Alcubierre originally wrote down the spacetime with a warp drive bubble inside. Unfortunately the matter the field equations say is necessary to form the bubble is physically unrealistic.
Why is the buble physically unrealistic? Just curious.
Also, the deeper problem is that quantum field theory forbids the kind of matter the drive requires from existing. Basically you need large negative energy densities, but quantum field theory doesn't allow energy densities that large.
Why is the universe predisposed to positive energy densities as opposed to negative? And what does this exactly mean? How can you have negative energy? I am not really understanding this process. Will do more reading.