The information loss problem for black holes is a quantum issue. If the Hawking radiation produced during black hole evaporation were truly thermal, then that would mean that the details of the black hole’s quantum state are being irreversibly lost, which would violate standard quantum time evolution. People now mostly think that the details of the state live on, in correlations in the Hawking radiation. But there are no microscopic models of a black hole which can show the mechanics of this. Even in string theory, where you can sometimes construct an exact description of a quantum black hole, e.g. as a collection of branes wrapped around the extra dimensions, with a gas of open strings attached to the branes, this still remains beyond reach.
If the Hawking radiation produced during black hole evaporation were truly thermal, then that would mean that the details of the black hole’s quantum state are being irreversibly lost, which would violate standard quantum time evolution.
OK, I know that’s a quite different situation, but just to clarify: how is that resolved for other things that radiate “thermally”? E.g., say we’re dealing with a cooling white dwarf, or even a black and relatively cold piece of coal. I imagine that part of what it radiates is clearly not thermal, but is all radiation “not truly thermal” when looked at in quantum terms? Is the only relevant distinction the fact that you can discern its internal composition if you look close enough, and can express the “thermal” radiation as a statistic result of individual quantum state transitions?
From a somewhat different direction: if all details about the quantum state of the matter before it falls into the black hole are “reflected” back into the universe by gravitational/electromagnetic waves (basically, particles) during formation and accretion, what part of QM prevents the BH to have no state other than mass+spin+temperature?
In fact, I think the part that bothers me is that I’ve seen no QM treatment of BH that looks at the formation and accretion, they all seem to sort of start with an existing BH and somehow assume that the entropy of something thrown into the BH was captured by it. The relevant Wikipedia page starts by saying
The only way to satisfy the second law of thermodynamics is to admit that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole.
But nobody seems to mention the entropy carried by the radiation released during accretion. I’m not saying they don’t, just that I’ve never seen it discussed at all. Which seems weird, since all (non-QM) treatments of accretion I’ve seen suggest (as I’m saying above) that a lot of information (and as far as I can tell, all of it) is actually radiated before the matter ever reaches the EH. To a layman it sounds like discussing the “cow-loss paradox” from a barn without walls...
how is that resolved for other things that radiate “thermally”?
For something other than a black hole, quantum field theory provides a fundamental description of everything that happens, and yes, you could track the time evolution for an individual quantum state and see that the end result is not truly thermal in its details.
But Hawking evaporation lacked a microscopic description. Lots of matter falls into a small spatial volume; an event horizon forms. Inside the horizon, everything just keeps falling together and collapses into a singularity. Outside the horizon, over long periods of time the horizon shrinks away to nothing as Hawking radiation leaks out. But you only have a semiclassical description of the latter process.
The best candidate explanation is the “fuzzball” theory, which says that singularities, and even event horizons, do not exist in individual quantum states. A “black hole” is actually a big ball of string which extends out to where the event horizon is located in the classical theory. This ball of string has a temperature, its parts are in motion, and they can eventually shake loose and radiate away. But the phase space of a fuzzball is huge, which is why it has a high entropy, and why it takes exponentially long for the fuzzball to get into a state in which one part is moving violently enough to be ejected.
That’s the concept, and there’s been steady progress in realizing the concept. For example, this paper describes Hawking radiation from a specific fuzzball state. One thing about black hole calculations in string theory is that they reproduce semiclassical predictions for a quantum black hole in very technical ways. You’ll have all the extra fields that come with string theory, all the details of a particular black hole in a particular string vacuum, lots of algebra, and then you get back the result that you expected semiclassically. The fact that hard complicated calculations give you what you expect suggests that there is some truth here, but there also seems to be some further insight lacking, which would compactly explain why they work.
nobody seems to mention the entropy carried by the radiation released during accretion
The entropy of the collapsing object jumps enormously once the event horizon forms. Any entropy lost before that is just a detail.
