While tantalizing, Alcubierre’s design has a fatal flaw. To provide the necessary distortions of spacetime, the spacecraft must contain some form of exotic matter, typically regarded as matter with negative mass. Negative mass has some conceptual problems that seem to defy our understanding of physics, like the possibility that if you kick a ball that weighs negative 5 kilograms, it will go flying backwards, violating conservation of momentum. Plus, nobody has ever seen any object with negative mass existing in the real universe, ever.
These problems with negative mass have led physicists to propose various versions of “energy conditions” as supplements to general relativity. These aren’t baked into relativity itself, but add-ons needed because general relativity allows things like negative mass that don’t appear to exist in our universe—these energy conditions keep them out of relativity’s equations. They’re scientists’ response to the unsettling fact that vanilla GR allows for things like superluminal motion, but the rest of the universe doesn’t seem to agree.
The energy conditions aren’t experimentally or observationally proven, but they are statements that concord with all observations of the universe, so most physicists take them rather seriously. And until recently, physicists have viewed those energy conditions as making it absolutely 100 percent clear that you can’t build a warp drive, even if you really wanted to.