Stephen Hawking on how to build a time machine
Hawkin has written a very accessible article on two ways to time travel (but only into the future, not the past):
To approach the speed of light means circling the Earth pretty fast. Seven times a second. But no matter how much power the train has, it can never quite reach the speed of light, since the laws of physics forbid it. Instead, let’s say it gets close, just shy of that ultimate speed. Now something extraordinary happens. Time starts flowing slowly on board relative to the rest of the world, just like near the black hole, only more so. Everything on the train is in slow motion.
This happens to protect the speed limit, and it’s not hard to see why. Imagine a child running forwards up the train. Her forward speed is added to the speed of the train, so couldn’t she break the speed limit simply by accident? The answer is no. The laws of nature prevent the possibility by slowing down time onboard.