I keep hearing this, but I haven’t yet found an explanation that I can grasp. Anyone care to explain?
This is pretty tough to get across without space-time diagrams. Even with, it may be hard to explain without a basic foundation in relativity.
If Joe in reference frame A sees Jane in reference frame B moving at .8c north, and Joe also sees some other object C travelling north at 1.2c, Joe can use the Lorentz-Fitzgerald transformation equations to determine that Jane will observe events associated with object C to go backwards in time.
There are some circumstances in which this situation could be described as an event that can actually happen. Lets take this case:
Joe sets up 8 bombs all with individual timers. They have no causal relationship to each other. They are all lined up over a vast section of space. He has set the timers so that from his view, bomb 1 will explode, then 2, etc with a precise, equal delay between each one. The bombs are spaced so that if you traced a line to connect with all of the explosions, for an object to keep up with the explosions, it would need to be travelling at 1.2c. Joe sees Jane travelling in the same direction as the order of the explosions at .8c. From Jane’s perspective, she will actually see bomb 8 detonate first, then 7, etc. (The time gap that Jane notices between each explosion will also be different from what Joe sees, but that’s not real important.)
That’s all hunky dory, and perfectly possible. Again, it is a little hard to explain why Jane sees it that way without explaining Lorentz-Fitzgerald transformations and showing space-time diagrams.
But now, what if we provide the same situation, but we establish a causal relationship? Suppose Joe has set things up so that he sends a radio signal to bomb 1 and that starts a countdown. Just before bomb 1 explodes, bomb 1 sends a signal to bomb 2 to start it’s countdown. This situation is exactly the same, except that now Jane will observe bombs exploding before they are signaled to detonate!
Whoa… I need a joint.
Just one clarification-- I really shouldn’t have said “radio signal”, since a radio signal (travelling at the speed of light) could not have accomplished the feat in the last example. So instead of a radio signal, imagine an imaginary FTL signal like ahem a subspace message. 
Actually, your little misstep is a good example of why information cannot be sent FTL: If information can travel FTL, someone sees violations of causality from their reference frame.
(Violation of causality: If A causes B, a violation of causality would be B happening before A. Not good. See the second example in UDD’s first post.)
Oh, almost forgot: UDD, glad to see you taking a more active interest in the SDMB! We can use all the nerds we can get here in GQ.
Thanks! I’m geeky alright! 
Ah, Jason Hinson
I learned a lot from him many years back when he was a grad student and was posting to rec.arts.startrek.tech
He is very good at explaining this stuff and I definitely recommend it.
I think I get it. I’ll let you guys know when I invent a non-paradox-causing FTL drive, utilizing the special reference frame idea.
There are no special reference frames. In relativity, all reference frames are equally valid.
He’s probably talking about something he read in the Jason Hinson stuff.
I don’t think Jason Hinson really promotes the real possibility of FTL, but he does talk about how sci-fi could do better in making an FTL concept that didn’t totally fly in the face of science.
Yeah, that idea was from the Star Trek part.
sturmhauke, I can prove you will never invent FTL travel. Because if you did, you would-have-been-will-be able to come back and had-will-have-been telling us about it yesterday. You promised!
Or maybe you have-been-will-be delayed by becoming your own grandfather.
Oh, didn’t I tell you? My real name is Dave Lister. I’m my own father, actually.