Is Time Travel really Possible?

In this clip Professor Brian Cox - a confirmed Doctor Who fan - undertakes an experiment with a light showing that time moves faster for a stationary clock than a moving clock, which appears to move more slowly over the same length of time. His conclusion is that time travel is possible, but only into the future!

Of course, we’re all time travelers, thats a fact: We move forward in time from one second to the next. But going back in time, is something far more elusive. And for those who yearn to see what the world will look like a century or a millennium from now, the slow tick of your watch as time passes just doesn’t cut it.
The theoretical underpinnings of time travel date back to 1905, when Albert Einstein wrote down his special theory of relativity that showed space and time are intimately linked, and to 1916, when Einstein’s general theory of relativity showed that space and time are malleable — that is, they respond to the presence of matter or energy by warping, bending, expanding, and contracting. By extension, this means if one can imagine space being filled with some exotic form of energy, then space and time could warp in a way so that time, as well as space, could bend back upon themselves like circles, allowing one to move forward in a straight line and still return to one’s starting point in both space and time.