Isn't it like this..
Like travels totally indifferent to time. In light's plane of reference, time is undefined.
In addition, as you approach the speed of light, time slows down until it becomes undefined (the speed of light).
Disregarding mass dilation and everything, if we were to somehow go faster than light, we could theoretically go back in time. Since going faster than this is impossible (from what we know), isn't it also impossible to travel BACK in time?
Travelling into the 'future' is possible, by accelerating to near the speed of light, and then slowing back down, and due to the slowing down of time, everyone not in your frame of reference will have aged faster than you. Thus, the future.
So technically, we can't see 'time travel tourists', because you (again, theoretically) cannot go back in time.
But yes, time travel is possible, but only into the future (at this stage).
..Right?