How fast must you go to time travel?

Time relativity uh??
There was an experiment conducted somewhere in the 2002, where two observers were used. The first one was asked to wait in the airport and the other one boarded the plane.Both of them were supplemented with an atomic clock (the most accurate clock in the world with very high degree of precision), and the time elapsed for the guy to step of the plane is taken (may have been decided by the use of cell phone).Amazingly, it was found out that the static observer was 0.001 behind the guy who has been travelling. The percentage error of the atomic clock is too small to be significant, and therefore the hard to swallow truth is that time is indeed stretchable.
However, as you can see from the above example, even in the speed of an airplane, we would only yield a time delay of a hundredth of a second, and therefore in order to yield a greater elapse, a greater speed would be required and is proposed that, for a substantial time delay, speed of light will be the most favorable.