FTL and imaginary mass?

I've seen some good explanations for FTL travels in several books. e.g. Nemesis from Asimov, where he explains that there are two dual universes, one with "real" mass and the other with "imaginary" mass (you know as in the complex numbers). In one of them it is not possible to go faster than the light, and in the other one it is not possible to go slower than the light. Objects with mass = 0 are the frontier between the two universes. In fact both universes coexist in the same space, but one cannot be sensed from the other. Asimov explains how an object with "real" mass can be transformed into an object with "imaginary" mass, thus accelerating it more than the light. The curious thing is that if you take a look at the Lorentz equations if such objects with imaginary mass exist. All the speculations of Asimov are right!! So, this doesn't break any physical law. It's just an speculation that cannot be belied!

First Asimov's speculations are 'right' because he knew about the laws of physics and wrote his story with the intent of creating a plausible sounding basis for his FTL drive. Rather like stories that base their FTL drives on the tendency of particles to 'quantum jump' between to points. Physics predicts this, so the author postulates that some method has been found to scale this up to the macro scale while the inhibitions against this have been disproven.

Second, ignoring the lack of any proof whatsoever for another universe of any type existing in parallel with our own, this method of FTL has a fundamental flaw. It ignores how an object with mass (like a ship) is supposed to get from a state of moving slower than light to one in which it is moving faster than light without actually ever moving at the speed of light. The Lorentz equations and others relating to relativity state that objects with mass must always move slower than light, will increase in mass as they approach lightspeed and will achieve infinite mass at lightspeed. They also state that objects moving faster than light will have imaginary mass and that this mass will increase as they slow down toward lightspeed and become infinite at lightspeed. So for a normal mass object it will take infinite energy to accelerate to lightspeed and for an imaginary mass object it will take infinite energy to slow down to lightspeed. You can get infinitely close to the barrier but you cant cross it.

Addendum:
It's true that if you have particles with imaginary rest masses then you can get real momenta and energies for superluminal motion (it might do fun things to gravity though!). That's not the problem with FTL in relativity - the problem is that if you have FTL using any method, then it's very easy to violate causality (i.e. to make a time machine). It's quite easy and fun to demonstrate this with spacetime diagrams!