If time travel is possible Josh, String theory is likely correct. Einstein does not account for extra dimensions, string theory does. If alternate universes exist, then that gets around about 99.99% of the paradoxes created by time travel because you would not be able to alter your own timeline, but rather an alternate universe's timeline and that timeline wasn't "altered" per se, that timeline things happen that were supposed to happen.
Quantum tunnelling may get around the whole time problem. It may be possible to go from point A to point B without moving in time at all (save for the amount of time it takes to get from A to B). If you are getting AROUND the light barrier, (that is tunnelling quantumly or warping space), the time's speed should not change (as I understand it, I am certainly no physicist though).
Most know that as you approach the speed of light in 3D spatial perspectives, time slows for you. The faster you go, the slower time travels for you, meanwhile those on Earth would continue to go through timeline as per normal. So, lets say you take off in a ship and ehad to the nearest star (Alpha Centauri trinary system, 3.something LY away). You are travelling at the Speed of Light. No time would pass for you but when you did get there (instantaneously to your perspective or very near to it) 3.something years have passed on Earth.
Tunnelling and Warping may be able to get around that as you are not necessarily travelling faster than light, you are circumventing 3 dimensional space all together and since 3D space and time are connected you are circumventing time as well.
Who knows, but its all rather fascinating to me.