# What does it mean when we say that information is potentially recoverable from a black hole

My understanding is that if the surface of a black hole is holographic, then information is potentially emitted from a black hole, say due to Hawking radiation or some other means.

What can say about this information? Is it physically possible and/or feasible that this type of emission would embed information about what went into it? Also, how does this measure up against the idea that the world lines inside the event horizon are completely disconnected from the outside?

I have some knowledge of the information paradox, but I was really hoping someone could explain it in simple terms or point me to a prior explanation along those lines.

The first thing to understand is that we have no actual knowledge of how information and black holes interact.

What we do have are theories that are well supported by experiment (General Relativity, which predicts Black Holes but which says nothing about information) and Quantum Mechanics (which says a lot about information (in this technical sense) but nothing about BHs.) We also have a variety of theories, none of which have any substantial experimental support, and all of which are incomplete (which means we don't know if there's actually a viable theory there -- all we have today is bits and pieces that look promising). One of the goals of all of these theories is to -- somehow -- meld GR and QM into a single coherent theory with greater explanatory power than the two separately.

It is very fair to say that some of the work which has been done to date which tries to link information and BHs is plausible and (at least) does not contradict any experimental evidence we have. And some of them (like what Hawking used in the prediction of Hawking radiation) are such a careful application of QM in the GR context that most physicists would be surprised if they turned out to be incorrect.

The bottom line is that GR and QM are both amazing theories which yet cannot be completely correct -- they must both be subsumed in some more encompassing theory. (Or at least everyone is convinced of that. I am too, BTW.)

Due to the mathematical underpinnings of QM and GR, physicists vaguely can see how some generalization of QM might, possibly be able to include GR someday. But virtually no one can see how GR could be extended to include QM. So the smart money -- just about all the money, actually -- is on extending QM in some way.

One of the most basic features of QM is that it is linear and preserves information (in a certain well-defined, but technical sense). If GR could be derived from some extension of QM, we'd expect that that extension of QM preserves information, and that GR also must preserve information.

On the face of it, GR by itself says that information which falls into a BH is lost. Zap. Gone. Never to return. Therefor finding ways to get GR to preserve information may be an important clue to the ultimate combined theory. And extensions of GR which preserve information seem more likely to be correct.

So the paradox is that BHs, which are predicted by our marvelously correct theory of gravity, GR, do not conserve information. But we have reasons to strongly suspect that BH built from the hypothetical gravitational extension of QM would preserve information. Something's wrong here!

One of the plausible theories that have been developed to resolve this says that Hawking radiation -- which seems very plausible, and which carries energy away from a BH in contradiction of vanilla GR -- might also carry the "lost" information away, eliminating the paradox.

Maybe.

But remember that there isn't any experimental evidence for any of this. It's all based on smart hard-working, competent scientists trying to use their brains and their intuition to guess what the undiscovered theory which merges GR and QM will predict and to turn it into consistent math. It's certainly better than a random-assed guess, but it is a far cry from established science.

Keep watching -- I hope that all this work will bear fruit and a real theory with experimental evidence behind it might emerge in our lifetimes.

• This is all very informative, thanks for the great explanation! One follow up: If Hawking is correct and a scientist with sufficiently advanced technology could observe some emission from the black hole, could you use the emission to say anything about what is going on inside? I guess I am still confused as to what exactly constitutes information in this context. – Sledge Apr 12 '19 at 18:22
• @Sledge: "[If you] could observe some emission from the black hole, could you use the emission to say anything about what is going on inside?" If I or anyone could answer that authoritatively, we're get Nobel Prizes two or three years in a row! The best I can say is that the absolute loss of information behind an event horizon is hard to square with QM, so if BHs can be described by an extension of QM, it seems plausible that we might be possible to pierce the event horizon. Maybe. With sufficiently advanced technology. – Mark Olson Apr 12 '19 at 18:32
• I hope you figure it out and get a Nobel Prize :). Thanks again for informing me. – Sledge Apr 12 '19 at 19:37

Just to add to Mark's excellent answer, experimental verification of any information carried by Hawking radiation is not easy, and it may remain so indefinitely, even if we could visit a black hole in a spaceship to make up-close measurements.

Hawking radiation (if it exists) is extremely difficult to detect, even if you are near the black hole, which isn't a healthy place to be if the black hole is active. And of course the radiation from the matter in the accretion disk will totally swamp the Hawking radiation.

For example, the SMBH M87* emits Hawking radiation with a mean temperature of $$9.5\times 10^{-18}$$ kelvin, at a luminosity of $$2.13\times 10^{-48}$$ watts.

A stellar mass BH is warmer & brighter, but still way too dim for us to detect. Eg, a 10 solar mass BH emits at a temperature of around a nanokelvin, with a luminosity of $$9\times 10^{-31}$$ watts.

I used this online Hawking radiation calculator to obtain those figures.