In one minute

Ken Olum takes up whether the spacetime metric can be manipulated to allow very rapid travel between distant points, as in the Alcubierre and Krasnikov examples. Defining faster-than-light travel is subtle, and he shows a metric that seems to allow it but is just flat space. He defines superluminal travel as a path that reaches a destination surface earlier than any neighbouring path. With that definition and the generic condition, he proves superluminal travel requires violating the weak energy condition, that is, negative energy density. Known examples already needed negative energy densities, and this result shows the requirement is general rather than a feature of particular designs.

Superluminal travel requires negative energies