I read about Hawking and Leonard Susskind and their debates about whether information is destroyed or not if it falls into a black hole. It was resolved in favor of information always being conserved, preserved, whatever (i.e. not destroyed).
I see how this could be consistent with determinism. However, how is this in keeping with quantum physics, when there is so much randomness. It seems that at any moment, all matter, energy, even every atom in our bodies, is indeterminate and "scrambled" somewhat. Even if you could pinpoint or describe every atom and its position perfectly in your body at one moment, by the next moment there is uncertainty. So how is this compatible with conservation of information?