, and I just didn't know about it, it would imply something about black holes in AdS spacetime. How does that resolve the paradox in general.
If you read about the discussion that follows, it basically has to do with the topological structure of the black hole. If the black hole's internal topology is nontrivial, then some of the information can "escape" to another space-time. If the black hole doesn't change the overall topology of the universe, then the information is necessarily conserved. I don't think it's reasonable to expect astrophysical black holes to ever have non-trivial topologies.

martinbn
If you read about the discussion that follows, it basically has to do with the topological structure of the black hole. If the black hole's internal topology is nontrivial, then some of the information can "escape" to another space-time. If the black hole doesn't change the overall topology of the universe, then the information is necessarily conserved. I don't think it's reasonable to expect astrophysical black holes to ever have non-trivial topologies.

I am sorry, which discussion do you mean? I was going to try Hawking's paper, but I discussion may be easier to follow. Alos does the argument rely on AdS/CFT?

Chalnoth
I am sorry, which discussion do you mean? I was going to try Hawking's paper, but I discussion may be easier to follow. Alos does the argument rely on AdS/CFT?
This discussion was in the lower part of the link I sent on this.

how does hawkings radiation differ from the energy released in a quasar?

Chalnoth
how does hawkings radiation differ from the energy released in a quasar?
Hawking Radiation comes from the curvature of space-time at the event horizon. The light from a quasar stems from infalling matter being heated to extraordinarily high temperatures as gets closer to the black hole.

Hawking Radiation comes from the curvature of space-time at the event horizon. The light from a quasar stems from infalling matter being heated to extraordinarily high temperatures as gets closer to the black hole.

how does that curvature create the virtual particle pair?

Chalnoth
how does that curvature create the virtual particle pair?
The curvature doesn't create the pair. It just separates the pair.

martinbn
This discussion was in the lower part of the link I sent on this.

Now, I've read it, but it doesn't help much. I still don't know if the argument relies on AdS/CFT and in what way. It seems that it does, but then since AdS/CFT is still a conjecture, it means that there is not proof yet. Also does it mean that this will (when/if AdS/CFT is proven) resolve the paradox for information loss in black holes in AdS spacetime, or is the argument for any spacetime?

Chalnoth
Now, I've read it, but it doesn't help much. I still don't know if the argument relies on AdS/CFT and in what way. It seems that it does, but then since AdS/CFT is still a conjecture, it means that there is not proof yet. Also does it mean that this will (when/if AdS/CFT is proven) resolve the paradox for information loss in black holes in AdS spacetime, or is the argument for any spacetime?
Well, as near as I can tell it's still good enough as a disproof, that is, it demonstrates that the statement that the Hawking radiation cannot encode the information about the stuff that entered the black hole is false.

But in the end, it's pretty trivial to say that if the fundamental laws of physics are unitary, then it cannot be possible for information to be lost.

martinbn