Re: general relativity website
- From: Gerry Quinn <gerryq@xxxxxxxxx>
- Date: Thu, 3 Apr 2008 01:11:39 +0000 (UTC)
In article <7Vr5YpGluA5HFwpt@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
NotI@xxxxxxxxxxxxxxxxxxxxxxxxxxxx says...
Thus spake Gerry Quinn <gerryq@xxxxxxxxx>
In article <62kohfF23emliU1@xxxxxxxxxxxxxxxxxx>,
jonathan@xxxxxxxxxxxxxxxxxx says...
The word "Apparently" is simply wrong. The observer *does* fall
through the Schwarzschild radius into a region from which she can
no longer communicate with the external observer. There's no
"apparently" about it!
I tried to post before on this subject, but it seems my thoughts on the
matter were 'over-speculative'. Unfortunately I have been unable to
figure out exactly the point at which this over-speculation begins, so I
hope the readers of sci.physics.research will be willing to point out
any errors I am making in the following argument:
Looking at what you wrote, I am not sure that it is not Steven Hawking
who was not exploring an overspeculative argument!
He's assuming that quantum theory is correct. I'd have thought that
comes within the realms of reasonable speculation.
My argument simply adds an infalling observer to his gedanken, and
considers the implications for what that observer can observe.
As I understand it, Stephen Hawking has recently been considering the
evolution of a system in which a black hole - as nearly as we can
determine - forms, perhaps absorbs an observer (although Hawking does
not mention this), and subsequently evaporates. If quantum theory is
correct, the final state of the system encodes somehow the initial state
and subsequent history of all the matter in the system, although the
information might be impractical to decode. (An analogy sometimes made
is the smoke from a burned book, which in principle encodes the text of
the book, but does not differ in any obvious way from the the smoke of a
book with different text.)
Hawking analyses the evolution of the wave function of such a system,
summing over the histories on all possible geometric backgrounds, and
concludes - if I understand matters correctly - that the contribution to
the final state of the wave function from topologically non-trivial
geometries is zero. That is to say, the final state of the wave
function is equal to the sum over the histories in which a classical
black hole did not actually form.
Now this final state contains the encoded history of the infalling
observer, albeit in hard-to-read form. The history of the infalling
observer, whatever it is, must therefore be a history compatible with an
existence that throughout took place in a spacetime of trivial topology.
I conclude, therefore, that if Hawking is correct, whatever happens to
the infalling observer must differ from the canonical description given
in typical literature about general relativity, i.e, the
"spaghettification" and eventual arrival near a mysterious central
singularity at r=0, where it is conceded by almost almost all theorists
that general relativity must break down. Because the part of such a
journey below the Schwarzschild radius r=2m takes place in a
topologically non-trivial spacetime. Correct?
It is not clear to me that this treatment, if it is Hawking's, is very
useful. Even if we correctly track the wave function, in the collapse
which takes place in measurement, the wave function, and the detailed
information in it is lost.
The only difference is that Hawking's treatment doesn't include an
observer who falls into the black hole.
I think you are missing the point here. Hawking considers the system as
something like what I have elsewhere called a 'Simplified Schrodinger's
Cat' experiment - i.e. a portion of the universe is locked away for a
time in an impenetrable box, and then the box is opened. We can think
of the wave function of the contents of the box as evolving unitarily
during the time when the box is closed. Then when the box is opened we
collapse this wave function by a measurement or series of measurements.
In the case of large complex interacting systems such as those we are
discussing, the collapse will generate a typical result that appears to
have not only a current configuration, but a classical history of which
traces will be evident. (For example, there may be marks on the wall of
the cat box indicating that the cat scratched it at some point.)
Hawking's box contains an assembly of matter sufficiently large and
dense that it should collapse into a black hole, and he doesn't open the
box until after the time the black hole would be expected to have
evaporated. He argues that when the box is opened, the wave function
will be the same as it would be if the black hole never actually formed
(because it contains no contributions from histories over non-
topologically trivial backgrounds).
If so... then after we collapse the wave function, and decipher if
possible the history of the infalling observer, how can this history
include a portion that takes place inside a black hole?
You could argue that we cannot in practice decipher the observer's
history from the mostly low-temperature Hawking radiation that will be
all that's left in the box. But the argument about what that history -
if it could be deciphered - can or cannot include, still seems sound to
me.
Abd finally, since Hawking has not been shown to be incorrect, and
nobody has provided any better solution to the information loss problem,
then
it would be rash to assert that the canonical description of what
happens the infalling observer is true, especially in a site intended
for the education of the public - especially when there are so many old
sites that assert this.
Not on account of Hawking's argument, I agree that it is rash to assert
too strongly what happens in the environs of a black hole in the absence
of a true unification between quantum theory and general relativity, and
have sought to avoid doing so in the brief remarks given on the website.
That concludes my argument. If there's an error in it, I'd love to know
where.
Note that the r=0 singularity is not involved
here, and (for a sufficiently massive black hole) all happens in
*weak* gravitational fields.
The above seems to assume that a breakdown of general relativity must
necessarily be associated with large local gravitational stresses.
However I see no reason why this must be so. Can someone point it out?
I agree. I think that general relativity should break down in a vicinity
of the singularity, not only at the singularity. I have an argument
using quantum theory that the radius of the vicinity depends on the mass
of the hole, not on the strength of the classical field which would be
calculated at that radius. My argument suggests that the point at which
classical concepts of space-time break down is actually at the
Schwarzschild radius, notwithstanding the possibility of extending the
mathematical description of a classical manifold beyond that point.
Many arguments, it seems, lead to that same point. I have others also.
- Gerry Quinn
.
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