In fact, it’s even possible (in some highly contrived situations) to pass through the event horizon of a black hole without having any indication whatsoever that a black hole even exists. We’re talking not just very small tidal forces, here, but exactly zero tidal forces, exactly zero curvature of spacetime, nothing at all out of the ordinary. Admittedly, these situations require a cosmic conspiracy against you, but they’re theoretically possible.

What would a tiny black hole hitting the Earth look like? The Tunguska Event?

How can you “observe” anything dimmer than Uranus? There is only a difference in degree between “observing” a far-away star via radio waves, in which you have to trust that the science behind your instruments is correct, and “observing” a black hole, in which you also have to trust in your instruments and science.

Similarly, how can we be certain atoms exist? We can’t see them with the naked eye. We can only assume they exist by trusting our measurement instrumentation.

If I recall, black hole radiation preserve information? Perhaps SETI should find one and watch the surface for reappearing dissertations of alien grad students?

It’s always the grad students who get the dirty jobs, isn’t it?

But as far as I know the question is unanswered at this time, actually. Quantum theorists, who have a lot of faith in unitary evolution, don’t like the idea of information loss. But if information thrown into a black hole is preserved and later radiates in the (near-)thermal Hawking radiation, then where does it stay in the meantime? It’s hard to see how it could survive anywhere within the horizon for long periods of time: since all paths there lead to the singularity pretty quickly, you have a problem getting it back out.

So maybe it survives on or near the horizon. But the horizon doesn’t locally look all that unusual, so it’s hard to understand why the information would transfer itself to horizon microstates as it passes this apparently-normal surface in spacetime. And because quantum information can’t be cloned (according to standard QM, which really seems like it ought to hold in such a benign low-curvature area) this information transfer seems like it means that quantum states thrown through the horizon would have to decohere.

But the horizon is a weird enough place in the global structure of spacetime that I can imagine there could be some loopholes in no-cloning. (It’s unlikely, for example, that the cloned states could actually both be observed by a single observer.)

When Hawking finally got around to publishing his claims on that, it turned out to be rather too hand-wavy for my tastes. I’m not sure I consider the matter settled. Even if so, though, the information is purported to all be in the correlations, so to extract any of the information at all, you’d need to observe the black hole for its entire lifespan and collect all of the Hawking radiation.

My take: quantum gravity may well eliminate the singularity, or at least render it harmless to quantum information.

What microstates? Wouldn’t those constitute “hair”?

This smells fishy to me. Remember, “decoherence” is right up there with “energy loss” as one of those things that results from considering an insufficiently general system. Just as heat is “energy lost to the environment”, so decoherence is “information lost to the environment”. The universe itself, as a quantum system, doesn’t decohere.

At least as far as I understand it.

The point about observers might save you in some weird construction, but I think the problem with this is that cloning is directly opposed to superposition. Unless there’s some artful dodge you can come up with, you can’t clone quantum information without quantum superposition breaking down entirely.

But even if the singularity is replaced with some ~Planck-scale quantum-gravity construct, then the information is still trapped well within the horizon until the black hole has mostly evaporated away; I don’t think there’s enough bandwidth in the final stages of evaporation to re-transmit all of it. (Of course, if black holes leave some stable quantum-gravity remnant, then the information could be trapped there forever.)

What microstates? Wouldn’t those constitute “hair”?

Well, yes. If the black hole actually does contain information then it must have hair. But the hair is very fine and difficult to see. The no-hair theorem is just a statement of classical GR, not quantum gravity.

*This smells fishy to me. Remember, “decoherence” is right up there with “energy loss” as one of those things that results from considering an insufficiently general system. Just as heat is “energy lost to the environment”, so decoherence is “information lost to the environment”. The universe itself, as a quantum system, doesn’t decohere.

At least as far as I understand it.*

Sorry, I think I was unclear here. I was saying that **if** the information is somehow transferred to microstates at the horizon as it falls through the horizon, then (because quantum states can’t be copied) it must be removed from the infalling states. The state horizon+(infalling information) would remain coherent.

The point about observers might save you in some weird construction, but I think the problem with this is that cloning is directly opposed to superposition. Unless there’s some artful dodge you can come up with, you can’t clone quantum information without quantum superposition breaking down entirely.

Well, as a quantum mechanic myself I am highly sympathetic to this point of view. But this is an axiom of quantum mechanics (and quantum field theories), not yet an axiom of full quantum gravity. It’s possible that Nature (in the person of quantum gravity) has other ideas.

The paradox is that the horizon seems locally so benign that it ought to be treatable with the theories we already have (QFT on nearly-flat background), which would seem to rule out information transfer to the horizon; but once the information gets close to the singularity where things get weird, it requires traveling backward in time to get the information back out.

When Hawking finally got around to publishing his claims on that, it turned out to be rather too hand-wavy for my tastes. I’m not sure I consider the matter settled.

When he gave his presentation at the GR17 conference in 2004 (I was there), he noted that “there are some logical gaps, but my graduate student is working a proof that will address them.” When the paper came out over a year later, its content was pretty much the same as that of the presentation, right down to his caveat about his graduate student addressing the (still-unfound) proof in a “forthcoming paper”. So maybe you’re right to be suspicious.