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Old April 3rd 16, 10:32 PM posted to sci.astro.research
Steven Carlip
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Posts: 9
Default Paradox unexplained

On 4/1/16 4:47 PM, Jos Bergervoet wrote:
For the black hole information paradox I would expect
two seemingly conflicting results (as is necessary for
a paradox by definition,) e.g. like:

1) We know that information is lost because [...]


We believe that matter in a pure quantum state can collapse
to form a black hole. Such a black hole will then evaporate
by Hawking radiation, which is thermal. When the black hole
has completely evaporated, the net result will be the conversion
of a pure state to a mixed state. This is what is meant by
"information loss" -- quantum mechanically, a pure state contains
the maximum information about a system, while a thermal state
contains the minimum amount of information.

2) But also that it is not lost because [...]


Quantum mechanics is unitary. This means that the "fine-grained"
information in a quantum state is never lost; pure states evolve
to pure states. (Think of this as a quantum version of time
reversal invariance -- if you are given a final state, you can
in principle evolve it back to the initial state.)

There are some obvious places to look for loopholes. I suspect
that at least the obvious ones have all been analyzed to death,
and all have unpleasant consequences. For instance, Hawking
radiation might not really be thermal; but to get back enough
correlations seems to require some very nonlocal interactions.

[...]
What I mean is: by using Kruskal-Szekeres coordinates
we can follow any molecule, or larger object, that
enters the black hole, and there is no clear indication
that it ever loses information at all! There might be
tidal forces tearing it apart, but that need not in
general destroy information and also that need not
happen at the event horizon (in fact the Schwarzschild
radius has no special local properties at all, as the
K-S coordinates prove). Finally, singularities may be
present somewhere inside, but we don't know the physics
there, so we cannot claim anything about what happens
to information at those sites.


That's absolutely correct classically. The problem only
appears quantum mechanically, when you allow black holes
to evaporate thermally via Hawking radiation.

Steve Carlip