Re: Other ways to preserve information
I'm giving you a thumbs up, AustinTX. Not because I think you're right, but because I don't believe you should be penalised for showing some imagination. It would have been nice if your downvoters explained the flaw in your reasoning (something to do with future light cones, I'd guess) but they've decided to ridicule you instead.
Personally, I don't know enough about physics to know which theories about information loss in black holes make sense and which don't, but it still doesn't stop me thinking about it. I don't think that white holes can work (we've never seen them), but what about the idea of black holes being a source of dark energy/dark matter? I think you'd need a few things:
* for the event horizon (or internal structure close to it) not to be smooth, but to encode information about things that have fallen in
* for that state to be updated over the life of the black hole
* for there to be some correlation between the Hawking radiation that's emitted and the things that fell into the hole in the first place
I don't understand how gravity works, so I don't know if information could be preserved using it alone. It probably wouldn't work because various conservation laws would be broken.
So my thinking, which is probably just as invalid as yours, is along the lines of:
* information encoded near the event horizon acts like a diffraction grating
* information spread out holographically across a large expanse of normal space/time
* spacetime around event horizon probably has to have a fractal structure
* underlying field equations have to go from using complex numbers to quaternions
* non-commutativity of quaternions never becomes an issue for normal matter in normal space, but adds a "twist" near singularity
* virtual particles travelling through "q-space" show up as dark energy/dark matter
* "twists" between normal matter/energy and dark matter/energy only happen near singularities
My idea is that as paired particles are created near the event horizon, one of them travels through normal Euclidean space, while the other goes through this "q-space". To preserve various censorship principles, anything travelling through the q-space would have to teleport to a point so far away, in space and time, that it shouldn't be possible to correlate inputs to outputs without taking infinite time. Eventually, though, all virtual particles will meet up with their twins again. It's just that they have to take different routes, through q-space and/or dark energy matter forms in the interim.
With all we don't know about the Universe, from dark matter to inflation, maybe someone more clever than me could come up with the maths to unify everything in a quaternion basis...
(downvotes expected :)