I have a "science-fictiony" idea that I haven't seen anywhere else yet. The idea is this: If we can see light from planets thousands of light years away, then we can see the past. Once our telescopes are good enough to basically do a "google maps" zoom-in on other planets, we will be able to watche the past on other planets. But then, if we can ever watch our own Earth from a thousand light years away, then we can see what happened in the past. The missing link is for us to be able to travel faster than the speed of light so we can go far enough to view Earth's past.
While not "obvious", I still feel like others have probably thought of this idea. It could make a cool science fiction story.
In Hubbard's Battlefield Earth, they do this with another planet. It was destroyed, and they fly/transport/whatever a camera out so many lightyears from it, so they can see what happened.
Here's an even crazier version: we develop a quantum computer the size of Jupiter with seemingly infinite computational capacity, and "scan" and simulate the earth. Similar to how a sufficiently advanced AI application today could probably take an overview picture of a pool table at any point in a game, and deduce the past shots that had to be taken in order for it to result in it's current state, you might be able to develop a virtual time machine.
That sounds enticing, but I think you could never rewind the state of the Earth without considering the variables external to it. If you couldn't also simulate anything that could alter the course of events, such as exposure to the Sun, I think you'd end up accumulating enough lossy transitions that the simulation would be rendered (ha) worthless in a deterministic sense.
If we consider that only simulating the atoms contained within the Earth is enough to have a perfect understanding of it's state across time, by logical conclusion simulating a house would be enough to rewind the history of it's structure.
"So we expand the computer to simulate everything. Hell, if we were to correctly determine the state of the universe at the big bang and simulate every atom since then we could answer everything about the past, have a perfect image of the present (intelligence dream!), predict the future... We could simply write an algorithm to know where or if intelligent life exists outside of Earth..."
Then, after some consideration I realized that the smallest possible computer capable of simulating every particle in real time... was probably reality itself.
Fair enough, although I bet with a "high-res" enough simulation and physics engine, you could probably account for most of those externalities that would impact the simulation via context clues, like (simplistic examples) crater == asteroid, increased radiation == solar flare, etc.
For example, if you took a video of a coin being tossed into a coin pond, and then CGIed the coin out of the video, you could probably hire a criminal forensics-style physicist who could go through the video frame by frame, and then tell you the type of coin, velocity, point of impact, etc. just based on the splash and ripples.
Chaos theory [1] will make sure that any minor change will result in drastically different result, so assumptions and guesses won't be sufficient.
[1] http://en.wikipedia.org/wiki/Chaos_theory
While not "obvious", I still feel like others have probably thought of this idea. It could make a cool science fiction story.