Paradox unexplained

On 4/3/2016 11:32 PM, Steven Carlip wrote:
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.

This is not quite clear if we cannot provide the solution
of the GR equations that show the formation (so indeed we
now can only say that we "believe" it). In particular, the
often shown Kruskal-Szekeres diagram like this one he
http://i.stack.imgur.com/U2EFS.gif
is certainly *not* the correct description of formation,
temporary existence and final complete evaporation!

What it may describe correctly is an eternally existing
black hole evaporating at the same rate as accreting new
mass (in homogeneous form, GW150914 is not a good example!)
Any mass in Region II (positive V axis) would never come out
and would not contribute to any paradox in this case. The
mass falling in would linger very long (in Schwarzschild
time) above the horizon and would obviously have ample time
to imprint its information on the Hawking radiation being
emitted there. In fact the in-falling information is just
bouncing of the horizon for this "eternal equilibrium".

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

This again is not so clear, as the Polchinsky-paper
http://arxiv.org/abs/1207.3123
states immediately in the abstract: we want it to be a pure
state! You are now claiming something that is not granted.

When the black hole
has completely evaporated, the net result will be the conversion
of a pure state to a mixed state.

For that, we clearly cannot use the static Schwarzschild
solution, and just using Kruskal-Szekeres coordinates won't
help since they still describe the same solution. Is there
any closed form solution for the "transient black hole"?

In any case I cannot quickly find it (so I can't even rule
out it might fit in the margin of this post..) But we can
look at Rindler coordinates for a uniformly accelerating
frame. The Unruh effect corresponds to Hawking radiation
and the Rindler horizon is the correct event horizon for
the accelerating observer. Now, for the non-eternal case,
we only have to make the observer reduce its acceleration,
corresponding to the black hole losing its mass. For the
observer, the Rindler horizon fades away as acceleration
is reduced (of course we get perturbed Rindler coordinates
by the "variation of constant" method).

So whatever matter was forever behind the horizon in the
eternal case, will simply come into view again with non-
eternal acceleration. This is not yet the correct solution
for the non-eternal black hole, but it suggests that the
paradox will be resolved just by allowing the black hole
mass to decrease, which the correct solution must do. In
any case, the event horizon cannot have the simple light-
like infinite wedge shape as it has for the eternal case.

...
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.

Yes, this part we all want to keep. (It might even be true!)

...
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.

That's not clear. if in-falling information just bounces back
at the horizon then that's local (as could happen in the
eternal equilibrium hole). And if information in region II
comes back into view by some curved shape of the non-eternal
horizon, then also nothing non-local is needed..

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

And claiming that Hawking radiation is a pure state, statement
i) in the above Polchinsky paper, does not avoid the paradox
either. I would really like to see a diagram/coordinate system
describing the non-eternal black hole for a better judgement!

--
Jos

There are a couple of things to keep in mind when discussing
this problem. First, in classical general relativity the
horizon is empty space -- there's nothing material there.
Second, for a large black hole, the curvature at the horizon
is very small. That means that, by the equivalence principle,
a freely falling (classical) observer will notice nothing
special happening as she crosses the horizon. The consistent
problem with many proposed "solutions" to the information
loss paradox is that they require drastic changes in the
physics in these empty, low curvature regions that are, at
least classically, locally indistinguishable from anywhere
else.

On 4/15/16 8:24 AM, Jos Bergervoet wrote:
On 4/3/2016 11:32 PM, Steven Carlip wrote:
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.

This is not quite clear if we cannot provide the solution
of the GR equations that show the formation (so indeed we
now can only say that we "believe" it).

Well, we can certainly write a classical solution in which
matter collapses to form a black hole. We can also make
this "semiclassical" -- that is, we can write down a quantum
state describing, say, a thin shell of radiation and use
the expectation value of its stress-energy tensor as a source.

Now, it *could* be that if we could somehow carry out this
same analysis in a completely quantum mechanical setting, the
results might be completely different. There are proposals
along this line, such as the "fuzzball" proposal of Mathur
et al. But if that's the answer, you have to explain why
the semiclassical approximation breaks down so drastically
in a region in which space is empty and curvatures can be
arbitrarily small -- that is, why the correspondence principle
of quantum mechanics fails in a place where there's no obvious
reason it should fail.

[...]

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

This again is not so clear, as the Polchinsky-paper
http://arxiv.org/abs/1207.3123
states immediately in the abstract: we want it to be a pure
state! You are now claiming something that is not granted.

You can *calculate* Hawking radiation, using what are now
standard methods of quantum field theory in a curved background.
The result is definitely not a pure state.

Again, it could be that this calculation is badly wrong. But,
again, the problem is to explain *why* it's wrong.

