What the theory of Relativity shows is that it is impossible to take an object with mass, from our frame of reference, and accelerate it in such a way that it ends up going faster than light.
The theory does not "forbid" FTL, it just makes it impossible to take an object going slower than light and make it move faster than light in a vacuum.
Faster-than-light speeds are already observed in situations where we can slow down the speed of light (but that is not what you have in mind).
The speed limit (c) is the speed of light in vacuum. However, light itself travels slower through some mediums. For example, in water, light travels at (2/3) of the "speed-of-light".
Sub-atomic particles that are emitted by nuclear reactions at very close to c (for example, at 0.95 c) can, therefore, travel faster than the speed of light IN WATER, and that means that the particles will emit Cherenkov radiation, making them detectable.
http://en.wikipedia.org/wiki/Cherenkov_radiationThe theory of Relativity allows the existence of particles that go faster than light (and they even have a name: tachyons), but they too have the same problem - in reverse - they can't be slowed down below the speed of light.
http://en.wikipedia.org/wiki/TachyonsHowever, we have never observed any, and we have never found any evidence that these things even exist.
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In science-fiction, there are three ways that are used to invent FTL (at least, by the authors who try to make it sound believable).
1. Remove the ship from the fabric of space and make it travel outside of normal space. Where the ship reappears usually depends on a mix of luck and the navigator's skills (and the requirements of the plot).
2. Create a bubble and cause this bubble to "surf" along the warped hyper-surface of space. Objects inside the bubble (including the ship) are not moving relative to their local space (the inside of the bubble). However, the "warp engine" must warp the fabric of space.
3. Use corridors that connect different regions of space (wormholes) so that the vehicle only travels a short distance in the space of this corridor, which is a shortcut between two points in space.
All three ideas are based on some theoretical ideas that do exist in cosmology, but have NEVER been observed in the real universe.
All three ideas (and the tachyons) have been used in Star Trek (if you consider all the series).