Let me just say, I'm not a Trekkie. I like Star Trek, but I don't even own any action figures. Kay? Now, I read in Popular Science about how warp drives work(yes, they can build them), they do bend space, but not the way Swift said. The bend the space in front of you so that it is smaller than the space behind you, propelling you forward. At least, that's the simple way of describing it. I don't remember the "facts." We have the technology to do this, or, at least, our technology is advanced enough that we could build the technology to do this. However, it would take more energy than we can produce right now.
Also, Swift, it is impossible to reach the speed of light, as we near it, light would begin to travel faster, and your ship would appear to travel slower. Special reletivity for the win.