I'll post the relevant paragraphs, all quoted directly (verbatim) from the blog post:
Physicists knew about this puzzle since the 1960s or so, but initially they didn’t take it seriously. At this time, they just said, well, it’s only when we look at the black hole from the outside that we don’t know how reverse this process. Maybe the missing information is inside. And we don’t really know what’s inside a black hole because Einstein’s theory breaks down there. So maybe not a problem after all.
But then along came Stephen Hawking. Hawking showed in the early 1970s that actually black holes don’t just sit there forever. They emit radiation, which is now called Hawking radiation. This radiation is thermal which means it’s random except for its temperature, and the temperature is inversely proportional to the mass of the black hole.
This means two things. First, there’s no new information which comes out in the Hawking radiation. And second, as the black hole radiates, its mass shrinks because E=mc^2 and energy is conserved, and that means the black hole temperature increases as it evaporates. As a consequence, the evaporation of a black hole speeds up. Eventually the black hole is gone. All you have left is this thermal radiation which contains no information.
That's correct for general relativity alone, but GR isn't enough on its own.
Hawking showed that the information is lost in the process of black hole evaporation as the black hole decays into anonymous radiation, and so once a black hole is gone so too is any trace of the matter it absorbed in its lifetime.
It's this bit that isn't okay in quantum mechanics, and that's problematic because quantum mechanics certainly seems to be bang on the money for a great deal of other phenomena.
One would have a hard time saying that QM was wrong. That's not to say that it is a complete theory, but QM has made many, highly accurate predictions that have served to edify the framework.
I don't know how certain it is that black holes evaporate. It may seem tempting to think that perhaps it is this notion of evaporation that could be overturned, but then you have black holes which simply exist forever, which would be rather problematic as well.
FWIW, I've been enjoying your comments in this discussion.
> It may seem tempting to think that perhaps it is this notion of evaporation that could be overturned, but then you have black holes which simply exist forever, which would be rather problematic as well.
Why is a bound state of matter in a black hole lasting until the infinite future more problematic than a bound state of matter in a proton lasting until the infinite future? Is a theory with non-decaying protons problematic compared to a theory with proton decay?
Essentially, gravitational collapse and horizon-formation is not the information loss problem -- the information still exists inside a growing black hole, we're just disconnected from it by virtue of being on the other side of the horizon. Compare with the information from the very early universe which has exited the observable universe thanks to the metric expansion. Or the information in the universe outside the Rindler horizon of an accelerated observer.
Expand the universe forever, and for every observer more and more information goes to the other sides of cosmological and black hole horizons.
Time reversal leads to interesting thoughts: galaxies with stones (and maybe people, chairs, and xylophones) coming into view from beyond the horizon all seems fine if we time-reverse our universe. Likewise for a black hole that had such things fall into it in our ordinary arrow-of-time direction, we should expect that things like stones could be spat out under time-reversal. The information loss problem arises when a black hole completely evaporates to thermal noise: how does the time-reversed black hole, formed from inrushing thermal noise, know that it should eventually spit out xylophones rather than violins?
We need that knowledge in our time-reversed black hole. Does it rush in along with the thermal noise?
The time reversal picture starts with big primordial black holes that fission into smaller ones, with those spitting out dust, gas, dead planets, space probes, stars and so on. Thanks to the time-reversed metric expansion, these spit-out observers also see a bunch of previously unseen black holes rush into view and spit out things like cats and space probes.
This isn't a problem, the recipe for all that can be deemed to be inside the primordial (in the time-reversed sense) black holes: it's part of the initial values surface, with the relevant values initially inside the black hole horizons.
What if we time-reverse from an expanded universe where all black holes have evaporated into thermal noise? Do we have to rely on fluctuations (Boltzmann brains!)? Or on "false noise" as the initial values surface, with dynamical laws that create detailed structure as we do an adiabatic compression of the seemingly structureless cold gas? Or both? We need to get lots of widely-separated black holes at early times when our collapsing universe is big and sparse, rather than at late times when everything is much closer and hotter. We also need it to be correct when we time-reverse the time-reversed picture.
I'm not sure that the problem is qualitatively very different when one thinks classically or quantum mechanically, although the latter sharpens the vocabulary somewhat ("unitarity!") and introduces some fuzzy questions about entanglement energy (Almheiri, Maroff, Polchinksi, Sully 2012 and subsequent fiery discussion).
The problem is that the singularity blocks time-reversal classically, and in the absence of time-reversibility one cannot have unitary evolution (T-symmetry is necessary but insufficient for unitarity, so some (semi-)classical solution that abolishes the singularity might turn out not to resolve the whole information loss problem).
