While I applaud any alternative theories gaining ground, and making established scientists think outside the box, there are a few serious problems with the proposed FTL engine and the framework around it.
So, while I think it's certainly worth checking out, if not for more than pondering an alternative view, probably with lots of unconventional insights, there are a few serious problems with it.
For starters, as nutbal said: you can do it, or you cannot. That's pretty much the bottom line. Either the universe allows it, or it doesn't. Period.
Another problem is, with entering an "alternative dimension". To keep it to the point: if it would change the basic physical rules as much as to allow impossible things (in our universe) like FTL, it will kill everyone aboard. People are too dependent on the rules that govern this universe to survive, to be able to withstand others. Although we might be able to come up with a solution to that problem, don't hold your breath. Ask again in a few centuries.
We're not even able to grasp or experiment with the rules that govern our own universe to that degree, let alone an alternative set of rules we cannot experience at all.
And for another one, there are many more of these "warp-drive" ideas, which all offer a likewise solution to the main problem: they think of a way to circumvent the rules of this universe by going outside it and using the rules of another one. All possible and impossible combinations of forces and gravity-folding have probably been offered as possible ways to do just that, by now. And plenty of other things as well.
I think all those ideas are worth to be investigated, especially when they're internally completely consitent, which this one seems to be. It just doesn't confirm to the current consensus. It might be a great set of theories, that help us along, or just nutball ideas. But we don't know until we try and see.
