If you're, like me, interested in physics, you'll remember that a month ago Hawking 'solved' the black hole information loss problem. An example
of the huge amount of news articles dedicated to this can be found at
PhysicsWeb.
The black hole information loss problem is a problem of the area were general relativity and quantum mechanics meet. When a black hole is formed in
classical general relativity all information of matter falling in is locked in the black hole. Black holes evaporate very slowly due to Hawking
radiation. This Hawking radiation doesn't carry any information about the matter that once fell in the black hole. The problem occurs when the black
hole eventually disappears. The information that was once in the black hole is lost. The problems of black hole information loss is not only if the
information is lost, but also is how the information gets out when there is no information loss.
I just read the transcript and summary of Hawking's talk on
John Baez' site. Although I
already thought the story of Hawking's solution was somewhat hyped, Hawking actually provides no real solution at all to the information loss
problem. He only shows, not even in a very convincing way, that no information is lost. This is also what most quantum gravity scientists already
thought and already showed with other techniques, according to John Baez:
A string theorist I know said that thanks to work relating anti-deSitter space and conformal field theory - the so-called "AdS-CFT"
hypothesis - string theorists had become convinced that no information is lost by black holes.
Baez is not baised against Hawking at all. But I'm going to summarize a bit what Hawking does using some quotes from Hawking and Baez and with some
of my own explanations.
Hawking looks at the problem by trowing some particles from infinitely far before the black hole in the black hole and looking how they end up
infinitely far behind the black hole. Using this approach we avoid the difficulties of quantum gravity, but it doesn't get us much closer to a
solution of the information loss problem as we'll see below. By far I actually mean far in 4-dimensional space, not spacetime, as John Baez explains
below:
Now, the way Hawking likes to calculate things in this sort of problem is using a "Euclidean path integral". Suffice it to say that we
replace the time variable "t" in all our calculations by "it", do a bunch of calculations, and then replace "it" by "T" again at the end. This
trick is called "Wick rotation". In the middle of this process, we hope all our formulas involving the geometry of 4d spacetime have magically
become formulas involving the geometry of 4d space. The answers to physical questions are then expressed as integrals over all geometries of 4d space
that satisfy some conditions depending on the problem we're studying.
The Euclidean path integral adds contributions from all possible topologies, all possible forms of space (think ball, donut, ball with singularity,
etc., but in 4 dimensions) together to reach a final answer. This problem, though, is scientists don't actually know how to do the complete Euclidean
path integral over all possible topologies.
Hawking solves this by trying to approximate the integral using only the topologies he thinks are relevant. These topologies are the topologies are
the one where there is no blackhole and the one where there is one. John Baez explains the problem very well:
We get one answer for each solution of the equations of general relativity that we deem relevant to the problem at hand. To finish the job, we
should add up all these partial answers to get the total answer. But in practice this last step is always too hard: there are too many topologies, and
too many classical solutions, to keep track of them all.
So what do we do? We just add up a few of the answers, cross our fingers, and hope for the best!
In the problem at hand here, Hawking focuses on two classical solutions, or more precisely two classes of them. One describes a spacetime with no
black hole, the other describes a spacetime with a black hole which lasts forever. Each one gives a contribution to the semiclassical approximation of
the integral over all geometries. To get answers to physical questions, he needs to sum over both. In principle he should sum over infinitely many
others, too, but nobody knows how, so he's probably hoping the crux of the problem can be understood by considering just these two.
The contributions of two topologies are as follows: where there is no black hole, no information is lost; where this is one, all information is lost.
Adding the two solutions together, we get 0 information remaining at the end (the information is lost) + all information remaining at the end (no
information is lost) = all information remaining at the end. The problem seems solved, but only after a lot of assumptions. I'm not willing to accept
all these assumptions.
But let's accept Hawking's technique. What does it show? No information seems to be lost when we approximate the solution of the problem. But does
Hawking provide a process for the information to get out of the black hole? I don't think so. All Hawking says about how the information gets out is
this:
The confusion and paradox arose because people thought classically, in terms of a single topology for spacetime. It was either R4, or a black
hole. But the Feynman sum over histories allows it to be both at once. One can not tell which topology contributed the observation, any more than one
can tell which slit the electron went through, in the two slits experiment. All that observation at infinity can determine is that there is a unitary
mapping from initial states to final, and that information is not lost.
My explanation of that: at infinity you don't know if a black hole was formed. That's why you have to add both solutions into the equation, the one
where there is a black hole and the one where there is no black hole. Adding them together means no information is lost. The information gets out
because both topologies can exist at the same time. It 'gets out' of the black hole through the 'no black hole solution'.
But what if you don't look at infinity, which is usually the case in the real world? You know for sure if there's a black hole or not. Hawking
doesn't provide a solution for the information loss problem in that case.
Hawking doesn't provide a real solution to the information loss problem and only says what other scientists have been saying all along. But he does
get all the attention. This is what I call
hype. I have more confidence that new quantum gravity theories will solve the black hole information
loss problem than Hawking's classical and semiclassical general relativity.
[edit: spelling]
[edit on 16-8-2004 by amantine]