On 4/7/16 4:13 AM, Nicolaas Vroom wrote:
Op zondag 3 april 2016 23:33:21 UTC+2 schreef Steven Carlip:

We believe that matter in a pure quantum state can collapse
to form a black hole.

This is in a certain sense equivalent that a star collapses and becomes
a neutron star

Not really. A collapsing star is very unlikely to be in a pure
quantum state.

Such a black hole will then evaporate
by Hawking radiation, which is thermal.

This is in a certain sense equivalent that a star explodes and
becomes a super novae.

No. Here things are very different, because a black hole has an
event horizon.

Think of the first photon coming out of a supernova. That photon
will be correlated with the remaining bits of the star, which, in
turn, affect the next photon coming out. This allows the second
photon to be correlated with the first. Similarly, the second
photon is correlated with the remaining bits of the star, so the
third photon can be correlated with the first two. If the supernova
explosion destroys the star completely, the photons that come out
can still be highly correlated.

A black hole is different. The first photon of Hawking radiation
will be correlated with something, but the thing it's correlated
with is behind the horizon. That means that it *can't* transfer
the correlation to the next photon, at least not by any local
physical process. So unlike the case of the supernova, there's
no easy way for the Hawking radiation photons to be correlated
with each other. That means that the correlations in the initial
state that formed the black hole get lost.

The issue is if in either of these cases you can speak about
information loss?

In the first case, there's "coarse grained" information loss --
it's *hard* to recreate the state of the star by looking at the
correlations among the photons that come out. But it's not
impossible. In the second case, the conventional picture of
Hawking radiation implies that there is no correlation among
the photons, so the information is genuinely completely lost.

To answer the questions you must have a clear definition of what
information means and what a pure and mixed quantum states are.

Yes, but this is standard quantum mechanics. You can make up
your own definitions, but then you'll no longer be talking about
the same problem.

To start with the second, my interpretation of a pure quantum state
is that an object as such is completely everywhere physical
and chemical identical. They have no structure.
The four important parmeters a Radius, Volume, Mass and density.
In a pure quantum state object the density is everywhere the same.

This is not what the term means.

My interpretation of a mixed state is that it has a structure.
For example in the Sun and in planets when you "travel" towards
the center the density changes.

This is also not what the term means. There's a nice explanation
in the Wikipedia page under "Density matrix." If you want to
talk about the black hole information paradox, you need to use
the correct definitions.

When the density and chemical composition inside a BH is everywhere
the same than the information content is zero compared to the encyclopedia
britanica. The text of a book contains knowledge and information.
Along that line when you burn a book it is information loss.

That's not what "information" means in this context. In the black
hole information loss problem, the term "information" has a very
specific, technical meaning -- it's described by the von Neumann
entropy of the density matrix.

[...]
When the black hole has completely evaporated,

The issue is here how do we know that BH physical can evaporate and
change into a gaseous (visible?) state.

"Evaporation" here has nothing to do with "gaseous" -- it just means
that the mass of black hole is converted completely to Hawking
radiation.

How do we know this happens? By doing a computation in quantum
field theory to predict the evolution of a black hole. Now, the
answer to the paradox may be that we're doing the computation
wrong, but that's not a real answer unless you can say exactly
*where* the computation is going bad.

The problem only
appears quantum mechanically, when you allow black holes
to evaporate thermally via Hawking radiation.

The problem is much more a physical, chemical problem.

No, it's not. You are free to invent a different problem, but
that's not the one that's called the black hole information
paradox.

Steve Carlip