[Dead Corpse]

Some things are simply impossible given the nature of the universe.

Agreed. And some rather surprisings things are very possible.

This could very well be one of those things.

Again, just because you can't see how this can be done, doesn't mean it won't work.

[Mycroft Holmes]

There is an interesting bit in special relativity that tells you what the mass of an object is at velocity:

m = mass at velocity
m₀ = rest mass
V = velocity of interest
c = speed of light

As an object is accelerated it acquires mass in accordance with the formula above. As V² approaches c² the ratio of the two approaches 1 and the square root of 1 minus the ratio approaches zero and the mass at velocity approaches infinity.

If somehow you were able to exceed the speed of light with a real rest mass you end up dividing by an imaginary number (the square root of -1, or i ) and you end up with an apparent mass with an imaginary component.

An interesting thought experiment is to start with an imaginary rest mass. This requires that the velocity always be greater than c to yield a real apparent mass. And no, I have know idea what it means for mass to have an imaginary component.

But there it is.

Check out Relativistic velocity transformation as a genitor of transformation equations for the gory details of the math.