Astronomy/Light from distant objects..
Heres a problem that Ive been struggling with for some time:
We know that when we look at a distant object in the universe we are actually observing the light from that object not in real time but the light from many years ago depending on the distance of the object.
We know also that the position of the object we observe is the position of the object in the past and not the position in space of the object now.
Now heres the question, but first we must assume that we have an optical telescope capable of infinite resolution regardless of the distance of the object we are observing.
Since we can easily calculate what position in space an object did occupy at any time in the past, if we pointed our telescope with its infinite resolution at the point in space that the Earth occupied say two billion years ago, what would we see?
In the context of this question, the Earth was in the same place two billion years ago as right now -- the center of our observable Universe. So you wouldn't need a telescope to see where the Earth was at that time. All you'd have to do is look around you, at the same place we are right now, so you'd see the Earth as it is right now.
However, even if it made sense to specify some different place that the Earth might have been at that time, if we looked there we would see nothing (or in the unlikely event we did see something, it would be merely a coincidence, as what we would see would be the same as if we looked at any random spot in the Universe.)
The reason for this is that even if the Earth had been in a "different" place at that time, it would have moved away from that place only by a distance equal to the typical movement (due to the expansion of the intervening space during the time period involved) of objects that we see as they were two billion years ago (in other words, from "there" to "here"). But all objects within the visible Universe "move" at only some fraction of the speed of light, while the light that they might have been seen by moves at the speed of light. So that light would have passed where we now are a long time ago, and would not be observable from our present location.
I hope this clears things up, but if you would like to discuss any point from a different perspective, just let me know.