# Black Holes, Information Loss and Causality Query

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## Main Question or Discussion Point

I take an interest in physics in my spare time (in IT during the day).

I have a query regarding the 'problem' of information loss at a black hole, and would be grateful for some enlightenment.

It seems generally regarded that any information going past the horizon of a black hole is 'scrambled' and irreversible. I mean 'information' in the sense of 'the sum of bits required to accurately describe the object'.

I was wondering whether that is assumed as truth or whether this is an irreversible process.

Possibly:
• Consider the bits of information like a 'tape' of 1's and 0's.
• Information gets added onto the disc of the black hole in a serial fashion. I'm thinking that almost all of the black hole will be equally dense, but surely when new information is being added in, its not going to be perfectly uniform in shape and perhaps new information would have a designated place to be 'written to' the black hole
• The information would be preserved
Is this 'way off' and what'd be the best thing(s) to read with regards to the subject of information preservation/loss (I have a good head for maths but lack the further education for it).

Thanks for any pointers.

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First of all, a black hole is deemed to be a singularity, infinitely dense and with no volume. So in regard to when information is added that it will not be perfectly uniform in shape, a black hole is understood to be a point with no surface or shape so that is not a problem. Also gravity causes mass to become uniform in shape anyway.

Secondly, the information is not lost. It becomes the mass of the black hole. Even if information is scrambled the physical make up of the information still exists, except in a mixed up form.

stevendaryl
Staff Emeritus
Secondly, the information is not lost. It becomes the mass of the black hole. Even if information is scrambled the physical make up of the information still exists, except in a mixed up form.
You're talking here as if the mystery has been solved, but I don't think it has. Or at least, there is no consensus about what the solution is. The problem with black holes is that outside of the event horizon, the only things that distinguish one black hole from another are (1) the total mass, (2) the angular momentum, and (3) the total charge. So there just doesn't seem to be any way, from the outside, to reconstruct what went into the black hole. If its mass came from bowling balls or cell phones or cows, it makes no difference to what the black hole looks like from outside. That wouldn't be a problem if black holes were eternal, because you could assume that all the missing information was inside the event horizon, and would just be inaccessible. However, according to Hawking, black holes don't last forever--eventually they radiate away through the process known as Hawking radiation. So after the black hole has completely radiated away, there would (apparently) be nothing left to record the information about what went into the black hole. That's the mystery of information loss in black holes: after a black hole evaporates, where does the information go?

I see what you mean. I guess that the energy from the hawking radiation could be seen as the information as the mass radiates away. What do you think of this?

Thank you for the replies, both of you.

I think I'm OK with where the information is going within the black hole, I'm thinking more about the bits of information and the reversibility of the process. I guess there's the subtle difference between 'the sum of bits' and 'the sum bits in their correct/original relational order'.

Ive watched this but the summary he mentions 31minutes in is where I'm coming from.

Essentially I'm wondering if it's possible that the bits/configuration of bits could possibly be added to the black hole in an orderly fashion...

... and whether the Hawking radiation could be seen in the same way. e.g. if there was a "first in last out" setup or some such where the order of information going in/out retains all information. I guess in a way I'm wondering if there's room for extending the idea of a 2-dimensional space (on the black hole horizon/near it) being converted into another 2-dimensional setup, but more like 1 dimension of space (the bit stream) and time (the sequence of bits going in or out)

stevendaryl
Staff Emeritus
I see what you mean. I guess that the energy from the hawking radiation could be seen as the information as the mass radiates away. What do you think of this?
That might be a possibility, but the current understanding of Hawking radiation is that it is like thermal radiation--the kind of radiation you would see emitted by any hot object. So it's not expected to encode the information of what went into the black hole. However, it's possible that a more complete analysis would say otherwise, but I'm out of my depth here.

naima
Gold Member
According to Susskind, no information can be lost in a quantum process because the physical process is unitary. All is reversible.
As there is an AdS/CFT equivalence between a model with gravity and a model with strong interaction but without gravity. The latter is described by quantum (reversible) processes. So information would not be lost in a BH in the former model. This show that that Black Hole is not synonimous to loss of information. I do not know if there is something our spacetime.

Thank you nalma.I ended up on the wiki page for AdS/CFT and there's a lot of meat to digest. It seems like the fuzzy idea I have is similar in notion to compactification.

As mentioned above, AdS black holes can actually have hair. An example is a holographic superconductor. The order parameter on the boundary corresponds to some complex scalar field in the bulk. Varying the temperature, you will get to a point where the vacuum expectation value of the order parameter you computed using the GPKW rule is nonzero without a source (in other words, the leading term for your solution for the field using the equations of motion is zero but you still have a subleading response). This signals an instability in the black hole and it will indeed start to discharge.

You should look at the recent paper by Hawking and collaborators. Here they use these soft theorems which I believe correspond to symmetries of the scattering matrix (I may be misquoting this) to look at the paradox.