Even Albert Einstein had no idea what would happen, if someone would travel faster than light. So he called it a paradoxon. Theory of Relativity explicitly forbids traveling faster than light. Mathematically seen, some things were really strange. For example the following equation:
l = l' * sqrt(1-v²/c²)
(called "Längenkontraktion" in german)
Lets say we travel at 2*c:
v = 2*c
v² = 4*c²
l = l' * sqrt(1-(4*c²)/c²)
l = l' * sqrt(1-4)
l = l' * sqrt(-3)
The same would happen with time...
t = t' / sqrt(1-v²/c²)
becomes...
t = t' / sqrt(-3)
and mass...
m = m0 / sqrt(1-v²/c²)
becomes...
m = m0 / sqrt(-3)
can anyone image what this means in practice ?
An important fact in Albert Einsteins Theory of Relativity is the frame of reference. The man who is travelling near the speed of light does not feel, that he does not get older, nor that he shrinks.
Only the people who see him travelling (or would, if they could) recognize this behaviour.
So, if it would be possible to travel faster than light, then the traveller would remember everything !
I think he would not travel in time.
When we take the definition for velocity as some distance in some time, than we can state, that the time AND the distance must have a kind of "raster", a very small quantity, which cannot be broken into smaller pieces.
Sounds familiar ?