[hugh3]

I've seen that explanation over and over, but I don't see why there's a problem with something arriving at B before B sees it leave A. We have the same situation with faster-than-sound travel, but it doesn't appear to be impossible.

It's a subtle point, and it's very difficult to explain in layman's terms. On the other hand, it's very easy to explain once you know how to draw and interpret a Minkowski diagram.

But basically, special relativity means that if you can travel faster than the speed of light then you can travel back in time. An explanation of why that's shorter than a full explanation of special relativity will seem unsatisfying.

So instead of reading handwavey explanations on the internet recommend going out and properly learning special relativity from a textbook. (D'Inverno is pretty good, though it's only one among many.)

A philosophy lecturer of mine said that nobody should be allowed to graduate university unless they understand (a) relativity, (b) quantum mechanics and (c) Gödel's theorem, and I'm inclined to agree. You just can't consider yourself educated in the 21st century without a basic grounding in the important advances of the 20th.

[Groxx]

I thought special relativity also means that it is impossible to travel faster than light. So anything outside its range of what's possible can be calculated as utter nonsense without invalidating the theory within its range. Similar to how quantum effects seem to work by entirely different and contradictory rules, while still very clearly working.

[hugh3]

Yes and no. It predicts the impossibility of travelling faster than the speed of light and predicts which kinds of impossible you'd get if you did.

The first level of impossible is that you can't accelerate a body past c no matter how hard you try since continued acceleration will just get it arbitrarily close to c (in every reference frame). The second level of impossibility is that if you did find a magical way to do that then you'd wind up with time travel.