The 2020–2021 claims
Lentz (2020) and Fell and Heisenberg (2021) constructed superluminal “solitons” whose energy density is positive for observers moving with the bubble’s coordinate frame. Santiago, Schuster and Visser pointed out that the energy conditions require positive energy for all observers, and showed that all physically reasonable warp drives violate the null energy condition. The debate shifted the field’s attention to what positive energy can actually achieve.
Positive-energy warp drives below light speed
Bobrick and Martire (2021) described any warp drive as a shell of matter with a modified interior and presented the first general model of subluminal, positive-energy warp drives. Fuchs et al. (2024) built such a solution numerically for constant velocity, by combining a stable matter shell with a shift similar to Alcubierre’s, and confirmed that it satisfies all energy conditions.
What that means
A subluminal warp drive does not beat light. Its interest lies elsewhere: it moves a region of space with its contents, which could change what acceleration and time feel like for passengers. It also shows the mathematics of warp drives can be made consistent with ordinary matter.