>In the Strugatsky Brothers' Noon Universe, FTL travel is impossible. All ships travel at near-light speeds and return centuries later (objective time). This all changes when the crew of a starship decides to try something new. Normally, constant or slowly-increasing acceleration is maintained for most of the voyage. The captain of the ship decides to try high acceleration for most of the trip (about 10g) in order to reverse the effects of time dilation, as this would fall outside of the Special Theory of Relativity. According to the captain, General Theory of Relativity allows for this. This works, and the ship returns to Earth six months later; however, several years pass for the crew.
This is plain WRONG. all but earliest 'Noon Universe' books have jump-style FTL. (The Land of Crimson Clouds doesn't mention FTL because it's not invented yet. This is book is about expedition to Venus.)
Some stories mention that some earlier sublight ships tried maneuvering with (I don't knew how to translate 'легенные ускорения' from Russian ) which resulted in first jumps. Later ships could do that without going to near-lightspeed first
Edited by vikarti.anatra
In Final Fantasy XIII-2, Hope and Alyssa use a time capsule which slows time on the inside of the device to travel centuries in time. This was because Hope knew that his plans wouldn't come to fruition in his lifetime so he made plans for the Academy to perform in his absence and went several hundred years into the future. It is hinted that the various advances in gravity control allowed this to be possible.
GPS satellites don't use time dilation for triangulation. What they do is there's a tiny error that relativity causes which if uncompensated for would escalate to major decreases in location accuracy.