Is my grandmother alive for some alien who is located on some place and is moving with some speed? (I am science fiction writer. I had a goal in my novel to argue that time travel to past will not be available even in future. I asked here how to argue that. I collected answers and analyzed them and in conclusion I came to following question:)
Question: It is said that there can be found theoretical observer somewhere in universe (moving with specific speed to specific direction) for whom for in his current moment there will be for example 1900 on earth, while you are reading this question in 2013. Is this statement true ?
If yes: Then can this phenomena used to build time machine ? (For example if such kind of observer exists he theoretically can teleport on prehistoric or on future earth).
If no: I d like to know why.
This subject is described in documentary movie - "Time in nutshell" on the example of alien. You can see the scene directly on link below (youtube)
http://youtu.be/MO_Q_f1WgQI?t=4m59s
It is awkward because if that is true for some alien on some place my grandmother is still alive.
Edit: Imagine the observer has no eyes to process light. It would be more interesting not to focus on the light or on the image of earth delivered to observer for the moment, but to focus on observer's INDIVIDUAL "now" or what is happening on earth for observer in the moment when he is far on another planet and moves with specific speed.
 A: If you define "now" to be all those points in space and time that have hypothetical, pre-synchronized, stationary clocks that read the same time as your clock, then there "currently" exists a hypothetical observer somewhere, who is moving relative to us, for whom "now" includes Earth, circa 1900.
But these notions of "now" are different for the two observers. Think of them as two different ways to slice 4 dimensional spacetime into 3 dimensional slices.
The reason you can't use this setup for time travel or communication with the past is that you can't exchange signals with any other point in spacetime in the "present", but only send signals into your future lightcone, and receive signals from your past lightcone.
So right now our hypothetical ultrarelativistic alien exists in a frame of reference in which your grandmother is still alive, but it can't talk to her, or you :)
A: The first statement is very much true. Light moves a finite, if very fast, speed. Even ignoring any movement/ relativistic effects this simply means that observers closer to earth will see it in it's most recent state.
It may sound strange for light, but we see exactly the same phenomenon in sound, an observer noticeably closer to the source of a sound will hear it before one further away. For example you might notice that a dog barking on the other side of the park seems to open and close it's mouth before any sound is heard.
In fact, all aliens on the surface of a sphere at a certain distance, the distance light travels in 113 years, would see 1900's earth if they looked at it.
Sadly, in answer to your second question, could this be used to build a time machine, almost certainly no.
The speed of light may be finite, but it is also (and here's where things start to get weird) the maximum speed anything in the universe can travel at. This is a consequence of Einstein's special relativity, one way of thinking about it (which has it's detractors but isn't too far from the truth) is that the objects mass increases exponentially as it approaches light speed, making it harder and harder to accelerate the object further, and would theoretically have an effectively infinite mass as it reached the speed of light.
So in short, though you might be able to see the past, you can never get there, at least not by moving through conventional space, but anything you might find about wormholes etc. is just hearsay (or at least severly lacking proof).
Although as an interesting side note, if an observer was moving quickly (would have to be near the speed of light) away from earth, they'd see time on earth slowed down (see Doppler effect) and vice versa if they were moving towards it.
A: No. Not that we know of unless we change the current laws of physics to allow faster than light travel or imaginary mass
