If you want to jump into the deep-end of the sci-fi pool, it's convincingly arguable that with a complete enough grasp of the physical laws, and sufficient processing power, you can reconstruct a past state up to Xs into the past and with Y% accuracy. (Of course "accuracy" is a pretty arbitrary measure).

For example, using the current trajectory of a baseball, it's fairly trivial to deduce where it came from 1.5 seconds in the past with, say, 99% accuracy. Now just extend that process to the entire Earth. It would be earth-shatteringly difficult, of course. And of course there are a hundred and one open questions about the nature of consciousness, whether a person reconstructed in such a fashion would be the "same" person, and of course the problem that describing a system isn't the same as reconstructing a system in reality.

But it's not impossible given our current understanding of the universe.

EDIT Somehow I missed the above post. Which covers all this.