3. An early approach. The Alcubierre drive and the necessity for negative energy.
By now all warping effects generated by masses, EM fields or electron beams were of a single type. That is, in gravitation there is just one way to warp the space. Let us say for simplicity that the gravitational potential created by all masses is downwards (this is the “classic” picture of a ball that warps the fabric of space-time in which it sits, downward). If we try to find the mass equivalent of the positive and negative electric charges we cannot find them in our known universe. There is just one type of known mass and this means that all matter warps the space in the same way (downwards).
But in the early 1990 Miguel Alcubierre speculated what would happen if we had also the other type of mass that would warp the space the other way – upwards (physicists called this the exotic matter). Then we could produce some type of “warp bubble” having the space warped in front of it the normal way we know (we called this downwards) and warped at its back the other way given by the exotic matter (unknown yet at the time when Alcubierre made first this speculation). This bubble would resemble with a traveling water wave, and the space ship would just ride on it. Or, to say a bit differently the bubble would contract the space in front of it and dilate the space on its back. Or again, with other words, the ship in the bubble would be in free fall (attracted the front of the bubble and repelled by its back), despite the fact that it is located in free space.
This metric is called the Alcubierre drive and its mathematical and geometric representations are given below.
$ds^2=(v^2 f^2 (r)-1)*dt^2-2vf(r)*dxdt+(dx^2+dy^2+dz^2)$
All nice and easy with the exception of two facts. First, at the time of beginning 90 years exotic matter was a physical impossibility and secondly, the quantity of exotic matter necessary to produce the upwards warping at the back of the bubble was huge (of the order of the known mass of the Universe). But the Alcubierre drive was indeed the first desired warp drive from Star Trek.
At the beginning people were skeptical, but until 2000 the geometry of the warp bubble was improved by different scientists. First by making smaller the diameter of the warp bubble and considering geometry of a “ship in a bottle” the necessary quantity of exotic matter was reduced to the size of Jupiter planet. Then by further improving the geometry of the bubble (nowadays it is considered that a torus surrounding the ship geometry is the best) the necessary mass is reduced further to reasonable (small enough) quantities.
But until about 1997-2000 the exotic matter was an (unrealizable) dream.