Theoretically we can travel at a perceived faster than the speed of light we just don't have the technology or resources to do it (pretty much works similar to how Star Trek warp works, using a bubble to warp spacetime).
I would disagree with that. It's not just a matter of not having the technology. There are still huge theoretical issues (even if you manage to reduce the required energy) that would make a warp drive impossible. I've read the paper by Harold White and he doesn't address these issues. So it might seem to some readers that a warp drive is indeed feasible.
Let me elaborate:
The curvature of space-time can be described by the metric g
ab. But this curvature of space-time doesn't exist on its own; it is connected to the mass (or equivalently the energy) and the momentum of matter and radiation, described by the energy-momentum-tensor T
ab. So in order to curve space-time in a specific way, you need mass at the appropriate location.
Alcubierre has found a metric that could be the basis for a warp drive, but the required energy would be way to large. White has managed to reduce this energy significantly by modifying the metric.
The problem is that he only considered the total amount of energy necessary. But:
1) The mass that is needed for a warp drive needs to be negative! This would be the exotic matter that has already been mentioned in this thread. Matter with a negative mass would be radically different from everything we know. It would move in the opposite direction of the applied force. It cannot be mathematically ruled out that such exotic matter exists. But so far there is no evidence for its existence.
2) The bigger problem is that the matter needs to be at the appropriate location to create the metric. To achieve that the matter must move faster than light. So the problem of the space ship moving faster than light has been shifted to the exotic matter moving faster than light. Hypothetical particles that move faster than light are called tachyons. However, tachyons would violate causality if Lorentz invariance is assumed (see
http://en.wikipedia.org/wiki/Tachyonic_antitelephone). And Lorentz invariance has been extremely well tested. That means that the existence of tachyons is pretty much ruled out. No tachyons, no warp drive.
So even theoretically, the possibility of a warp drive is just incredibly unlikely.