Note that it's not enough to simply have "a pure state" --
for the process to be unitary, one must have a *different* pure
state for each possible initial state of collapsing matter.
This almost certainly means that "late" Hawking radiation,
emitted near the end of evaporation, must be correlated with
much "earlier" Hawking radiation. But late Hawking quanta
are never in causal contact with early quanta. So this would
seem to require some highly nonlocal interactions. This would
mean a breakdown of the effective field theory description,
again in a place where curvatures are small and there's no
evident reason for the description to break down.

When the black hole
has completely evaporated, the net result will be the conversion
of a pure state to a mixed state.

For that, we clearly cannot use the static Schwarzschild
solution, and just using Kruskal-Szekeres coordinates won't
help since they still describe the same solution. Is there
any closed form solution for the "transient black hole"?

There are many proposals. We have no idea which, if any, of them
is correct.

In any case I cannot quickly find it (so I can't even rule
out it might fit in the margin of this post..) But we can
look at Rindler coordinates for a uniformly accelerating
frame. The Unruh effect corresponds to Hawking radiation
and the Rindler horizon is the correct event horizon for
the accelerating observer. Now, for the non-eternal case,
we only have to make the observer reduce its acceleration,
corresponding to the black hole losing its mass. For the
observer, the Rindler horizon fades away as acceleration
is reduced (of course we get perturbed Rindler coordinates
by the "variation of constant" method).

So whatever matter was forever behind the horizon in the
eternal case, will simply come into view again with non-
eternal acceleration. This is not yet the correct solution
for the non-eternal black hole, but it suggests that the
paradox will be resolved just by allowing the black hole
mass to decrease, which the correct solution must do.

Many people have tried this. It's very hard (so far, not
possible) to get it to work. In simple models one can
calculate quantitatively exactly what sorts of interactions
in the late stages of evaporation are needed to "purify"
the earlier Hawking radiation. (Eugenio Bianchi has some
nice work on this.) The answer seems to be that either
normal Hawking evaporation has to change drastically while
the black hole is still very large -- again, when there is
no apparent reason to expect the semiclassical description
to fail -- or else one needs to end with a very long-lived,
extremely high entropy "remnant."

[...]
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.

Yes, this part we all want to keep. (It might even be true!)

Or might not -- this is as much of a possible loophole as
anything else.

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.

That's not clear. if in-falling information just bounces back
at the horizon then that's local (as could happen in the
eternal equilibrium hole).

That makes no sense. There's nothing *at* the horizon. It's
just empty space. It's true that "new" matter falling in can
interact with Hawking radiation coming out -- this is something
't Hooft has been working on lately -- but I don't see how it's
relevant to the setting in which the paradox is posed, which is
a black hole forming from collapse of a pure state and then
evaporating.

And if information in region II
comes back into view by some curved shape of the non-eternal
horizon, then also nothing non-local is needed..

Again, the devil is in the details. No one has managed to make
a model in which this works without drastically changing the
physics in low curvature, nearly classical regions where there
seems to be no reason for it to change. That is, either the
information in region II has to reappear very early on, when
the black hole is still very large and quantum effects should
be negligible; or else it has to stay "in view" for an extremely
long time after the black hole has gotten very small, basically
stretching out the black hole lifetime to nearly infinity and
creating all sorts of problems associated with ultra-high
entropy "remnants."

It's easy to identify assumptions and say, "Maybe this one is
wrong" or "maybe that one is wrong." It's a whole lot harder
to identify a plausible reason that any of the assumptions is
wrong, and harder yet to actually show that that solves the
problem.

Steve Carlip

Op vrijdag 8 april 2016 10:01:20 UTC+2 schreef Steven Carlip:
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.

The whole question becomes: what is a pure quantum state versus
a non-pure (mixed?) quantum state.
Does it physical make sense to talk about a pure quantum state
except under laboratory conditions?

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. etc

A black hole is different. The first photon of Hawking
radiation etc

IMO (here I have to be very carefull) the concept of correlation
is very difficult, because you have to define what you mean
in this specific context and how it is measured.

IMO the issue is much the type of particles or energy range of
photons that can be emitted from any object.
This diversity is a function of the processes that happen inside
an object.
How larger this diversity how more information is available.
How smaller this diversity it is the opposite.

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.

I agree with the conclusion but not with your reasoning.

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.
I agree for laboratory conditions.
The concepts are very tricky in reality, related to actual objects
in space.

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.

I fully agree with you.
The practical problem is what is the density matrix of a BH?
of a star, a sun, a planet

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 real answer should be to make a prediction about the evolution
of an object (BH) which we should be able to verify
The problem is that that is very difficult for a BH.
For example it is impossible(?) to demonstrate that a BH has
evolved from something into "nothing" i.e. Hawking radiation
In practice this means that it is very difficult to claim that
the computation is right or wrong.

