(I'm using the convention that 'c' is the speed of light here)
I'll answer this in two parts. As for moving at greater than the speed of light, that's a question scientists have to raise their hands up in the air about, shrug, and go "Some particles might exist that can do it." As I've heard it, when we truly can unify all the forces (i.e. Quantum Gravity and figuring out how it merges with the strong and weak nuclear forces and the electromagnetic force at high enough energy) we may know. As it stands, the speed of light is kind of like the fence that keeps everyone in their own little playgrounds. Us in ours, and things that may move faster than c, in theirs. So mind you, while we say the speed of light is the fastest thing is, it's the fastest thing we can actually observe, so it still is a pretty nice limit, given everything else is theoretical.
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So more directly answering your question, I've been curious before about the use of those theoretical particles in space travel. We wouldn't be able to go faster than the speed of light, because we have mass, but if those super c particles can impart momentum in some way to our own world (Which I doubt, otherwise we should be able to observe them) we could have a very effective way to accelerate ships quickly to near c speeds.
As for a back door method, such as wormholes and the like, mathematically, it is possible to create one. You just need negative energy and positive pressure as I remember it. Kind of funky, not impossible, but requires some rather odd material to make. That would be something you could traverse, in theory. Any other kind as a solution to Einsteins theory of General relativity, collapse rather spectacularly.
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A wormhole is pretty much a solution to General Relativity that connects two "Events" as they are called in the business, where "distance" is zero. I don't know much about it since I am only beginning to study GR, but that sounds like what it would be. Mind you, I dont think anyone knows what form it would take. Big, Small, Purple, Blue? Who knows
Will we be able to create one for our own purposes? I don't see how, but given the crazy stuff mankind has figured out before, who knows. The issue is you have to get to the other end and make the other wormhole as "I" understand it. I am not even sure how one has the two ends technically connected. I suspect is has to do with forming the hole in a very specific way so that you can choose the other place where it takes place by the math involved. And who knows, maybe we'll get lucky and that means we dont have to travel to the other end. It's all up in the air at this point.
Also, neat side point. Placing wormholes in certain places, i.e. High Gravity fields, you can travel back in time theoretically.
Neat stuff.