they have done the atomic clock expiraments with the shuttle ( much faster than an airplane). Thier computers have to actualy adjust for the "time loss" differance between their systems and ground systems to keep them in sync ( not the music group )

the paradox in time travel is funny since the only way that theoreticly possible to exceed the speed of light is to use a gravity well so intenst that light cannot escape it ( a black hole) and slingshot through/around the gravity well ( thus an escape velocity faster than light can acheive )

of course to accelerate up TO the speed of light to do the slingshot, shifts one forward in time. so by the time you slignshotted into the past and decelerated below speed of light ( thus forward in time again as well ) you would ultimatly equal out the passage of time coming out to where you would be passing yourself going in.