From: Mike Stay <metaweta@gmail.com> http://en.wikipedia.org/wiki/Thorne-Hawking-Preskill_bet
--I fail to see the relevance. I ask "did Joe fall in, or not?"
From: Henry Baker <hbaker1@pipeline.com> Story 3: Scenario 1. I'm looking out at the universe from the Earth, and in every direction I see a red shift which is larger, the "further away" it is. I conclude that I am in an expanding universe.
Scenario 2. I'm looking out at the universe from the Earth, but at some very large distance from Earth, there is a gigantic black hole, which bends _all_ the light that I see, so that no matter in which direction from Earth I look, I'm actually seeing the same black hole, but from different directions. Furthermore, objects & radiation going into this black hole become red-shifted due to the enormous gravity of the black hole.
How do I tell these two scenarios apart? Does it even matter; perhaps they are equivalent?
I got this idea by considering what our universe looks like to Joe as he approaches the black hole; the black hole actually fills up _more_ than 50% of the sky, due to the bending of the light rays. Just before Joe falls in, the black hole fills up 99.9% of Joe's sky, and the universe that he's exiting looks like a very distant black hole to him.
--Interesting claims, but I doubt true. First, the "universe Joe is exiting" is blue shifted in his view not redshifted. Second, light rays from the black hole horizon surface cannot reach Joe (while outside hole) at all. What Joe sees is not immediately obvious to me, though I think somebody has computed a movie and there is known math on this. I think Joe's view will be very distorted like thru a funhouse mirror but he'll see the outside-the-hole universe in over 50% of his perceptual sky.
From: Robert Munafo <mrob27@gmail.com> Since I am totally unable to understand Hawking, I suppose I am qualified to give the obvious answer, and not feel too bad about being wrong (-:
--you don't need to understand Hawking, you just need to know the general claimed properties of Hawking radiation (I think).
Mary, while watching the black hole shrink, sees the red-shifted image of Joe disappear. This happens after a sufficient length of time that Joe's image has already been redshifted so far that the uncertainty principle (viewed as the energy-time relation deltaEdeltat > h) prevents Mary from distinguishing when Joe's red-shifted image became invisible.
--true. Joe gets exponentially red shifted in Mary's view, which soon overcomes even Mary's ability to wait 10^70 years. So Mary's "view" of Joe "never falling in" effectively gets blacked out, she can't see him with normal light. If however Joe were transmitting magic nonphoton information-particles which just carry info not energy, at lightspeed, then Mary would continually "see" Joe never falling in.
So the "paradox" created by quantum effects (i.e. Hawking evaporation) is also resolved by quantum effects.
--not really. I mean, Joe still never falls in, even though Mary has trouble seeing him. --A better objection is this: in Mary's view, Joe gets ultra-near the horizon without fall in. But as the black hole Hawking-shrinks, the horizon shrinks, ultimately to far smaller than an atomic nucleus, with Joe still incredibly close to (but outside) it. Hence Joe really is crushed, even in Mary's view where he never falls in. But even that does not really resolve the paradox. Here is why: Joe's component particles (neutrons, etc) stay outside, in Mary's view. Their characteristic counts (e.g. "lepton number") hence are preserved. But in Joe's view, those particles all fell in. The Hawking radiation then knows only about the mass and charge of the hole, and will NOT preserve lepton number, etc. So Joe still is preserved (Mary's view) versus not (Joe's view) for some weaker notion of "preserved." This still seems a contradiction.
On 5/27/12, Warren Smith <warren.wds@gmail.com> wrote:
Joe jumps into a Schwarzschild black hole. Mary stays behind and watches him fall.
The standard stories are then as follows: [...] 4. NOW, new addition to above stories. The black hole gradually is shrinking due to "Hawking radiation." It will vanish completely in about 10^70 years (let's say).
So Mary, who is very long-lived, will then say "the new state of the universe is: there is no black hole anymore, Joe never quite fell in, and so Joe is still with us. In fact, I'm going to go meet him now, since he's only 1 hour older by his personal clock."
But Joe will say "I fell in, I was crushed into a point, and my mass-energy was Hawking-radiated away. I'm gone."
How do you resolve this paradox?
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
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