How did the Emperor get to the delimbed Vader faster than an ambulance in rush hour traffic? 
The speed limit of c imposed by relativity is a local limitation, not a global one. The best way to decide whether something violates the speed limit is to imagine the Enterprise in a race against a photon located just off the bridge. When the Enterprise engages the warp drive, space in front of the vessel is warped, and the Enterprise travels at sub-light speed through the warped space. In this scenario, the Enterprise would lose the race with the photon, because the photon would move through the warped space created by the warp engines at light speed, beating the Enterprise to the destination.
Now, in a race with a photon that is located far enough away from the ship to be unaffected by the warp engines, the Enterprise would win. But this does not violate the speed limit.
As someone said up-thread, his shuttle flew at the Speed Of Plot.
Only if you reverse polarity on the phase inverters otherwise you will blow out EPS couduits all over the ship.
Oak, there’s simply no answer, because the laws of physics–the laws of NATURE–are different in the TrekVerse. (And if we’re talking the last movie, the laws of human psychology are different too.) Time dilation is simply not an issue for them, and Albert Einstein’s work is entirely different. Likewise, what we call *intelligent design *they call evolution. About the only thing we share with the people of that universe is the belief that Zoe Saldana looks best in miniskirts.
Not if you convoluted the phase modulation of the Zilch coils.
Honestly, the impulse drives and even the thrusters always bugged me more than the warp drive. I mean, relativity is fairly recent, and has some conceivable loopholes. But it’s hard to think of a physical law that’s been better established over a longer period than Newton’s Second Law of Motion. We’ve had to slightly tweak our definitions of momentum over time to hold onto it, but nothing’s ever threatened the basic concept. As my high school physics teacher put it, “If you find that momentum isn’t conserved in your system, you’ve made a mistake somewhere.”
I should point out that if they so choose, they can travel through time if the plot requires it. So they do play pretty free and loose with the rules of physics.
My WAG is that “warp” drives literally distorts or warps space in front of the ship. So if the Enterprise is traveling from A to a star B that is 1 light year away, it actually shrinks the distance so it never actually exceeds the speed of light. But to an outside observer, it travels the distance between A and B much faster than the speed of light.
The other common sci-fi FTL conventions are “hyperspace” (like in Star Wars) where the ship leaves our universe to one where it can actually traval superluminal speeds without relativistic effects and reenters our universe at its destination or “jumping” (like Battlestar Galactica) where the ship basically folds space like a piece of paper and instantly moves from point A to point B
But basically all it amounts to is the writers need to move the ship from point A to point B. The only thing to decide is 1) how much travel time is needed and 2) how cool do they want to make the lightshow appear on screen.
Not with the Heisenberg Compensators working at max efficiency. 
What I could never understand is why they would ever travel at less than maximum warp when going from star to star. The ships never seemed to have any problem hitting Warp 8 - speeds higher than that wer sometimes presented as being hard on the engines, but Warp 8 didn’t appear to be any harder than Warp 3, 4 or 5. So why would you ever go Warp 3? Just wasting time for the hell of it? I’d think Starfleet would want its battleships to be busier than that.
Now, halfway through the Next Generation series there was some lame ass episode about how high warp speeds caused some sort of interstellar environmental problems with some kind of particle fields or clouds or some sort of plot-y-ons. It was idiotic. But prior to that, and anywhere the plotyons weren’t affected by warp, there was no reason to select Warp 5 instead of Warp 8. So why did they?
Better dilithium crystal mileage.
Or to preserve anti-matter stores.
Zog help me, I remember that too!
RickJay, no ship goes its maximum safe speed at all times. Sometimes you’re not in a hurry, sometimes local navigational conditions favor a slower speed, sometimes you want to save fuel (reaction mass, deuterium, in ST terms), sometimes you just want to save wear and tear on your engines.
The real purpose of the Heisenberg Compensator is to keep them from randomly jumping around in their scripts.
Far more important are the Bergenholms.
I agree with you for a couple of reasons. First, usually there is only one speed in hyperspace. Even if you have a bunch (the way I do FTL travel in my sf universe) you wouldn’t have Warp 4.5. Second, they can clearly see ships in different warps from them, which you couldn’t do if warp meant hopping into hyperspace. Finally, they went into emergency reverse warp to get away from the Romulan weapon in Balance of Terror. If they had hopped into hyperspace this wouldn’t be a problem.
However, I think some other space is used for subspace radio. I seem to remember a particularly bad TNG episode built around alien abductions, where the aliens came from some other subspace. But it might be a nightmare some aliens planted in my mind.
[sets up the gag]
Just how do they work, anyway?
[/sets up the gag]
[takes guess at the gag]
I’m really not certain.
[/takes guess at the gag]
Quite well, thanks.
Stolen from Michael Okuda, if I’m not mistaken.