Re: Black hole information loss.

[Lubos Motl <motl@feynman.harvard.edu>]

On Mon, 1 Sep 2003, Starblade Darksquall wrote:

> Why is there an information loss in black holes?

First of all, Hawking *thought* - and he had good reasons to be described
below - that there was an information loss in black holes. I think it is
fair to say that according to the current mainstream physics community,
there is no information loss, not even in the black holes. However one
must admit that there are some confusing details that must be clarified
quantitatively before one can argue that all the puzzles about the
information loss have been solved.

So first of all, why should we think that there might be an information
loss?

If someone falls inside the black hole, she will have no chance to
reappear outside, and after some finite time, she will be inevitably
killed near the singularity. The information about her hairstyle won't be
available to the observers outside because the observers outside will only
see a single black hole whose identity is fully determined by its mass;
charge; angular momentum. Due to the black hole no-hair theorems, black
holes - unlike Hillary Clinton - can't have any hairstyles to distinguish
themselves from one another.

This was not a problem in the 1960s. One could have always said that the
information about her hairstyle is stored inside the black hole, and it is
not lost. Such an answer allows us to save unitarity; the so-called
unitarity essentially implies that the evolution from time t_1 to time t_2
conserves the total probability, and this evolution is one-to-one. For
example, it can be reversed and the information about the system at time
t_2 (the wavefunction) can be used to calculate the state of the Universe
at time t_1.

However in the middle 1970s Hawking calculated a shocking fact - that the
black holes evaporate. According to his calculations, the radiation coming
from a black hole is always the same thermal radiation whose details don't
depend on the girl's (or woman's) hairstyle. After the black hole
evaporates, it seems that the state of the Universe is totally independent
of her hairstyle: the information seems to be lost. One can't evolve the
Universe backwards to calculate what she looked like before she fell in.

Of course, there are three possible answers:

1. The information is lost indeed. This answer was advocated by Hawking
(and others). Hawking plus Kip Thorne made a bet against John Preskill
(who preferred the answers 3,2 below). The winning side will get
information itself: any encyclopedia that the winner chooses.

2. The information is not lost because the black hole does not disappear
completely; there is a "remnant", a small Planck-sized seed that keeps on
storing the information. This answer was popular for some time - e.g. my
advisor used to work on it - but recently it has become very awkward.

3. The information is not lost although the black hole evaporates
completely. This would mean that the only place where the information is
stored is the radiation. Although Hawking showed that it must essentially
look thermal, it does not have to be strictly thermal (a mixed ensemble,
described by a density matrix). It can be a particular (pure) microstate
representing the thermal ensemble (i.e. with the same macroscopic
properties), and the detailed correlations between these particles of
radiation carry the information about her hairstyle.

Although Andy Strominger and others would be partially sceptical about the
following sentences, I think that the developments in string theory in the
1990s have showed that the third option is the most likely one and even
Stephen Hawking, the advocate of the first option, admitted that. We have
found realizations of black holes where the entropy can be obtained
correctly from a counting of some microstates (of a configuration of
D-branes and strings). By looking at these microstates, one is allowed to
say that black holes are allowed to have some microscopic hairstyles after
all. Each microstate naturally leads to a different microstate of the
radiation. Moreover, AdS/CFT and Matrix Theory have provided us with some
explicitly unitary dual descriptions of reality that can still contain the
black holes. The information should not be lost.

The second option seems to contradict the holographic principle today;
there should exist no small regions of space that can contain huge
information.

The first option would seem to require some generalization of quantum
mechanics to replace the current canonical rules of QM. No such acceptable
generalization has been found, and because we have found ways how the
first option can be avoided - at least in some "mathematical" model that
has enough features to match the reality - we have reasons to take the
option one less seriously.

To claim the full victory (as described in the third option), one should
understand better:

1. what sort of description can be used by the infalling girl. Even though
she's going to die soon, is she allowed to describe the reality by laws of
physics? What is she gonna feel? Are the usual classical approximations to
laws of physics valid from her perspective? Are her observations
calculable from the Hawking radiation (she won't be able to tell anybody,
but anyway this question might make sense).

2. what is the amount of information contained in various pieces of the
radiation (quantitatively), and what sort of correlations between the
interior and the exterior we need to postulate to avoid xeroxing of the
information and other possible problems.

> If information is TRULY lost, except for charge, momentum, angular
> momentum, and energy (here I consider mass simply a form of energy)
> then what about Baryon and Lepton number?

It depends whether these numbers are exactly conserved. In the Standard
model, they are not precisely conserved, and one can find "instantons" and
other effects that allow us to violate these two conservation laws. It
means that one can create a black hole out of a neutron star which had a
huge baryon number, and this black hole can still evaporate to radiation
whose total baryon number is zero!

Of course, the alternative is that the lepton number, the baryon number,
or at least some combination of them (B-L, for example) is conserved, much
like the electric charge. In this case, this exactly conserved number
would have to be conserved even in the process of the black hole
evaporation, just like the electric charge. One must then explain why
there does not seem to be any force attracting this new type of charge, a
force analogous to the electrostatic force. At any rate, this force would
have to be very weak. Grand unified theories predict that at least the
combination of B,L described above is a generator of a U(1) subgroup of
the full gauge group, and therefore it must be conserved exactly.

> Furthermore, when things fall into black holes, there can't be perfect
> spherical symmetry, or any kind of perfect symmetry, BECAUSE if the
> black hole grew instantaneously, then this would violate relativity,

Good point. When the black hole is being created, it does not possess this
type of perfect symmetry. However the deviations from the perfectly
spherical shapes are dynamical and it turns out that they decrease
exponentially. The right mathematical framework to study these things are
the so-called "quasinormal modes" - some specific damped vibrations of the
background.

If you create some bubbles out of soap, they can eventually also become
spherical, can't they? Does it mean that you ruled out special relativity
by this experiment? Nope! :-) Of course, to reduce the deviations e-times
we need time that is not smaller than the time necessary for light to
traverse the black hole. This rule is satisfied, and special relativity is
OK.

Best wishes
Lubos
______________________________________________________________________________
E-mail: lumo@matfyz.cz   fax: +1-617/496-0110   Web: http://lumo.matfyz.cz/
	phone:          work: +1-617/496-8199  home: +1-617/868-4487
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      Superstring/M-theory is the language in which God wrote the world.