It is possible to go faster than the speed of light, all that it requires is a decent power plant on a spaceship in order to accomplish it. The effect of travelling at the speed of light or slightly higher is that it would take just 30 minutes or less to reach Mars orbit. Contrary to Einstein's theory there is no physical barrier regarding the speed of light and speed does not compress an object into an infinite line which later travels backwards.
So I guess all those experiments on time dilation they have verified with atomic clocks are bunk?
No, we can't travel faster than the speed of light in a linear fashion for a multitude of reasons. If we could, then we already would have, since all we need is a decent power plant, right? Likewise, in all our astronomical observations, why have we yet to observe a particle that does. You'd think a supernova might be able to push matter faster, but even /they/ are limited by the upper bound of the speed of light when they explode.
Also, one minor nitpick: you can't travel backwards in time. Can't be done, not in a traditional sci-fi sense. The accelerating expansion of the Universe prevents this.
But what we /might/ be able to do is fold space and travel through it, or exit space and re-enter it... though I'd argue the former may be easier than the latter.