Here is the problem with saying that something can go faster than the speed of light. All massive things are affected by their relative velocity. As they go faster, they get shorter in the direction they are traveling, and they become heavier. The equation that describes this is sqrt(1-(v/c)**2) . For values of v that are very small compared to c, this is 1.0. For example, if you drive 100 Km/hr, you will gain about 1 part in ten billion weight: if you weigh 50 Kgs at rest, you will weigh 50.0000000005 Kgs at 100 Km/hr. However, if you drive 240,000 Km/sec or 4/5 c, then you will effectively weigh 50 / sqrt (1-(16/25)) = 50 / sqrt(9/25) = 50 / (3/5) = 83 Kg.

And we observe this experimentally. Protons, which are very very small, suddenly wieght as much as fruit flies. We believe that this theory describes the real world.

And therein lies the problem. When something goes faster than the speed of light, then its effective mass becomes imaginary. You have a B.A. in mathematics from a prestigious university (Auburn? I think?), so do the math. We do not under stand the meaning of negative mass as we have never observed gravitational repulsion, and imaginary mass has no meaning either. Also, in order to go from slower than light to faster than light requires an infinite amount of energy, and that can't happen. So even if it is possible to go faster than the speed of light (and the equations are consistent - you can have a universe where nothing goes SLOWER than the speed of light), it is challenging to understand how something in our universe could interact with something in this other universe. Therefore, it will be really hard to develope experimental evidence that this other universe exists.

Now, if you are looking for a challenging mathematical exercise, one that is worthy of your talents and energies, try modifying Maxwell's equations to admit the existance of magnetic Monopoles.