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.

The evolution of a BH is a physical issue.
I do not see in principle any problem that a BH completely
evaporates. The problem starts, when it is possible to verify
such a process (sequence of events) that this should not be in
conflict with other laws.

Nicolaas Vroom

Op zaterdag 16 april 2016 08:38:51 UTC+2 schreef Steven Carlip:
First, in classical general relativity the
horizon is empty space -- there's nothing material there.
Second, for a large black hole, the curvature at the horizon
is very small.

Snip

You can *calculate* Hawking radiation, using what are now
standard methods of quantum field theory in a curved background.
The result is definitely not a pure state.

Again, it could be that this calculation is badly wrong. But,
again, the problem is to explain *why* it's wrong.

The first thing is to verify why your calculation is correct.
For example you have to very that the BH "emits" radiation.
and that the predicted energy range is correct.

That's not clear. if in-falling information just bounces back
at the horizon then that's local (as could happen in the
eternal equilibrium hole).

That makes no sense. There's nothing *at* the horizon. It's
just empty space. It's true that "new" matter falling in can
interact with Hawking radiation coming out -- this is something
't Hooft has been working on lately -- but I don't see how it's
relevant to the setting in which the paradox is posed, which is
a black hole forming from collapse of a pure state and then
evaporating.

Gerard 't Hooft at page 43/44 of this document:
http://www.staff.science.uu.nl/~hoof...cturenotes.pdf
discusses the same issue.
IMO the evolution of a BH is a very complex lengthy process.
When you consider the sketch of a BH in:
https://astronomynow.com/2016/03/11/...ve-black-hole/
the center is completely black i.e. empty.
The question is if that is true. I doubt that.
One question is: if there is empty space around a BH.
At page 29 G'tH writes:
" Thus, as soon as matter falls in, the marginally trapped surface
is replaced by a larger one. We can therefore conclude that
the area of the horizon increases when matter falls in."
Which implies that the region is not empty.
At page 42/43 G'tH writes:
"According to Hawking's derivation of the radiation process,
any black hole, regardless its past, ends up as a thermodynamically
mixed state. Would this also hold for a black hole that started
out as a collapsing star in a quantum mechanically pure state?
Can pure states evolve into mixed states? Not according to conventional
quantum mechanics."
Immediate next he writes:
"From a physical point of view, the distinction between pure states
and mixed states for macroscopic objects is pointless.
Black holes should be regarded as being macroscopic."
I agree with this last sentence. In a sense it removes the problem
what pure and mixed states are.

That is why I wrote in a previous posting:
The problem is much more a physical, chemical problem.
At the same time it is also an information problem in the sense that
we cannot directly observe a BH. That means it is extremely difficult
to observe that the life cycle time of a BH is finite.
It is a murder without a body. For a star this is much simpler.

Nicolaas Vroom

On 4/16/2016 8:38 AM, Steven Carlip wrote:
There are a couple of things to keep in mind when discussing
this problem. First, in classical general relativity the
horizon is empty space -- there's nothing material there.
Second, for a large black hole, the curvature at the horizon
is very small. That means that, by the equivalence principle,
a freely falling (classical) observer will notice nothing
special happening as she crosses the horizon.

This of course makes it likely that the whole firewall idea
was meant as a provocation. (The intended message may have
been "Compared to the other alternatives this is still the
most likely one, so imagine how bad things are!")

The consistent
problem with many proposed "solutions" to the information
loss paradox is that they require drastic changes in the
physics in these empty, low curvature regions that are, at
least classically, locally indistinguishable from anywhere
else.

But some of those solutions might perhaps still work if the
"firewall" exists not exactly at the Schwarzschild radius
(since indeed there is nothing special there.) The
supertranslations, for instance, are probably everywhere in
space. (But that was a question I already asked in a separate
thread, since the topic here is about the precise definition
of the problem and the supertranslations are, or at least
taste like, some solution!)

....
Well, we can certainly write a classical solution in which
matter collapses to form a black hole. We can also make
this "semiclassical" -- that is, we can write down a quantum
state describing, say, a thin shell of radiation and use
the expectation value of its stress-energy tensor as a source.

You then start with the Vaidya model, I presume (as the Hawking-
Perry-Strominger paper in their first example). But we should
use the quantum-mechanical amplitude distribution of the fields
that are the source (as opposed to merely expectation values)
and thus arrive at a quantum-gravity description..

Now, it *could* be that if we could somehow carry out this
same analysis in a completely quantum mechanical setting, the
results might be completely different.

Something like the Mermin-Wagner 2D instability could perhaps
create a "firewall" after all! But I don't see how anything
special exactly on the Schwarzschild radius could be explained.
(Surely Polchinski must be joking, I still think.)

