Susskind, in his lectures at Stanford, made a bold claim that the universe has a unique future and a unique past. Moreover, his view was that the both future and past can be determined from any given point in time. A reasonable view for a physicist, and it follows our perception of time as linear. We may not hit rewind, still, and play, but, we experience it as a movie.
If I read 't Hooft correctly, who is developing an alternative to QM, then he beliefs that the future can have multiple pasts, i.e., two states may converge to one new state. There's loss of information. An equally bold claim, but somewhat predicted by mathematics. Multiply or add two numbers and you can't uniquely reconstruct the original values.
It seem the problem boils down to a game of billiards: Is it possible to hit the balls such that a new position doesn't tell what the original position was? Often, it would seem so, but there's a way out in the sense that we could consider the state of whole room, not only the table.
Anyway, in case of doubt, I suggest they ask Ben Davies.
Just kidding here, I don't know anything about physics. Now I am really going back to programming...