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.
Well firstly time dilation? Time is always constant and is not effected by an object in vacuum approaching and exceeding the speed of light. There is no resistance or drag effect in a vacuum zero g environment. So even with todays technology it is possible for a spaceship built on Earth to exceed the speed of light. What is required is enough fuel and a powerful enough engine which is capable of sustaining a burn for enough time in order to reach and pass the speed of light. So such a spaceship would require a power plant that is capable of achieving that. In our system we have planets and moons which are capable of assisting a spaceship in order to help it accelerate more to achieve exceeding the speed of light. It is possible to travel back in time, evidence of Time travel: 1/ Stonehenge, crystal skull of Belize and other monuments on Earth. 2/ 11:11 on the clock has relevance to time travel 3/ Tungaska Comets intercept. 4/ John the Baptist who was in fact Elijah in the bible so existed in two places at once. 5/ Black Holes feature an anomaly in time when an object passes through it into the former stars fuel dimension.
"Trust me I know what I'm doing" Detective Sledge Hammer