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

This again is not so clear, as the Polchinsky-paper
http://arxiv.org/abs/1207.3123
states immediately in the abstract: we want it to be a pure
state! You are now claiming something that is not granted.

You can *calculate* Hawking radiation, using what are now
standard methods of quantum field theory in a curved background.
The result is definitely not a pure state.

The basic definition of quantum field theory is a quantized
string which is in a pure state. (Weinberg vol. 1, Sect. 1.2,
"The birth of quantum field theory.") If you calculate merely
expectation values you don't calculate the actual time-
evolution of the actual quantum field.

..
This almost certainly means that "late" Hawking radiation,
emitted near the end of evaporation, must be correlated with
much "earlier" Hawking radiation.

Of course. And a deterministic time evolution guarantees that
all Hawking radiation in the end is exactly correlated to the
initial pure state, so there is no problem. (Unless we mess
with the unitarity, but why would we?) Our only problem is to
seek out the path of the information flow without non-local
jumps. It's a topological problem.

But late Hawking quanta
are never in causal contact with early quanta.

They certainly are, since QFT is causal. No quanta will
be created unless at the same event others are annihilated.
There is an unbroken chain of events. That is what the terms
in the Lagrangian do in a *local* quantum field theory. And
our standard model is a local QFT.

.. So this would
seem to require some highly nonlocal interactions. This would
mean a breakdown of the effective field theory description,

If the supertranslations effectively make a copy of passing
early quanta then the information is available. The no-cloning
theorem might not apply (like in a CNOT gate) if they just
entangle the information (with a pure gauge, or zero photon,
whatever) which *still* is deterministic, unitary time-evolution.

again in a place where curvatures are small and there's no
evident reason for the description to break down.

As the Hawking paper says, it's not yet an exact explanation
of how the information flow works (in any case the paper does
not attempt to depict the exact flow) but it opens some new
possibilities.

....
For that, we clearly cannot use the static Schwarzschild
solution, and just using Kruskal-Szekeres coordinates won't
help since they still describe the same solution. Is there
any closed form solution for the "transient black hole"?

There are many proposals. We have no idea which, if any,
of them is correct.

The Penrose diagram of the causal structure of the transient
black hole, as I understand it, is like this:
http://i.stack.imgur.com/Qtjrx.png
But in Hawking-Perry-Strominger Fig. 2 they have another which
looks more weird. Whereas their Fig. 1 (for the Vaidya model)
seems normal. I also have nothing against there time split and
"turn-on" of evaporation. What I don't understand in Fig. 2:

1)Why is the singularity not shown? It exists in a seperate
region of the manifold in http://i.stack.imgur.com/Qtjrx.png
but Hawking et al. seem to ignore its presence.

2) Why are there curved corners in the inner square? If that's
the horizon, it should be light-like and keep its diagonal
direction until its 2-sphere size vanishes (but then the
evaporation would be finished, which is not what the drawing
suggests).

...
That's not clear. if in-falling information just bounces back
at the horizon then that's local (as could happen in the
eternal equilibrium hole).

That makes no sense. There's nothing *at* the horizon.

OK, there can't be a firewall or anything special there, so
if we assume that matter falling in will be locked in a remnant
but information about it remains outside, it's solved.

So what was wrong with just accepting a remnant disjunct from our
universe? You still can have Hawking radiation. You still can
have the infalling matter encoding pure-state Hawking radiation.
It's all about keeping some information outside.

What Fig. 2 in the paper seems to suggest that *not only* the
information paradox is solved, but also the remnant is non-
existent! I feel like I could (given some time) understand the
former, but not the latter. What am I missing? (Yes, lots of
things, probably. :-) )

--
Jos

In article ,
Nicolaas Vroom writes:

You can *calculate* Hawking radiation, using what are now
standard methods of quantum field theory in a curved background.
The result is definitely not a pure state.

Again, it could be that this calculation is badly wrong. But,
again, the problem is to explain *why* it's wrong.

The first thing is to verify why your calculation is correct.
For example you have to very that the BH "emits" radiation.
and that the predicted energy range is correct.

If the calculation is correct, then the radiation is essentially
undetectable for all but the smallest black holes. So, while one could
verify it in principle, in practice one cannot verify it directly.

the center is completely black i.e. empty.
The question is if that is true. I doubt that.

Apply your own standards. You don't even have a calculation. At least
provide something better than "I doubt that" to support your claim.

One question is: if there is empty space around a BH.
At page 29 G'tH writes:
" Thus, as soon as matter falls in, the marginally trapped surface
is replaced by a larger one. We can therefore conclude that
the area of the horizon increases when matter falls in."
Which implies that the region is not empty.

Not necessarily. At least classically, it reaches the singularity in a
finite time, so the volume just beyond the horizon is empty except just
after something has fallen in.