But that's what he said: "according to his [the rider's] clock" it would take about 3 seconds to reach the center of the Milky Way. So yes, he is talking about how fast the riders perceive it, which is all they care about, since they wrote off their entire families for dead before they left.
Now the strange thing about traveling at 1516c (i.e. far greater than the speed of light), is that the time dilation equation yields an imaginary time, in this example 1 / sqrt(1 - 1516^2). I'm not sure how that translates into a perceived travel time of 21 years.
Warp engines make a little stable bubble of space and shift what's around it, so onboard time matches galaxy time, and you can jaunt a significant way across the galaxy and still be home in a few years Earth time.
Yeah, I should've been clearer. But writing off your entire family as dead is only a consequence of riding the proton, so it has nearly no advantage. And again, there's suspended animation, so not only can you make the trip nigh-instantly (to you) on the ship, you can get back before people forget you exist.
It wasn't your clarity, it was your tone. If you're gonna go around "BZZZT WRONG!!!"-ing people, you really ought to be sure you understand the physics. As written, your post completely misses the boat about what relativity is all about.
I think the imaginary time should be taken as an indication that it doesn't make sense to talk about travelling at v > c, in terms of a Special Relativistic framework at least :)
Now the strange thing about traveling at 1516c (i.e. far greater than the speed of light), is that the time dilation equation yields an imaginary time, in this example 1 / sqrt(1 - 1516^2). I'm not sure how that translates into a perceived travel time of 21 years.