> And this is the sense in which physicist talk about information, the description of the state space. If you throw something into a black hole the only things that remain visible are things like the mass, the charge or the (angular) momentum but you just lost all the details about the thing you threw into the black hole which is a problem for our understanding of physics.
Why is that a problem? The information could still exist, it'd just be inaccessible...
This seems no different to me than a spaceship going beyond the Hubble horizon.
It is a problem in either case - if it really disappears then time reversibility, a real corner stone of physics, is violated, if it does not disappear the problem is that we don't understand (well) where it goes. As far as I know the favourite theory is that the information is contained in the Hawking radiation and I believe to remember that there was a paper not too long ago that showed how to recover one (or a few) (qu)bit(s) from Hawking radiation in a special case. Because time reversibility is such a deep concept it seems likely that we just don't understand well where the information goes, I doubt that many physicists believe the information really disappears.
We believe that certain symmetries apply to the laws of physics. For example, we believe that the laws of physics are independent of the observer's position. I mean, look (visualize me stepping sideways here). So we can demonstrate that one pretty easily. And they're independent of rotation. Again, look (visualize me turning 90 degrees here). And exchanging left and right. I mean, look... (visualize me pausing with a confused look on my face as I try to figure out how to exchange left and right).
I can't actually do that experiment. And it turns out, when we got deep enough, we found out that things actually behaved differently (parity non-conservation).
When it comes to time reversal, we can't actually do the experiment, either, so we don't really know whether physics behaves the same when time is reversed. We expect, philosophically, that it will, but we don't know. But it seems to me, given how relativity mixes time and space, if physics is not the same with left and right reversed, then it can't be the same with time reversed either.
Saying we consider time reversibility true for more or less philosophical reasons seems a bit of an understatement to me. Conserved quantities prevent states differing in at least one conserved quantity from ever evolving into the same state, i.e. conserved quantities partition the phase space and states cannot cross those partition boundaries. This also has to hold for all isolated subsystems. And conserved quantities arise from symmetries like homogeneity and isotropy of space which are pretty solid empirical and experimental facts. It's all interlinked and I imagine it would not be to easy to eliminate time reversibility from the laws of physics without causing some odd consequences.
The entire point is that it shouldn't become inaccessible, because that is WHY time symmetry appears to break. Because it means that if you flipped the direction of time, something with a causal effect appears seemingly randomly out of nowhere.
Why is that a problem? The information could still exist, it'd just be inaccessible...
This seems no different to me than a spaceship going beyond the Hubble horizon.