To understand Broeck's trick, imagine that a race of two-dimensional people live in an enormous rubber sheet. Now connect a large bubble to this rubber sheet, with a very narrow neck. Just like the Tardis, this bubble is, to our two-dimensional friends, small on the outside, but huge on the inside. Now the really thrilling thing about bubbles with a small neck like this one, is that they take only a minuscule amount of energy to make. But using this mathematical trick, a bubble big enough to hold the Starship Enterprise could be made with just a gram of negative matter.
Negative matter is weird stuff.
Negative matter has a negative energy, and has less mass than plain-old empty space. This is the next problem. We don't know, yet. So we have a theory that says it's possible to get to the stars without crossing the distance in between, but we have no idea of how to build the machines to do it. So for the time being, it's back to the campfire for a bit more star-gazing.