It is now that the speculation begins. When a velocity greater than light is introduced into the equations of special relativity we are left with the conclusion that an observer who is travelling faster than the speed of light relative to us is also travelling backwards in time. Equivalently, we are travelling backwards in time relative to him, from the intrinsic symmetry implied by travelling backwards in time. To answer this, consider two objects, one on either side of the light barrier. We will start with them stationary, and pseudo-stationary, relative to each other.
Lets assume it's an attraction.
As his time runs backwards, he would see the objects move apart. Similarly, if we begin by assuming that such objects repel we will find they attract for the observer on the other side of the light barrier. We can reason the same way for all forces and, indeed, all interactions in general. Therefore there can be no interaction of any kind between objects on either side of the light barrier. If such objects do exist we have no way of observing them directly.