That being said, as Edgar added to Vintage's answer, if you put a mirror 13.5 light years away, and watched your reflection from earth, that would be the same as being 27 light years away.
So if I doubled the number of mirrors (2 in orbit, 2 on earth) and halved the distance to 6.75 light years I could accomplish the same thing.
If you take that example to it's conclusion, could I construct an (expensive/complicated/etc.) device here on earth that had so many mirrors it could let me look into the past at all?
The physics-answer seems "yes" so my question is "Why haven't we tried that?" and one obvious limitation, I suppose, would be just how many mirrors you would need.
Light travels 5,878,499,562,554 miles (5.78 trillion) a year[1].
Given that, if I just wanted to see an hour into the past, I think that means I would need to observe earth from: 5,878,499,562,554 / 365 days / 24 hours = 671,061,594 miles away.
Or I could stick a mirror in space 335,530,797 miles away (~ 540,000,000 km) from earth and stare at it.
Mars, at the widest distance from Earth, is 401,000,000 km away[2], which is close enough for my purposes (I'm not picky)... so I guess if I stuck a mirror on Mars and looked at the reflection of earth I could see something like 45 minutes in the past.
The Moon is almost exactly 1000x closer to the earth than Mars[3], so I wonder if I used it for my mirror array instead if I could just put a station with 500 mirrors on it to accomplish the same thing.
Or build something on earth with millions of mirrors in it to accomplish the same thing.
I would normally think something like this impossible, but I just watched a docu on the LHC and now I wonder if even at a micro-second scale, if we have tried building something like this and observed two points in space using a computer and seeing if the visual data coming in is micro-seconds apart from each other?
For example (assume I have a camera and visual-diff software sufficient for this and that my "mirrors" have sufficient magnification capabilities to make this seem like an easy setup), if I pointed one camera at a monitor drawing a unique pattern 2' away from me, then point another camera at a mirror that has bounced the image 10 miles before being displayed... I imagine, like sound, there would be a lag in that image if we bounced it enough times.
(DOH)
It suddenly dawns on me that using this method to look into the past is effectively the same thing as recording something with a video camera and playing it back later... you are literally capturing the light for review at a later date.
So as cool as this idea is, I think I just answered my own question as to why we haven't tried to build a million-mirror-array before... cause I can buy a video camera for $300 instead :)
[1] http://www.universetoday.com/45047/how-far-does-light-travel...
[2] http://www.universetoday.com/14824/distance-from-earth-to-ma...
[3] http://www.enotes.com/science-fact-finder/space/how-far-moon...