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Staticman
2011-Feb-25, 08:25 PM
There is something I don't quite understand about black holes. In theory, an external observer cannot ever see in finite time how an object traverses an event horizon.
But this seems to be a self-defeating condition. If I were approaching an event horizon (suppose a very massive black hole so that we can neglect tidal forces at the neighbourhood of the event horizon) I could certainly act as an external observer (of myself) as long as I don't reach the event horizon, but then I can never reach it in finite time as long as I'm observing myself reaching it. I mean, a conscious living organism can't help being an external observer of himself.That is, the proper and coordinate time referred to itself of an observer must coincide, since in a way the proper time is nothing but the coordinate time of the measuring clock location. How is this dealt with in the theory?

korjik
2011-Feb-25, 08:32 PM
No, the observer is by definition internal to himself. Without tidal effects, you can assume the observer is in his own frame. With tidal effects, then the extreme points of the observer arent in the same frame, and things can get really messy.

The falling observer, looking back out and adjusting for redshift (well, blue actually), would see the outside universe go faster and faster until it was an infinitely fast blur. Other than that, he would have no way of knowing when he crossed the event horizon.

Staticman
2011-Feb-25, 08:48 PM
No, the observer is by definition internal to himself.

I don't know what this means. The observer can certainly observe himself and his environment.
The rest of your post doesn't address my question at all.

Strange
2011-Feb-25, 09:44 PM
the important thing is that the observer is external to the infaller"s frame of reference (not sure that is the right term in this context), not just external to the BH. In other words sufficiently far outside the BH. So, no you can't observe yourself and see yourself time dilated.

baric
2011-Feb-25, 10:41 PM
I could certainly act as an external observer (of myself) as long as I don't reach the event horizon, but then I can never reach it in finite time as long as I'm observing myself reaching it.

It seems like you making an analogous mistake in perception as with the paradox of Achilles and the Tortoise (http://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise).

In the Event Horizon scenario you described, an external observer is someone who is not moving towards the black hole and is therefore not affected by the relativistic effects created by that movement.

edit: ugh, should have read all of the responses first. What Strange said.

Staticman
2011-Feb-26, 12:29 AM
the important thing is that the observer is external to the infaller"s frame of reference (not sure that is the right term in this context), not just external to the BH. In other words sufficiently far outside the BH. So, no you can't observe yourself and see yourself time dilated.



In the Event Horizon scenario you described, an external observer is someone who is not moving towards the black hole and is therefore not affected by the relativistic effects created by that movement.

In this case the frame of reference, referred to the state of motion of the observer is not relevant, the theory of black holes says that the coordinate time until reaching the EH computed by the observer is infinite while the proper time measured locally is finite.
As long as you don't reach the Event horizon, you can always fly away from the black hole, so anyone can escape the BH as long as it doesn't pass the point of no return and any observer is sufficiently far outside of the BH, so this doesn't answer my question either.
I mean how distant from the observed situation must an observer be to be considered an external observer?

korjik
2011-Feb-26, 07:54 AM
I don't know what this means. The observer can certainly observe himself and his environment.
The rest of your post doesn't address my question at all.

Can you see your own eyeball? The faller is in his own frame, by definition. You cannot measure the dilation of the frame you are in.

With the setup you describe (no tidal effects) then nearby objects have a small difference in the gravity field, so have a very small dilation. So the area around the observer isnt much different from the observer. If you are near the event horizon in that case, you cant tell when you passed it from purely local effects. It is only when you see the rest of the universe speed up to infinity that you would see that you crossed the horizon.

The event horizon is not a physical object that you can run into, or that you can directly see. In empty space with no tidal effect, there would be no way to tell from local effects when you crossed the horizon.

Staticman
2011-Feb-26, 08:50 PM
Can you see your own eyeball? The faller is in his own frame, by definition. You cannot measure the dilation of the frame you are in.

With the setup you describe (no tidal effects) then nearby objects have a small difference in the gravity field, so have a very small dilation. So the area around the observer isnt much different from the observer. If you are near the event horizon in that case, you cant tell when you passed it from purely local effects. It is only when you see the rest of the universe speed up to infinity that you would see that you crossed the horizon.

The event horizon is not a physical object that you can run into, or that you can directly see. In empty space with no tidal effect, there would be no way to tell from local effects when you crossed the horizon.

Ok, but can you answer how far from the observed situation must an observer be to be considered an external observer?
On the othe hand, how can the external observer certify that the infaller has crossed the event horizon if the clock of the infaller(proper time) can't be accessed.

cjameshuff
2011-Feb-26, 10:27 PM
Ok, but can you answer how far from the observed situation must an observer be to be considered an external observer?

The question doesn't make sense. It's like asking how close one needs to stand next to someone else before you can consider them to be that person. The external observer is external because they aren't the infaller...they could pass arbitrarily close to each other as the infaller goes in.



On the othe hand, how can the external observer certify that the infaller has crossed the event horizon if the clock of the infaller(proper time) can't be accessed.

The question seems to assume the external observer can observe the infaller crossing the event horizon.

forrest noble
2011-Feb-26, 10:58 PM
Don't know if I'm hitting on your meaning quite right, but: Your perspective concerning what you would see as you approach the event horizon would not be the same as the perspective of an outside observer (or yourself) that could see you from afar.

Strange
2011-Feb-26, 11:13 PM
In the Event Horizon scenario you described, an external observer is someone who is not moving towards the black hole and is therefore not affected by the relativistic effects created by that movement.

