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I'm interested in the picture of black hole complementarity where an observer (Bob) far away from the black hole watches another observer (Alice) fall in, and develops a very different picture of events. I want to stay within the framework of black hole complementarity, and limit this to Bob's reference frame. Mainly:

  1. Can Bob practically watch Alice die from her emitted photons?
  2. Alternatively, is time dilated so much in Alice's reference frame that Bob would have to wait until the end of the universe to watch this?

I think there are arguments against #2, and I might only have this confusion because of arguments I've read which were not fully informed, which I may now be repeating.

There's also the matter of cause of death for Bob to write on the coroner's report. It seems that conflicting accounts exist, although they ultimately go back to the firewall concept.

The asymmetric mass, from the point of view of the exterior observer, smears itself symmetrically on the surface when it gets close.

second source:

The AMPS proposal is that what Alice encounters at the horizon does not look like empty space at all — rather B and A are unentangled, which means that Alice sees many energetic particles. Monogamy of entanglement is rescued, but not poor Alice. She is incinerated by an intense wall of fire as she attempts to pass through the event horizon.

While these graphic accounts of Alice's death sound concrete, they're not necessarily inconsistent with point #2 above. If time dilates within certain asymptotic properties, then it could look somewhat like Zeno's paradox. There are ways this could prevent Alice from ever fully merging with the surface of the black hole. But could it prevent Bob from ever being able to confidently able to say that Alice died? Of course Bob has to recalibrate his video camera as it shifts ever-more toward the IR part of the spectrum, but does that video ever show Alice boiled to death or dismembered and smeared into the surface?

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I'll try to answer your questions, 1. Bob does in fact 'see' that Alice has died, however not directly. He sees her death through Hawking radiation. This can happen two ways, the first is that if Bib wants to see Alice at the event horizon he has to use some means of 'measuring' her whereabouts. He could do this by shining a flash light on her but, due to the strong gravitational force, the amount of energy it would take to light her would mean that Bob would inadvertently fry her. If Bob decides he will not light her up and fry her, but waits a while* he will see her as a stream of photons emitted from the black hole - from this he will infer that she has been fried in a firewall at the event horizon. 2. You are correct in stating that there is gravitational time dilation, * as I said before, Bob will have to wait a while to see Alice burn up; to be more precise Bob will have to wait until her clock appears to stop - an infinite amount of time.

As a last note, I think your confusion concerning the extracts above, is that what happens in extract 1, is when a person reaches dangerously close to the singularity - however this depends on the size of the black hole and could happen a long time after passing the event horizon (although Alice would be fried so wouldn't get past the event horizon.), or with a tiny black hole you would be stretched before the event horizon.

So it would depend on the size of the black hole as to whether Bob sees her stretched out or burnt up. Hope that helps :-)

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I've been reading book The Black Hole War, and it has cleared it up.

The characters in Susskind's version of this tale are Stephen (the physicist), and some evil galactic emperor (and his assistants). The book only says that his assistants detect the radiation which evidences Stephen's death. This might actually happen a long time after our hero crosses/hits the event horizon. So there is no apparent burning or visible dismemberment in any way.

At some other point in the book, after introducing the story, the author goes into the philosophy of how we can get different stories to contradict in black hole complementarity. He uses a very convincing argument which relies on the uncertainty principle.

The temperature of the horizon only gets hot when the in-falling object gets extremely close to the horizon (this is using a r=infinity perspective). So the horizon is frothing with quantum junk, but the layer is extremely small. Physically that's not very convincing (the stories could still contradict), but it is when combined with the uncertainty principle. In order to probe information extremely close to the horizon, you'll need to use a photon with a wavelength smaller than the distance between the object and the horizon. In the area where the quantum foam is relevant, this energy is too high to accurately return velocity information, and will burn the object on its own.

So it would seem that in this "movie" of an in-falling space ship, our only evidence for their demise is at least partially indirect. Now, the Hawking radiation might contain information about the spaceship... which would be very compelling information arguing for their demise. Whether the info was preserved or not was the topic of a very long-running scientific argument. Either way, no reputable theory has ever predicted that a macroscopic sequence of death could be reconstructed. This type of death would be as instant and painless as theoretically possible.

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