I'm interested in NASA's work on the Alcubierre drive [1]. Still likely to require much more energy than we'll be able to produce in the near future, but 100 years ago we were just getting a firm handle on the basic mechanics of flight.
The Alcubierre drive is just a solution to the equations of general relativity that most probably can not be achieved in practice. Sure, maybe one day we will have drives like that, but we do not have any idea currently that even remotely resembles a warp drive permitted by the laws of nature.
> I think we understand negative energy density, we just don't know if it's possible in reality.
Exactly as in magic. When you propose things are possible if only X material with some magical property necessary for thing to work, that's speculative fiction. Especially when those constructs only make sense mathematically. Math isn't physics, but physics is math, there's an important implication there.
[1] http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/2011001...