On Sun, May 27, 2012 at 1:55 PM, Warren Smith <warren.wds@gmail.com> wrote:
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?"
That's exactly the subject of the bet. Hawking's resolution was to say this: "So in the end, everyone was right, in a way. Information is lost in topologically nontrivial metrics, like the eternal black hole. On the other hand, information is preserved in topologically trivial metrics. The confusion and paradox arose because people thought classically, in terms of a single topology for spacetime. It was either R^4, or a black hole. But the Feynman sum over histories allows it to be both at once. One can not tell which topology contributed the observation, any more than one can tell which slit the electron went through, in the two slits experiment. All that observation at infinity can determine is that there is a unitary mapping from initial states to final, and that information is not lost." So whether there was a black hole or not, the information about Joe does not (according to Hawking) get lost in the black hole, but is recoverable from all the Hawking radiation that eventually leads to the evaporation of the black hole. John Baez wrote this in his summary of Hawking's presentation [my notes in brackets]: ====== He's studying the process of creating a black hole and letting it evaporate away. He's imagining studying this in the usual style of particle physics, as a "scattering experiment", where we throw in a bunch of particles and see what comes out. Here we throw in a bunch of particles [Joe], let them form a black hole, let the black hole evaporate away, and [Mary] examine[s] the particles (typically photons for the most part) that shoot out. The rules of the game in a "scattering experiment" are that we can only talk about what's going on "at infinity", meaning very far from where the black hole forms - or more precisely, where it may or may not form! The advantage of this is that physics at infinity can be described without the full machinery of quantum gravity: we don't have to worry about quantum fluctuations of the geometry of spacetime messing up our ability to say where things are. The disadvantage is that we can't actually say for sure whether or not a black hole formed. At least this seems like a "disadvantage" at first - but a better term for it might be a "subtlety", since it's crucial for resolving the puzzle: [Hawking:] Black hole formation and evaporation can be thought of as a scattering process. One sends in particles and radiation from infinity, and measures what comes back out to infinity. All measurements are made at infinity, where fields are weak, and one never probes the strong field region in the middle. So one can't be sure a black hole forms, no matter how certain it might be in classical theory. I shall show that this possibility allows information to be preserved and to be returned to infinity. [snip some stuff on Euclidean path integrals...] He says that if you just do the integral over geometries near the classical solution where there's no black hole, you'll find - unsurprisingly - that no information is lost as time passes. He also says that if you do the integral over geometries near the classical solution where there is a black hole, you'll find - surprisingly - that the answer is zero for a lot of questions you can measure the answers to far from the black hole. In physics jargon, this is because a bunch of "correlation functions decay exponentially". So, when you add up both answers to see if information is lost in the real problem, where you can't be sure if there's a black hole or not, you get the same answer as if there were no black hole! ====== -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com