However, a cosmos with black holes that never evaporate seems to abolish most of the "final values surface" problem: we don't know what the quantum numbers are exactly, but at least we know where they are: they're mostly localized inside black holes.
Finally, in the time-reversed picture we blow apart our poor primordial protons during reverse-baryogenesis anyway, but at least stable protons in our usual arrow-of-time direction means we know where almost all the funky GUT epoch numbers are in our very very far future (ignoring black hole evaporation).
As I understand it, the trouble is with "what happens to the information inside the black hole?", not with whether it's there at all or not (which isn't disputed - we see stuff fall in, so it's gotta go _somewhere_ and it isn't in our observable part anymore). In addition, because of the nature of a black hole, how would an experiment trying to test any theory about what happens in a black hole even work? As far as I'm aware, we don't know of any mechanism where stuff inside the black hole affects stuff outside the black hole (hawking radiation doesn't, as far as I'm aware, explain _how_ the spontaneous quantum fluctuations come to be - they're just theorized to happen to satisfy the equivalence principle near the event horizon), but that's exactly what we'd need to confirm or deny anything about whatever happens past the event horizon.
On top of this, just the existence of hawking radiation means black holes vanish over time - but without us being able to say that e.g. a book with mass 1kg or a bag of sugar with mass 1kg was once thrown in. We can't distinguish the two cases - the information (as far as we know today) is lost.
Gravity is infinite at the singularity (the middle of the black hole). Everything gravitates towards that point. Our best understanding is that no information can exist here.
Black holes "evaporate" over time -- by emitting Hawking radiation. This is probably where the information goes, in my layman understanding.
> Black holes "evaporate" over time -- by emitting Hawking radiation. This is probably where the information goes, in my layman understanding.
No, the Hawking radiation and evaporation is exactly what causes the problem. If black holes were forever expanding, we could simply say "they have a structure inside that we can't detect, but that structure preserves the information; but, since it's past the event horizon, it will be, even in principle, forever beyond reach of our understanding and experiment".
However, if black holes eventually disappear, it means you have something like book => unknowable inside of the black hole event horizon => something observable outside. The problem now becomes that, from Hawking's discovery, the "something observable outside" is random thermal radiation, which can't contain information by definition. Hence, not just something unknowable, but a paradox (an inconsistency in the formal model).
hsn915|3 years ago
I'll post the relevant paragraphs, all quoted directly (verbatim) from the blog post:
Physicists knew about this puzzle since the 1960s or so, but initially they didn’t take it seriously. At this time, they just said, well, it’s only when we look at the black hole from the outside that we don’t know how reverse this process. Maybe the missing information is inside. And we don’t really know what’s inside a black hole because Einstein’s theory breaks down there. So maybe not a problem after all.
But then along came Stephen Hawking. Hawking showed in the early 1970s that actually black holes don’t just sit there forever. They emit radiation, which is now called Hawking radiation. This radiation is thermal which means it’s random except for its temperature, and the temperature is inversely proportional to the mass of the black hole.
This means two things. First, there’s no new information which comes out in the Hawking radiation. And second, as the black hole radiates, its mass shrinks because E=mc^2 and energy is conserved, and that means the black hole temperature increases as it evaporates. As a consequence, the evaporation of a black hole speeds up. Eventually the black hole is gone. All you have left is this thermal radiation which contains no information.
wanda|3 years ago
Hawking showed that the information is lost in the process of black hole evaporation as the black hole decays into anonymous radiation, and so once a black hole is gone so too is any trace of the matter it absorbed in its lifetime.
It's this bit that isn't okay in quantum mechanics, and that's problematic because quantum mechanics certainly seems to be bang on the money for a great deal of other phenomena.
One would have a hard time saying that QM was wrong. That's not to say that it is a complete theory, but QM has made many, highly accurate predictions that have served to edify the framework.
I don't know how certain it is that black holes evaporate. It may seem tempting to think that perhaps it is this notion of evaporation that could be overturned, but then you have black holes which simply exist forever, which would be rather problematic as well.
raattgift|3 years ago
> It may seem tempting to think that perhaps it is this notion of evaporation that could be overturned, but then you have black holes which simply exist forever, which would be rather problematic as well.
Why is a bound state of matter in a black hole lasting until the infinite future more problematic than a bound state of matter in a proton lasting until the infinite future? Is a theory with non-decaying protons problematic compared to a theory with proton decay?
