Lots of interesting things here. It does seem Rowan and Harold were discussing *classical* mechanics. (Can there be theoretical newtonian black holes? Actual ones?) Kind of ironic that using a black hole one could do all kinds of Fields medal-worthy research but be unable to report back about it. --Dan Mike wrote: << On Sat, Jul 25, 2009 at 10:21 PM, <mcintosh@servidor.unam.mx> wrote:
Quoting Rowan Hamilton <rowanham@gmail.com>:
Classical mechanics is *not* invariant under time reversal, as others have pointed out, since this violates the Second Law of Thermodynamics.
But that is not true, at least for a time independent or symmetric Hamiltonian. The Second Law is a statistical, or even empirical law, and is not part of Classical Mechanics; look at Poincare's recurrence theorem, for example.
From the perspective of an outside observer, the infalling matter never gets into the black hole. Time-reversing that gives a picture in which there's matter just outside the Schwarzschild radius that moves away from the star; that certainly happens all the time, so there's no contradiction with the second law. It's possible, though very difficult, to arrange things to end up in a low entropy state--for instance, Honda's Rube-Goldberg commercial used no computer graphics and required 606 takes.
http://video.google.com/videoplay?docid=-4187430023476942057 For an observer falling into the star, the light outside gets more and more blue-shifted, because from his perspective time outside is passing more quickly. Crossing over the Schwarzschild radius, the light is infinitely blue shifted and infinite time passes. (So if you want to solve the halting problem, leave your computer in orbit around a black hole and jump in! It will do infinitely many calculations in a finite time from your perspective.)
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele