[af3d]

> While we don't yet have a good microscopic theory of what's going on, macroscopically we know that the information (entropy) doesn't just vanish into three numbers.

What information could one possibly extract from a "packet" of Hawking radiation? If the black hole was originally formed from a huge mass consisting of 80% iron and 20% xenon, for example, could such a thing be deduced by inspecting the radiation emitted by it? I would suspect that the answer would be "no". (Of course, I am just being an arm-chair physicist here.)

[rcxdude]

That is the core of the issue: hawking radiation would seem to be completely random, and therefore have no relation to what went into the black hole. But basically the entirety of physics works in a time-reversible fashion: if you could flip the direction of all the particles in a system, it would evolve back to its previous state (including such situations as two fluids mixing: entropy is how the precise arrangement of that mixed state that 'unmixes' itself is staggeringly unlikely to be seen randomly, but according to most models of physics, it should exist). But this seems to break down when it comes to black holes (it also breaks down in the various magical collapse interpretations of quantum mechanics, but the quantum wavefunction itself is also time-reversable)

[af3d]

> But basically the entirety of physics works in a time-reversible fashion: if you could flip the direction of all the particles in a system, it would evolve back to its previous state

What does that even mean though? Certain systems may indeed time-reversible, but I would argue that most are not (practically speaking). Imagine for example a meteorite which has fallen to Earth. In order to "reverse the process", not only would it have to "reassemble itself" from the innumerable pieces embedded in the ground, it would also have to be flung back passed the escape velocity of our planet!

> But this seems to break down when it comes to black holes (it also breaks down in the various magical collapse interpretations of quantum mechanics, but the quantum wavefunction itself is also time-reversable)

I still don't understand the issue. Entropy is essentially just a measure of how close to a system is to the "average value". A high-entropy system being very close to it (and hence, "highly disordered"), while a low-entropy system might be two or three standard-deviations from the mean. A black hole with little angular momentum, charge, and/or mass would necessarily have a lower entropy than otherwise, but in any case we can calculate that without knowing a thing about what is going on inside of it. Moreover we can deduce that such a black hole would indeed be "easier to time-reverse" than one with a higher-entropy, but what does that even tell us? As far as I can tell, not a whole lot.

[daxfohl]

The first one is talking about the quantum realm. So, absent of measurement or some kind of collapsing of the wave function, pure quantum states are 100% reversible. So the question is, where does the transition happen from the quantum world to the world we know. Whence Einstein's question about "when I stop looking at the moon does it disappear". So far, nobody knows. So far, we haven't observed any limits to how big a pure quantum system can get, and there's no "spontaneous" collapse if we don't measure something.

So the question is, could a pure quantum state model a meteor crashing into Earth? It doesn't seem like it. Friction, heat, and so on cannot be reversed classically. The question of Schrodinger's Cat even becomes moot because in an isolated system, the processes a body requires to sustain life (such as friction and heat) can't be modeled in the first place, so the cat will turn into a sloppy goop before anyone pulls the trigger. So, what's going on? Why does quantum mechanics seem to model everything that happens in the microscopic world, but in the macroscopic world we see things that it can't? Where does that crossover between microscopic and macroscopic occur? If measurement is what causes quantum wave collapse, then would none of this happen if nobody was there to measure it? And what created the measurers? 99 years since Schrodinger's equation, and we're not particularly any closer.

Black holes also seem to violate reversibility. They absorb information, but the radiation they give off is random. So, it's impossible to perform the process in reverse. This is spooky in a different way than the above because it's purely mathematical. For "regular" micro/macro quantum/classical paradoxes, we're generally talking about the classical realm of experiments. But for black holes, it's pure math, of our two fundamental theories of nature, and showing that they don't line up. Though, it's perhaps less spooky because the obvious answer is that one or both of the theories is slightly wrong, so we just need to fix it. The measurement problem, or understanding waveform collapse, I think is the more interesting problem, but that's just me.