Essentially, gravitational collapse and horizon-formation is not the information loss problem -- the information still exists inside a growing black hole, we're just disconnected from it by virtue of being on the other side of the horizon. Compare with the information from the very early universe which has exited the observable universe thanks to the metric expansion. Or the information in the universe outside the Rindler horizon of an accelerated observer.
Expand the universe forever, and for every observer more and more information goes to the other sides of cosmological and black hole horizons.
Time reversal leads to interesting thoughts: galaxies with stones (and maybe people, chairs, and xylophones) coming into view from beyond the horizon all seems fine if we time-reverse our universe. Likewise for a black hole that had such things fall into it in our ordinary arrow-of-time direction, we should expect that things like stones could be spat out under time-reversal. The information loss problem arises when a black hole completely evaporates to thermal noise: how does the time-reversed black hole, formed from inrushing thermal noise, know that it should eventually spit out xylophones rather than violins?
We need that knowledge in our time-reversed black hole. Does it rush in along with the thermal noise?
The time reversal picture starts with big primordial black holes that fission into smaller ones, with those spitting out dust, gas, dead planets, space probes, stars and so on. Thanks to the time-reversed metric expansion, these spit-out observers also see a bunch of previously unseen black holes rush into view and spit out things like cats and space probes.
This isn't a problem, the recipe for all that can be deemed to be inside the primordial (in the time-reversed sense) black holes: it's part of the initial values surface, with the relevant values initially inside the black hole horizons.
What if we time-reverse from an expanded universe where all black holes have evaporated into thermal noise? Do we have to rely on fluctuations (Boltzmann brains!)? Or on "false noise" as the initial values surface, with dynamical laws that create detailed structure as we do an adiabatic compression of the seemingly structureless cold gas? Or both? We need to get lots of widely-separated black holes at early times when our collapsing universe is big and sparse, rather than at late times when everything is much closer and hotter. We also need it to be correct when we time-reverse the time-reversed picture.
I'm not sure that the problem is qualitatively very different when one thinks classically or quantum mechanically, although the latter sharpens the vocabulary somewhat ("unitarity!") and introduces some fuzzy questions about entanglement energy (Almheiri, Maroff, Polchinksi, Sully 2012 and subsequent fiery discussion).
The problem is that the singularity blocks time-reversal classically, and in the absence of time-reversibility one cannot have unitary evolution (T-symmetry is necessary but insufficient for unitarity, so some (semi-)classical solution that abolishes the singularity might turn out not to resolve the whole information loss problem).
However, a cosmos with black holes that never evaporate seems to abolish most of the "final values surface" problem: we don't know what the quantum numbers are exactly, but at least we know where they are: they're mostly localized inside black holes.
Finally, in the time-reversed picture we blow apart our poor primordial protons during reverse-baryogenesis anyway, but at least stable protons in our usual arrow-of-time direction means we know where almost all the funky GUT epoch numbers are in our very very far future (ignoring black hole evaporation).
seanw444|3 years ago
Sukera|3 years ago
As I understand it, the trouble is with "what happens to the information inside the black hole?", not with whether it's there at all or not (which isn't disputed - we see stuff fall in, so it's gotta go _somewhere_ and it isn't in our observable part anymore). In addition, because of the nature of a black hole, how would an experiment trying to test any theory about what happens in a black hole even work? As far as I'm aware, we don't know of any mechanism where stuff inside the black hole affects stuff outside the black hole (hawking radiation doesn't, as far as I'm aware, explain _how_ the spontaneous quantum fluctuations come to be - they're just theorized to happen to satisfy the equivalence principle near the event horizon), but that's exactly what we'd need to confirm or deny anything about whatever happens past the event horizon.
On top of this, just the existence of hawking radiation means black holes vanish over time - but without us being able to say that e.g. a book with mass 1kg or a bag of sugar with mass 1kg was once thrown in. We can't distinguish the two cases - the information (as far as we know today) is lost.
jeremyjh|3 years ago
thwd|3 years ago
Black holes "evaporate" over time -- by emitting Hawking radiation. This is probably where the information goes, in my layman understanding.
tsimionescu|3 years ago
No, the Hawking radiation and evaporation is exactly what causes the problem. If black holes were forever expanding, we could simply say "they have a structure inside that we can't detect, but that structure preserves the information; but, since it's past the event horizon, it will be, even in principle, forever beyond reach of our understanding and experiment".
However, if black holes eventually disappear, it means you have something like book => unknowable inside of the black hole event horizon => something observable outside. The problem now becomes that, from Hawking's discovery, the "something observable outside" is random thermal radiation, which can't contain information by definition. Hence, not just something unknowable, but a paradox (an inconsistency in the formal model).