# Why Does Black Hole Entropy and Information Loss Matter?

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• Omega0
Omega0
TL;DR Summary
A question if Black Hole entropy is a problem.
We know that there is no law of conservation for the entropy. It is quite the contrary: If we have a closed system without exchange of heat the entropy cannot get less. It will reach the max. If we have not a closed system but a stream of entropy only into a system, the entropy will increase.
From my understanding the information stored with raising entropy is getting less.

In Thermodynamics we are free to draw a virtual sphere around a black hole, the system boundary.

My question is a very basic one: Why is it a problem that a black hole gets incredible amounts of entropy and creates more and more until it is not "feeded" anymore, tearing apart the things falling into it? Who cares if information is destroyed which is always the case if entropy dominates - and because physisicst seem to care about the information, why?

Just a little example: If I fly a rocket into the sun the information stored in the rocket, whatever it is, is gone, lost in entropy. When I fly a rocket in a black hole and it is completely torn apart approaching the singularity, if not long before - suddenly we care about the information!? It is gone! Period... Okay, you got my point.

I just don't see the problem, if I am an external observer...

Thanks for your help to understand the problem better.

PS: Okaaayyy, one thing I didn't take into account at all: How could I measure how much entropy a black hole has because I only get it via a comparison, interesting... uuuh, this may be interesting, thanks again.

Omega0 said:
If I fly a rocket into the sun the information stored in the rocket, whatever it is, is gone, lost in entropy.
"Lost in entropy" is not the same thing as "information gone". The information is still there; it's just not practical to retrieve it any more. At least, that's what quantum unitarity (which is the principle that gives rise to the black hole information paradox) says.

Omega0 said:
When I fly a rocket in a black hole and it is completely torn apart approaching the singularity, if not long before - suddenly we care about the information!? It is gone!
But in this case, if we treat the singularity the way classical GR treats it, the information that hits the singularity is gone--not just as in "not practical to retreive it any more", but gone even in principle. And that violates quantum unitarity, whereas the information just being scrambled and not practically retrievable inside an object like the Sun does not.

Omega0
PeterDonis said:
"Lost in entropy" is not the same thing as "information gone". The information is still there; it's just not practical to retrieve it any more. At least, that's what quantum unitarity (which is the principle that gives rise to the black hole information paradox) says.
Okay, I appear to be too bad in QM... you say it not practical to retrieve the information any more. If I take a sugar cube and eat it, how would you theoretically - if not practically - reconstruct it a day later?

Omega0 said:
If I take a sugar cube and eat it, how would you theoretically - if not practically - reconstruct it a day later?
First you need to define exactly what you mean by "reconstruct". For example, if I know exactly how many molecules of sugar were in the sugar cube you ate, and the exact measurements of the cube, I could chemically synthesize a sugar cube with exactly that number of molecules and that exact shape. Would that count as "reconstructing" the sugar cube? If not, why not?

The point is that the meaning of the terms "information" and "entropy" is not as simple as you might think. Also, in QM, particles of the same kind are indistinguishable, and that affects what can count as "the same".

PeterDonis said:
First you need to define exactly what you mean by "reconstruct". For example, if I know exactly how many molecules of sugar were in the sugar cube you ate, and the exact measurements of the cube, I could chemically synthesize a sugar cube with exactly that number of molecules and that exact shape. Would that count as "reconstructing" the sugar cube? If not, why not?
Okay, let's say this is a reconstruction - and I try to ignore the problems which we already have with an "exact shape".
PeterDonis said:
The point is that the meaning of the terms "information" and "entropy" is not as simple as you might think. Also, in QM, particles of the same kind are indistinguishable, and that affects what can count as "the same".
Sure, you mean the different statistics for Bose or Fermi particles? Well, in this statistics there isn't any specific information any more, right? Statistics is a big process of calculating mean values, mathematically, and we'll get some findings, like entropy, pressure, internal energy.

I am not aware of any laws, apart from computer science things, having to do with "the conservation of information". Sounds esotheric to me. I know from experience that information can get lost ;-)

A solid idea in solid state physics, for example, is not to believe to store something for eternity in solid bodies but to keep it away from the brutal power of external transfer of entropy, as long as you can. QM rules always and kill anything.

What I mean is: Find some configuration where you say, that is real information for me. Describe a sugar cube with the number of molecules and the dimensions and the temperature, okay! But eat it and the information is digested, if you don't have taken it down to a piece of paper.

You will never ever get it back from any measurements of anything which happened before. If you have the information on a piece of paper - good! If not, if you believed that the information was intrinsic to your sugar cube and I ate it and was flying into the sun feel free to get the information back from the sun! I guess you won't get it. It is nothing you can get back, with the only exception of an exact time inversion and this would be a bit esotheric, isn't it?

But I still may not have understood the concept.

Omega0 said:
you mean the different statistics for Bose or Fermi particles?
No. I mean that neither bosons nor fermions are distinguishable. Both Bose and Fermi statistics are different from Maxwell-Boltzmann statistics, which are the statistics of distinguishable particles.

Omega0 said:
I am not aware of any laws, apart from computer science things, having to do with "the conservation of information".
It depends on what you mean by "information". There is a sense of "information" for which quantum unitarity does mean "conservation of information". That is the sense of "information" that is relevant to the black hole information paradox.

Omega0 said:
A solid idea in solid state physics, for example, is not to believe to store something for eternity in solid bodies but to keep it away from the brutal power of external transfer of entropy, as long as you can.
Um, actually, solid bodies "keep away from the brutal power of entropy" about as long as anything.

Omega0 said:
QM rules always and kill anything.
As noted above, there is a sense in which QM unitarity conserves information. Nor is the second law of thermodynamics specifically caused by QM.

Omega0 said:
Find some configuration where you say, that is real information for me. Describe a sugar cube with the number of molecules and the dimensions and the temperature, okay! But eat it and the information is digested, if you don't have taken it down to a piece of paper.
As I have already said, "information" can have multiple meanings, and there is at least one for which any unitary process conserves information--and that meaning is the one relevant to the black hole information paradox. Your eating and digestion are unitary processes (or at least that is how QM models them), so they conserve information in the sense that is relevant for the black hole information paradox.

If you wonder why I keep coming back to the sense of information that is relevant for the black hole information paradox, it's because that is what I understood you to be asking about in the OP of this thread. If you want to discuss other senses of "information", you need to start a new thread with a different question.

It might be worthwhile to outline what that sense is. My QM is insufficient.

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