Time travel is an interesting one.

There are a number of different possibilities:

First off, impossibility. Reasonably unlikely, although time travel as we see portrayed in films is highly unlikely to work.

Second, possibility. Well, we know that some anti particles (i believe the positron, for example) move backwards through time. The speed of light is quite key in this one. It's been likened, by some authors, as a sort of mountain ridge. Lorentz has been remembered for the transformations that govern what happens to things as they approach the speed of light. Things like length and time dilation/contraction. Using the transformations, we see that if you travel faster than light then you will be travelling backwards in time.

On a side note it's interesting to note that interstellar travel would not take very long to the travellers themselves, as time would contract so much near the speed of light that thousands of years could pass in apparent seconds.

However, it is impossible to accelerate up to and beyond the speed of light, so this is an impractical method.

Other methods for actually travelling have included wormholes, as stated, and there are a fair few more.. metaphorical methods. The problem with wormholes is a big one. How do you create a wormhole the right size consistently, how do you keep it open, how do you know where it goes? And of course, how do you create it so it's stable enough for a person (or ideally craft) to jump through. And of course, how do you get back? If you're travelling in time, what are the odds of a massive particle accelerator at the other end?

Assume that there is a computer so incredibly powerful that it can store a simulation of planet earth, a perfect virtual reality that can be stopped, fast forwarded and rewound (up to the present day, of course). In theory one could insert oneself into the virtual reality and travel through it back until the first day that the computer started recording - so if it was around for a 1000 years it might actually be useful. Obviously this is going to be incredibly difficult to pull off, on purely technical grounds.

And now to the actual problem of time travel itself. Say we've created a machine that'll do it through some exotic means. What happens when you go backwards or forwards in time?

One could argue that we will never invent backwards time travel because we haven't been visited by time travellers yet. As the future is in theory infinite, it stands to reason that if it were invented at some point, we would be being visited by time travellers on a regular basis. There is also the issue of time travellers' immunity - ie how to stop the grandfather paradox. It's been postulated that if you could go back in time, it would be logically impossible to change anything as you went back in time before you went back in time, as it were. There is the example of the man who goes back in time to see how a fire started, only to learn that it is his visiting which started it in the first place. You'd be stuck in an endless loop. This raises some interesting questions, and it's also quite easy to see how quickly it will get confusing.

There is also the other worlds theory. If you went back in time, and jumped back forwards, how do you know that you'll get back to the same world you left from? And what happens if you're in the original world when someone goes back in time, if they change something, would you just vanish? Would your universe stay the same and the traveller return to a different one? This is getting seriously philosophical, but there's the chance that every single action possible in the universe spawns another universe where a different action happens.

Travelling forwards is another matter. Arguably a lot easier to do. All you have to do is travel very fast and slow down, and presto, you've travelled through time in a short period (i discussed this in the speed of light bit). Of course you wouldn't be able to get back! If there was a machine that could do it, ie move you forward to any period you chose, you would only be able to travel back to when the machine was first made - if ever invented this is probably the only way we'd end up time travelling "properly".

So yes. BIG topic, but it's fun to get stupidly confused about it!