Well, there are two things (different components of the same thing, really). The relative velocity of the infaller and the gravitational effects of the black hole. I think it is the latter which is at issue here. So it is not so much the fact that the observer must be stationary but that he is not affected by the gravity of the black hole. Therefore, ideally, he should be an infinite distance away. But as long as he is "sufficiently" far away (and not also in free fall towards the black hole) he will see the infaller slow, red-shift and disappear (but not actually cross the event horizon).

Strange
2011-Feb-26, 11:14 PM
On the othe hand, how can the external observer certify that the infaller has crossed the event horizon if the clock of the infaller(proper time) can't be accessed.

The external observer can calculate when the infaller will pass the event horizon (even if he cannot see it happen).

ETA: And if you want to just go by observation, then I guess the observer can assume the infaller has passed the event horizon (at some point in the past) when he is no longer visible.

Strange
2011-Feb-26, 11:21 PM
In this case the frame of reference, referred to the state of motion of the observer is not relevant

Indeed. That is why I said it wasn't the right term (it was late and I had just got off a plane!)


As long as you don't reach the Event horizon, you can always fly away from the black hole, so anyone can escape the BH as long as it doesn't pass the point of no return and any observer is sufficiently far outside of the BH, so this doesn't answer my question either.

I'm not sure I understand what you are saying there. Why do you think being able to fly away is relevant?

Staticman
2011-Feb-27, 11:13 AM
The question doesn't make sense. It's like asking how close one needs to stand next to someone else before you can consider them to be that person. The external observer is external because they aren't the infaller...they could pass arbitrarily close to each other as the infaller goes in.Well since you have answered it, it must make some sense after all. If the distance is arbitrary, imagine yourself approachin the event horizon feet on, you shouldn't ever be able to observe your feet traversing the horizon,right? and yet you claim you would fall in in a finite time. How would you explain this?



The question seems to assume the external observer can observe the infaller crossing the event horizon.No, it doesn't assume that at all.


The external observer can calculate when the infaller will pass the event horizon (even if he cannot see it happen).Yes, but based in an assumption, he can't check the infaller clock.


ETA: And if you want to just go by observation, then I guess the observer can assume the infaller has passed the event horizon (at some point in the past) when he is no longer visible.
Sure, we can assume anything we want, but I was asking for something a little more rigorous.

Jeff Root
2011-Feb-27, 12:51 PM
Staticman,

An "exterrnal observer" is an observer who is not close to the
thing being observed. I use the term "distant observer". I don't
know who used the term "external". That term seems unclear.
Maybe it is a translation from another language.

Distant observers cannot see anything cross the event horizon.
Everything which crosses the event horizon appears to distant
observers to fade out and redshift to invisibility. In principle, light
from a falling object crossing the event horizon might continue
to reach distant observers forever, but in reality the light would
redshift beyond detectibility very rapidly. One moment light from
the falling object, approaching the event horizon, would appear
to be redshifted only slightly, and a tenth of a second later it
would no longer be visible.

The closeness of an observer to the observed object depends
on the distance between them, the speed difference between
them, and the gravitational potential difference between them.
If the distance is small, the speed difference is small, and the
gravitational potential difference is small, then they can be
considered to be close together.

So, you ask, how big do these differences need to be?

The graph at the following link shows how big.

The graph shows how time dilation increases with increasing
relative speed. The graph for the effect of gravity would be
very similar. The thing to notice is how the time dilation is
very small at low speeds-- hardly increasing at all above the
base value of 1 even at 0.5 c, but gradually increases until
it is very large at speeds approaching the speed of light:

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Time_dilation.svg/1000px-Time_dilation.svg.png

The graph is from this page:

http://en.wikipedia.org/wiki/Time_dilation

The farther apart in speed and gravitational potential, the
larger the relative time dilation. But large time dilations
only occur when the difference in speed or gravity are very
large. At ordinary speeds and gravitational potential
differences, the time dialation can usually be ignored.
Only when using super-precise clocks, able to measure
very small time dilations (such as in GPS), do ordinary
differences in speed and gravitational potential have
an effect that matters to anybody.

If you were falling into a black hole a short distance behind
an object falling in ahead of you, it would not vanish as it
and you cross the event horizon. The farther behind it you
are, though, the greater the difference in gravitational
potential, so the more its light will redshift. Far enough
behind, and it will redshift to invisibility.

-- Jeff, in Minneapolis

Jeff Root
2011-Feb-27, 01:02 PM
If you are near the event horizon in that case, you cant tell when
you passed it from purely local effects. It is only when you see the
rest of the universe speed up to infinity that you would see that
you crossed the horizon.
An observer hovering at the event horizon would see the rest of
the Universe apparently "speed up" to infinite "speed", and light
from it infinitely blueshifted. An observer falling across the event
horizon would see the rest of the Universe apparently "slow down"
(I don't know by how much), and light from it redshifted.

It would be a practical impossibility to hover at the event horizon,
since any rocket propellant-- even light-- would simply fall away
from the rocket engine instead of pushing upward on it. It would
be possible to slow the speed of one's fall with a rocket, though.

-- Jeff, in Minneapolis

HarveyS
2011-Jul-14, 09:38 AM
Jeff,

This is an older thread, but ....

You've mentioned the apparent speeding up of the rest of the universe. Does length dilation play a role in this, similar to what occurs in SR? Do distances collapse for an observer who is IN a powerful gravitational field?

Thanks,
HarveyS

Andrew D
2011-Jul-14, 02:59 PM
from a previous discussion: (http://www.bautforum.com/showthread.php/114524-Yet-another-black-quot-hole-quot-question-emphasis-on-hole)


The free faller does not observe the universe racing ahead in time. To do this you'd have to stop falling so that the light could blue shift.