[wanda]

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.

[raattgift]

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).