Greetings from the Australian National University in Canberra, where Dr Peter Riggs from the Department of Quantum Science, is speaking on "Time travel: Its implications for physics and philosophy". He asserted that time travel to the future is not philosophically problematic and theoretically possible according to Einstein. Time dilation, by traveling fast allows a one way trip to the future, as confirmed by experiment. Cosmonaut Sergei_Krikalev has spent the longest time in space and as a result has traveled 1/48 of a second into the future. Time travel to the past is more of a problem.
Dr Riggs illustrated the structure of space time as two cones on end (the "lite time cones"). To travel backwards in time a "time-like curve" can be used, using the distortion of gravity around a massive body. This starts to sound like the Blink Dr. Who Episode, where time travel was explained with space-time as "wibbly-wobbly timey-wimey".
It occurs to me that as time dilation effects are observable, they would need to be taken into account in everyday laws. As an example, a component on a satellite will age more slowly, so will effect a warranty on the product.
Also while Dr. Riggs briefly discussed the transmission of information across time, it would seem to be easier to engineer physical travel but introduce its own problems in therms of physics.