Time travel includes not only going back in time, but also going into the future. Therefore it very well could be that time travel to the past is impossible but time travel to the future is possible. Time travel to the future is actually proven by a linear accelerator. Particles with a life span of some certain time, when accelerated to close to the speed of light, have been shown to "appear" to live around 300% longer, which is not the case. They are actually experiencing time at a slower rate than us. Though this is the physics side of the argument.
Stephen Hawking has a "simply test" involving throwing a "time travelers party" at noon that will last until 1. But he doesn't release the notice/invitations until after the party. (i.e creates a program that is on a timer to send out invitation.) Therefore he waits for the time travels to show up as the clock approaches 12. No one shows and it's a big disappointment. Of course this is a slight form of comedy he actually has a theory as to why we haven't seen any time travelers. And it has to do with something of paradoxes. His theory involves that the state of natural laws make it impossible for paradox to ever happen. (Ex of paradox: a man going back in time to kill himself. Who shot and who is dead/alive.)