First of all, I believe in time travel and I believe we can be close to evolve much in this area in the coming years.
This is not really a paradox, but a functional question about time travel. I wonder this for years, and still only had two ideas.
Why do people always disregard the spatial position of the traveler before, during and after the trip?
What I mean is, for example, I travel 500 years into the future. Over the next 500 years my continent will not be at the same spot (tectonic plates movement), planet Earth will not as well, not even our universe. If you make this trip to appear exactly in the same point in space in 500 years you probably will appear in the middle of nowhere and die like an astronaut adrift.
The first way would be to make it in a way we can calculate exactly where in space you will appear (and choose on planet Earth), but it would be, at least until today, an impossible calculation, because we have not an accurate notion of our universe movement.
The second way would be to say that in the case of a machine, the machine would be stopped during the trip. For the travelers could last seconds, but the machine would be stopped at the same place, walking along with the Earth in the universe, for 500 years. This second way I think the most plausible, but would have an absurd cost with maintenance to keep it running smoothly all along.
This cases look to be only to "stopped machines", but they're not. A spaceship near to a black hole, for instance, it will travel in time, but I'm sure they won't find the way home if they travel too much.
I have this doubt due to the movies and stuff because them no longer explain a lot. In the case of this question, I did here because I see that people do not wonder about it. I hope you understand what I mean on this thread.
Do you have something to supplement? :)