A question for physicists
I've recently been ploughing my way through Carl Sagan's Cosmos on www.tv-links.co.uk. In one episode he mentions the possibility of time travel backwards by going faster than the speed of light. I've always considered time travel backwards to be impossible, but I was also in disbelief when he said that time would actually slow down at the speed of light, i.e. what might seem like days for travellers at the speed of light would actually be years, even millenia on Earth, it goes against my common human intuitions on time. I'm well aware of the weaknesses of the human mind to understand this. I have a great philosophical, ethical and political mind but when it comes to this I don't have a fucking clue.
Could a physicist clear this up for me?