From a string-theory perspective, the explanation of the jump in entropy would be something like this: In string theory, you have branes, and then strings between branes. Suppose you have a collection of point-branes (“D0-branes”) which are all far apart in space. In principle, string modes exist connecting any two of these branes, but in practice, the energy required to excite the long-range connections is enormous, so the only fluctuations of any significance will be strings that start and end on the same brane.
However, once the 0-branes are all close to each other, the energy required to excite an inter-brane string mode becomes much less. Energy can now move into these formerly unoccupied modes, so instead of having just N possibilities (N the number of branes), you now have N^2 (a string can start on any brane and end on any other brane). The number of dynamically accessible states increases dramatically, and thus so does the entropy.
nobody seems to mention the entropy carried by the radiation released during accretion
The entropy of the collapsing object jumps enormously once the event horizon forms. Any entropy lost before that is just a detail.
OK, that’s the part that gives me trouble. Could you point me towards something with more details about this jump? That is, how it was deduced that the entropy rises, that it is big rise, and that the radiation before it is negligible? An explanation would be nice (something like a manual), but even a technical paper will probably help me a lot (at least to learn what questions to ask). A list of a dozen incremental results—which is all I could find with my limited technical vocabulary—would help much less, I don’t think I could follow the implications between them well enough.
The conclusion comes from combining a standard entropy calculation for a star, and a standard entropy calculation for a black hole. I can’t find a good example where they are worked through together, but the last page here provides an example. Treat the sun as an ideal gas, and its entropy is proportional to the number of particles, so it’s ~ 10^57. Entropy of a solar-mass black hole is the square of solar mass in units of Planck mass, so it’s ~ 10^76. So when a star becomes a black hole, its entropy jumps by about 10^20.
What’s lacking is a common theoretical framework for both calculations. The calculation of stellar entropy comes from standard thermodynamics, the calculation of black hole entropy comes from study of event horizon properties in general relativity. To unify the two, you would need to have a common stat-mech framework in which the star and the black hole were just two thermodynamic phases of the same system. You can try to do that in string theory but it’s still a long way from real-world physics.
For what I was saying about 0-branes, try this. The “tachyon instability” is the point at which the inter-brane modes come to life.
The information loss problem for black holes is a quantum issue. If the Hawking radiation produced during black hole evaporation were truly thermal, then that would mean that the details of the black hole’s quantum state are being irreversibly lost, which would violate standard quantum time evolution. People now mostly think that the details of the state live on, in correlations in the Hawking radiation. But there are no microscopic models of a black hole which can show the mechanics of this. Even in string theory, where you can sometimes construct an exact description of a quantum black hole, e.g. as a collection of branes wrapped around the extra dimensions, with a gas of open strings attached to the branes, this still remains beyond reach.
OK, I know that’s a quite different situation, but just to clarify: how is that resolved for other things that radiate “thermally”? E.g., say we’re dealing with a cooling white dwarf, or even a black and relatively cold piece of coal. I imagine that part of what it radiates is clearly not thermal, but is all radiation “not truly thermal” when looked at in quantum terms? Is the only relevant distinction the fact that you can discern its internal composition if you look close enough, and can express the “thermal” radiation as a statistic result of individual quantum state transitions?
From a somewhat different direction: if all details about the quantum state of the matter before it falls into the black hole are “reflected” back into the universe by gravitational/electromagnetic waves (basically, particles) during formation and accretion, what part of QM prevents the BH to have no state other than mass+spin+temperature?
In fact, I think the part that bothers me is that I’ve seen no QM treatment of BH that looks at the formation and accretion, they all seem to sort of start with an existing BH and somehow assume that the entropy of something thrown into the BH was captured by it. The relevant Wikipedia page starts by saying
The only way to satisfy the second law of thermodynamics is to admit that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole.
