I believe the 'No-hair theorem' is closest to a 'law' that says Black holes destroy information [1]. If it is true, then when you throw anything into a black hole, information about what you threw in (whether it is a chair, a star, a planet, etc.) is 'lost' as to the outside world they all yield the same observable parameters of the black hole.
IANAPhysicist, but couldn't information be radiated away? When you have a particle and antiparticle annihilating, the information about what collided and when is carried away by the radiation from that annihilation event; nothing remains at ground zero to be inspected.
As matter traverses the accretion disk and falls towards the event horizon, couldn't information about it be radiated away? As an observer, you could definitely tell whether somebody threw a planet or a planet-sized bunch of paperclips into a black hole by observing the accretion disk as it happened.
When it comes to black holes, no one is a physicist.
The problems appear when you try to apply GR and the rest of classical physics - which all assume spacetime is continuous and analytically smooth - to a situation it can't handle.
It's a good tool for normal spacetime, it's fine for making predictions all the way up to an event horizon, but it's absolutely unable to say anything useful about what happens at an event horizon - never mind beyond one.
Because the question isn't "What happens to an astronaut or a chair at the event horizon?" It's "What happens to wave equations and quantum fields at the event horizon?"
If all information is lost at the the event horizon, quantum theory stops working in a catastrophic way. There are no fields, no particles, no interactions, possibly not even raw spacetime.
If it isn't lost, then something else happens, but no one is sure what it is yet.
Hawking's theory works on the basis that some relationships persists across the horizon - actually they stretch back to the formation of the black hole - but he seems to have assumed that it's possible to ignore the limits set by the Planck length/time. There are good reasons for thinking this is unlikely to be true.
Without a theory of quantum gravity - or rather of quantum spacetime - this is all guesswork. It isn't even possible to prove the No Hair Conjecture.
So although it's currently assumed that mass, angular momentum, and charge are conserved (and therefore not all information is lost), there's no proof for this, and no explanation why these features would be conserved while others aren't.
I know nothing, but from reading Wikipedia, I ran across something that really appealed to me - the idea that "black holes" are really fuzzy balls of strings (or whatever lies within the particles we know) where you would otherwise expect an event horizon. Anything falling into them comes apart into that stuff when it gets there.
To me, that feels right, even though I can't say anything about the math.
> the information about what collided and when is carried away by the radiation
This is where the thermal nature of the radiation emitted by the black hole comes in. Physicist use the term "thermal radiation" to mean it is in a mixed state that cannot encode information (crude analogy: as if someone has pressed all the keys of a keyboard at once, you see that some keys are being pressed but this "signal" cannot be decoded).
As it stands, as far as we know, Hawking radiation is completely thermal and random, so as the article states, you can't tell the initial state from the final state even if you collect all the radiation.
> observing the accretion disk
Well that is not part of the black hole now, is it.
> There are various ideas about how the paradox is solved. Since the 1997 proposal of the AdS/CFT correspondence, the predominant belief among physicists is that information is preserved and that Hawking radiation is not precisely thermal but receives quantum corrections.
Maybe that is wrong, but not sure what the basis for the claim to the contrary is.
Another citation which speaks to the views of Hawking on the matter:
> Now if information is really lost down a black hole as Hawking originally proposed [64], and if the Hawking radiation really has negligible correlations between what is emitted early and late, then it might be true that A/4 −tr(ρ ln ρ), suitably regularized, would never decrease. But since this information-loss proposal has been controversial since near the beginning [65, 66], and since now even Hawking has given it up [67];
> “If you jump into a black hole, your mass energy will be returned to our Universe, but in a mangled form, which contains information about what you were like, but in an unrecognisable state.”
The reason the black hole information paradox is a paradox is because it presents us with an unresolved contradiction ("There are various ideas about how the paradox is solved"). So there are several theories with try to resolve the contradiction, but they are all competing theories (i.e. physicists do not agree). Also, some of those theories assume Anti-de Sitter space which contradicts the positively mesaures cosmological constant.
So in the sense that before the paradox is resolved, we don't know if the radiation is thermal or not, but the idea of the radiation being thermal was based on the existing bog-standard theory of QM and GR. What is under debate is how that needs to be modified, which we haven't agreed yet.
Kindly riddle me this. If a black hole was a closed system, then the premisses, that information inside will become lost, would be trivially true by the (2nd?) law of thermodynamics.
There's energy going in, so it isn't hermetically sealed. Thus, the accretion disk is part of the system. But if there's no correlated information coming out, it's closed one-way. You say there is radiation coming out, theoreticly, and I know that radiation is information. It's information in one strict sense, but not in the other--what are the different scopes; Is the radiation not observable?
Are the laws of thermodynamics seemingly violated, that is, is the theory not complete (rhethoric question); Thus your remark was in effect non-constructive, as you cannot prove one unknown with another, can you?
Nevermind the kind of scary question whether any system in the grand scheme of things is closed at all.
BTW another comment mentioned conservation of momentum and charge. I wonder, in the focal point of an ideal lense, in theory, can the image be reconstructed? Well, by looking at the flame quite trivially, at least, albeit not in the perspective of the focal point (not easily without ambiguity, surely). Is this what Tao's one-pixel-cam is about?
Outside the event horizon, sure. But imagine the (extremely) far future when the universe is dominated by black holes and even those photons have been absorbed. You would not be able to extract any information about the past universe aside from its mass.
This may be a naive question, but, how do we know that the mass we measure for a black hole is equivalent to the things that went into the black Hole? We can’t have any observational data on what went into them in aggregate - is it not possible that the mass of black holes that we estimate is incorrect in some fundamental way? Or just that e.g. energy that enters them also becomes mass?
Yes the radiation from the infalling body gives the remote observer some information about what is going on with the body. From their viewpoint, the process of fall into the hole takes infinite time, or in other words, it never completes. The longer the time of observation, the longer the wavelengths of the radiation from the body, so the less and less information is obtained, until the radiation is so red shifted that it is not measurable. That is when the acquisition of information stops. The body still falls down after that, it is a never-ending process but for practical purposes the body is gone.
[1] https://en.wikipedia.org/wiki/No-hair_theorem