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Ok, so on Science channel was a special about Hawking/Susskind debating black holes, which can somehow remove information from the universe.

A) In stars, fusion converts 4 hydrogen into 1 helium, with a small fraction of the mass being converted to energy.

This happens all the time, and nobody is that amazed about it anymore. So, I have to assume that science is ok with the idea of fusion happening, and so, converting matter into energy doesn't destroy the information of the matter.

Let's take that as Assuption 1:
** 1: Converting matter to energy is OK.

B) In empty space, quantum fluctuations of the energy levels are presumed to allow "pair creation" where a particle and its anti-particle can be created out of the really tiny amounts of energy that exist in empty space. For quantum fluctutations, if I understand it, the uncertaincy principle actually dictates that the amount of energy can fluctuate, allowing a pair to be created even if there "shouldn't be enough energy", because the amount of energy in a small space is uncertain.

The tiny amount of energy becomes a particle + anti-particle, for a tiny instant, and then they fall back into each other, and are converted back to the same tiny amount of energy.

Anyways, ignoring the fact that I'm fuzzy on all the requirements for pair creation -- it is generally accepted as part of quantum physics that it can happen.

So, again, I have to assume that science is ok with the idea of pair creation. And so, converting energy into matter, must also not destroy the information value of the energy, and that information value must remain even after the 2 particles annihilate and go back to being energy.

Let's take that as Assumptions 2 + 3: ** 2: Converting energy into matter is OK. ** 3: Pair creation, doesn't mess up anything.

C) Ok, now black holes. My (weak) understanding of Hawking's idea on how black holes emit energy is that pair creation can happen close to the black hole. Since the position of energy is uncertain at the quantum level, some of the energy that "should be" inside the black hole's event horizon, can be treated as uncertainly outside the black hole, and then that extra energy can cause pair creation. If the black hole then pulls in both particles, then nothing special happens -- the mass/energy stays inside the black hole.

But if one or both of the particles moves away from the black hole, and somehow escapes, that can cause the energy to leave the black hole. This is assumed to be a very unlikely event, but still within possibility.

Anyways, that's my (very rough) understanding of Hawking's theory on how black holes can loose mass over time, when in theory "nothing can escape a black hole". Let's assume Hawking's correct...

If a black hole continues to loose mass over cosmic time, it will eventually disappear, and the problem is stated that when it vanishes: All of the information which the black hole had formerly consumned, will be lost.

Which contradicts the Law of Conservation of Information. At least, that's how the Science channel presented it.

So, my idea/question:

** Every time the black hole looses mass, it's through the processes of energy->matter, or matter->energy->matter, involved in pair creation. Based on assumptions 1, 2 + 3 above, none of these should violate the Law of Conservation of Information. It seems that the very slow process of loosing mass, should also be a very slow process of "leaking" information back into the rest of the universe.

*** So, WHAT's the problem? ***

By my understanding: By the time the black hole vanishes, it's OK -- because all of it's information should also have leaked back into the rest of the universe, and no information will be lost.

OK, so please tell me why this is wrong. It seems intuituve to me, but really smart people have spent years looking into this. So, am I missing something?

Thanks! -Chuck

ps. Also, if my statement of fusion, pair creation, and/or hawking radition is wrong -- BUT NOT IN A WAY THAT MATERIALLY AFFECTS THE QUESITON -- please overlook that and just focus on the question.

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Observing the hawking radiation that comes out of the black hole tells us a nothing about the contents of the black hole itself, though. If I converted matter into energy, the energy would be coming from the matter itself. With hawking radiation, the radiation coming out would have never even interacted with the particle its pair annihilated. –  Justin L. Jun 7 '11 at 6:46
    
@justin: Hi, my intuition (which could be wrong) is that the pair creation is made possibly by the uncertain position of the energy/information which "should be" inside the black hole, but which uncertainly can be considered outside it. So then it's actually the energy from inside the black hole, with the information from inside the black hole, that created the pair. So then it seems possible for it to retain that information after all? –  Charles Teague Jun 7 '11 at 23:01
    
@justin, sry I was not clear. I meant - if the pair creation is going to be able to pull energy out of the BH, then my assumption is that the particles are being created by energy which is inside the BH, but which is uncertainly located, and so you end up with some of the energy actually outside. My thought was this energy-from-inside can represent info from inside, and if that energy just happens to create a particle which escapes, then you could have information escaping. I'd welcome anyones comments on how sound this idea is ... –  Charles Teague Jun 8 '11 at 4:32

1 Answer 1

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Hawking thought - and could "rigorously" deduce from semiclassical gravity - that the information has to be lost because it can't get out of the black hole interior once it gets there.

enter image description here

To see why, look at this "Penrose causal diagram" that may be derived for a black hole solution. Diagonal lines at 45 degrees are trajectories of light, more vertical lines are time-like (trajectories of massive objects), more horizontal lines are space-like.

If you look e.g. at the yellow surface of the star (its world line), you see that it ultimately penetrates through the green event horizon into the purple black hole interior. Once the object - and the information it carries - is inside, it can no longer escape outside (don't forget: time is going up), into the light green region, because it would have to move along spacelike trajectories.

So the information carried by the star that collapsed to the black hole inevitably ends at the violet horizontal singularity and it may never be seen in a completely different region outside the black hole.

The information loss of course depends on the detailed geometry of the black hole that is not shared by a helium nucleus, so it shouldn't be surprised that helium nuclei and black holes have different properties.

As we know today, the information is allowed to "tunnel" along spacelike trajectories a little bit in quantum gravity (i.e. string/M-theory). This process is weak but this weak "non-local process" allows the information to be preserved.

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The last paragraph needs more explanation. Are you saying that within the string/M theoretic interpretation of black holes the violet singularity is replaced by "what?" that presumably allows information to get out. In the case asked, of complete evaporation, is the Hawking radiation interpreted in terms of tunneling, and thus complete evaporation would release the information back to the universe? –  anna v Jun 7 '11 at 6:28
    
Hi. If I understand the "classical" interpretation -- wouldn't the mass/energy also be required to remain inside the event horizon? I guess I don't see how Hawking can say that energy is allowed to escape without also allowing information to escape. (Now if we assume quantum type of interactions, then I think its saying that the tunneling makes it possible for both to escape) –  Charles Teague Jun 7 '11 at 22:55
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@anna: Since nobody really understands how information gets out of black holes, any additional explanation you get is still going to be unilluminating. –  Peter Shor Jun 8 '11 at 13:25
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@Ron Maimon: They are not Bohr complementary; they are Susskind complentary. This has nothing to do with the usual complementarity in quantum mechanics. Bohr complementarity is really quite well understood, and has been for over 70 years. At this point, Susskind complementarity still has no real mathematics behind it. –  Peter Shor Oct 8 '11 at 21:16
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@Ron: How? Do you have any references? Not on holography (this is in t'Hooft's papers, and there is serious math behind that) but why Susskind complementarity is a special case of Bohr complementarity. –  Peter Shor Oct 8 '11 at 22:19

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