But nobody seems to mention the entropy carried by the radiation released during accretion. I’m not saying they don’t, just that I’ve never seen it discussed at all. Which seems weird, since all (non-QM) treatments of accretion I’ve seen suggest (as I’m saying above) that a lot of information (and as far as I can tell, all of it) is actually radiated before the matter ever reaches the EH. To a layman it sounds like discussing the “cow-loss paradox” from a barn without walls...
For something other than a black hole, quantum field theory provides a fundamental description of everything that happens, and yes, you could track the time evolution for an individual quantum state and see that the end result is not truly thermal in its details.
But Hawking evaporation lacked a microscopic description. Lots of matter falls into a small spatial volume; an event horizon forms. Inside the horizon, everything just keeps falling together and collapses into a singularity. Outside the horizon, over long periods of time the horizon shrinks away to nothing as Hawking radiation leaks out. But you only have a semiclassical description of the latter process.
The best candidate explanation is the “fuzzball” theory, which says that singularities, and even event horizons, do not exist in individual quantum states. A “black hole” is actually a big ball of string which extends out to where the event horizon is located in the classical theory. This ball of string has a temperature, its parts are in motion, and they can eventually shake loose and radiate away. But the phase space of a fuzzball is huge, which is why it has a high entropy, and why it takes exponentially long for the fuzzball to get into a state in which one part is moving violently enough to be ejected.
That’s the concept, and there’s been steady progress in realizing the concept. For example, this paper describes Hawking radiation from a specific fuzzball state. One thing about black hole calculations in string theory is that they reproduce semiclassical predictions for a quantum black hole in very technical ways. You’ll have all the extra fields that come with string theory, all the details of a particular black hole in a particular string vacuum, lots of algebra, and then you get back the result that you expected semiclassically. The fact that hard complicated calculations give you what you expect suggests that there is some truth here, but there also seems to be some further insight lacking, which would compactly explain why they work.
Here’s a talk about fuzzballs.
The entropy of the collapsing object jumps enormously once the event horizon forms. Any entropy lost before that is just a detail.
From a string-theory perspective, the explanation of the jump in entropy would be something like this: In string theory, you have branes, and then strings between branes. Suppose you have a collection of point-branes (“D0-branes”) which are all far apart in space. In principle, string modes exist connecting any two of these branes, but in practice, the energy required to excite the long-range connections is enormous, so the only fluctuations of any significance will be strings that start and end on the same brane.
However, once the 0-branes are all close to each other, the energy required to excite an inter-brane string mode becomes much less. Energy can now move into these formerly unoccupied modes, so instead of having just N possibilities (N the number of branes), you now have N^2 (a string can start on any brane and end on any other brane). The number of dynamically accessible states increases dramatically, and thus so does the entropy.
OK, that’s the part that gives me trouble. Could you point me towards something with more details about this jump? That is, how it was deduced that the entropy rises, that it is big rise, and that the radiation before it is negligible? An explanation would be nice (something like a manual), but even a technical paper will probably help me a lot (at least to learn what questions to ask). A list of a dozen incremental results—which is all I could find with my limited technical vocabulary—would help much less, I don’t think I could follow the implications between them well enough.
The conclusion comes from combining a standard entropy calculation for a star, and a standard entropy calculation for a black hole. I can’t find a good example where they are worked through together, but the last page here provides an example. Treat the sun as an ideal gas, and its entropy is proportional to the number of particles, so it’s ~ 10^57. Entropy of a solar-mass black hole is the square of solar mass in units of Planck mass, so it’s ~ 10^76. So when a star becomes a black hole, its entropy jumps by about 10^20.
What’s lacking is a common theoretical framework for both calculations. The calculation of stellar entropy comes from standard thermodynamics, the calculation of black hole entropy comes from study of event horizon properties in general relativity. To unify the two, you would need to have a common stat-mech framework in which the star and the black hole were just two thermodynamic phases of the same system. You can try to do that in string theory but it’s still a long way from real-world physics.
For what I was saying about 0-branes, try this. The “tachyon instability” is the point at which the inter-brane modes come to life.