masses. Later in 2003, by slightly modifying the Van den Broeck metric, Serguei Krasnikov reduced the necessary total amount of negative mass to a few milligrams. Van Den Broeck detailed this by saying that the total energy can be reduced dramatically by keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble. However, Van Den Broeck concludes that the energy densities required are still unachievable, as are the small size (a few orders of magnitude above the Planck scale) of the spacetime structures needed. In 2012, physicist Harold White and collaborators announced that modifying the geometry of exotic matter could reduce the mass–energy requirements for a macroscopic space ship from the equivalent of the planet Jupiter to that of the Voyager 1 spacecraft (c. 700 kg) or less, and stated their intent to perform small-scale experiments in constructing warp fields. White proposed to thicken the extremely thin wall of the warp bubble, so the energy is focused in a larger volume, but the overall peak energy density is actually smaller. In a flat 2D representation, the ring of positive and negative energy, initially very thin, becomes a larger, fuzzy torus (donut shape). However, as this less energetic warp bubble also thickens toward the interior region, it leaves less flat space to house the spacecraft, which has to be smaller. Furthermore, if the intensity of the space warp can be oscillated over time, the energy required is reduced even more. According to White, a modified Michelson–Morley interferometer could test the idea: one of the legs of the interferometer would appear to have a slightly different length when the test devices were energised. Alcubierre has expressed skepticism about the experiment, saying: "from my understanding there is no way it can be done, probably not for centuries if at all". In 2021, physicist Erik Lentz described a way warp drives sourced from known and familiar purely positive energy could exist – warp bubbles based on superluminal self-reinforcing "soliton" waves. He also claimed that he will work on reducing the (positive) energy requirement. Placement of matter Krasnikov proposed that if tachyonic matter cannot be found or used, then a solution might be to arrange for masses along the path of the vessel to be set in motion in such a way that the required field was produced. But in this case,