I didn't call what a distant observer sees an "illusion".
That is highly misleading. What the distant observer sees is
light from the falling object. Light from a falling object
naturally is not the same as the falling object.
Quote:
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Originally Posted by Astrowannabe
Because consider that we watch him for 1000 years getting ever
closer to the black hole. Then, he decides to turn around and
come back (or perhaps he was on a trajectory that only had him
orbit very close to the event horizon and then swing back). At
any rate, the astronaut may have only experienced 3 or 4 seconds,
but the rest of the universe has still aged 1000 years.
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Whoa! Whoa! Whoa! Nothing like that can happen.
Let's say we are talking about a supermassive black hole, with
a mass equal to millions of solar masses. That means it will be
comparable in size to the Solar System. Maybe out to the orbit
of Saturn, or Uranus? Somebody should come along with an actual
set of numbers. This large size makes things easier for us to
deal with. The gravitational well is spread out, which means it
strongly affects a large volume of space, and tidal forces at the
event horizon are vastly lower than in a stellar-mass black hole.
It would actually be possible for a spacecraft to cross the event
horizon without being immediately spaghettified.
You are orbiting several light-weeks away, out of danger. You
have the new, improved SuperDuper UltraMega HyperDiaperScope,
capable of seeing my spacecraft at that distance. *
I get as close as possible to the black hole without falling in,
just swinging around it and firing my engines furiously to keep
from actually being sucked in. (Black holes really suck if you
get close enough.) You see me whizz across the black background
at very nearly the speed of light. I and my spacecraft are
seriously squished in your view by the relative speed. Light
and signals from my spacecraft are highly redshifted.
I'm not sure what more I can accurately and usefully say about
that scenario, so let's switch to a slightly different one.
I fall straight into the black hole. You watch me fall in.
Again, light and signals from me are more and more redshifted as
I get closer and closer to the event horizon. We have calculated
the exact nanosecond (in my reference frame) that I will cross
your event horizon. (The location of the event horizon depends
on your distance from the black hole and your relative motion.)
The clock I am holding up for you shows my proper time. It will
be 12:00:00.00 at the instant I cross your event horizon. You
see it read 11:59:59.00 and it is obviously slowing. It is also
getting dim despite the powerful lights inside my spacecraft, as
the rate photons are reaching you decreases. A second later you
see my clock reading 11:59:59.90, but it is very dim and grainy,
and extremely redshifted. A second later you can barely make out
that my clock reads 11:59:59.98. A second after that, you see
only a handful of photons which were redshifted into the radio
portion of the spectrum. And a few photons a second after that.
That's it. You watch for five more days, and nothing. The last
second of light from me that you could detect lasted maybe four
seconds for you at most. The rest was redshifted so much that
it didn't contain enough information to determine whether it was
signal or just noise, even with the new, improved SuperDuper
UltraMega HyperDiaperScope. *
Quote:
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Originally Posted by Astrowannabe
If you see him falling into a black hole, and 1000 years later
you still see him falling into the black hole that's because he's
still falling into the blackhole. He hasn't crossed the event
horizon yet, in either your reference frame or his. So this
doesn't invalidate my question.
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For a supermassive black hole, one light-hour in radius, it
would take roughly one hour of my proper time for me to fall
from your event horizon to the singularity. I would be
spaghettified shortly before reaching the singularity.
For a stellar-mass black hole, two or three miles in diameter,
I would be spaghettified before you saw me reach the event
horizon, and it would take only microseconds of my proper time
after that for my atomized remains to reach the singularity.
You are going to see events-- and me-- stretched out some,
but within a second or two, the rate at which photons from me
reach you will have fallen so low that there will no longer be
any detectable signal. Only a finite number of photons leave
me in my last second before crossing your event horizon, and
more and more of those photons fall into the black hole rather
than escaping, so I disappear pretty quickly. And as I've
repeatedly said, those photons are redshifted, so they have
less energy when they reach you than when they left me. Lots
of reasons for me to vanish quickly.
And I'll repeat that all you are seeing is the light from me--
not me. I'm long gone by the time the light reaches you.
-- Jeff, in Minneapolis
* SuperDuper UltraMega HyperDiaper and SuperDuper UltraMega
HyperDiaperScope© Copyright 2006 by Jeff S. Root.
The SuperDuper UltraMega HyperDiaper is a full metal diaper.