I am a second year physics student at Flinders University, and I believe time exists and that time travel is possible.

Time exists, because time is what lets us distinguish between two events. Though how you see time is another matter entirely, that is whether the future is the future, the past the past, or the present the present. To our way of thinking time began at the big bang, because that was the moment at which space came into being. And since the concept of space-time suggests that time and space are intertwined, this means that in fact time travel is theoretically possible. This is according to general relativity, space-time is 'warped' by strong gravitational fields. Hence this suggests that if a spaceship was piloted through such a zone that time would pass more slowly than that of space outside of the gravational field. Also einstein showed that when approaching the speed of light time in this moving frame will be slower than the time of an obserever in a stationary reference frame.

So iff we had unlimited resources, it is quite possible that a 'time machine' could be built, so according to the laws of physics, time does exist, and that it is possible to travel through it because in a sense we travel through time all the time. That is the normal passing of time. So what is to stop us moving through time in other ways.