Black holes move and there's certainly some weird time/information things going on there.
Photons "move", but don't experience time. They can't not move...
We move and experience time dilation while doing so.
The discovery of information can appear to alter the past in experiments. Those experiments are in labs. Those labs are on the Earth. The Earth is in the Milky Way. Estimates are that the Milky Way is moving around 600kps
relative to other objects.
So, we're all moving..
But, it's all relative. There is no cosmic reference point, no signpost that say's "You are Here." Would it even be possible to go back in time and appear "somewhere else" than at the point of origin in the future? If not, does that mean there really is a Universal Sign post that sticks on every bit of "information" like a convention nametag? Every bit of information claiming "I am Here" with some sort of immutable frame of reference?
Apparently, Nature doesn't like the whole backwards time thing very much. We don't see it in the macro world. We don't even see it when it occurs in the quantum world either. We can't. We can't "know" it beforehand.
Until we can actually know that time travel into the past is possible for objects bearing mass, I don't think we're really going to know where such an object would end up once it succeeded. Would the first experiments, even if possible, consist of lots of test objects simply disappearing? If they were due to come back in the future, what happens when they don't? Or, what if they come back completely intact and unchanged? Is it the same object or just a duplicate collection of information? (I know, there are no quantum photocopiers.. supposedly.)
Like CE, this subject gives me a headache. I've got a book around here on Time, I should probably finish it and see if the answer lies within.