Editing Alcubierre drive (section)

===Wall thickness===
The amount of negative energy required for such a propulsion is not yet known. Pfenning and Allen Everett of [[Tufts University|Tufts]] hold that a warp bubble traveling at 10-times the speed of light must have a wall thickness of no more than 10<sup>−32</sup> meters—close to the limiting [[Planck length]], <span class=nowrap>1.6 × 10<sup>−35</sup></span> meters.<ref>{{Cite arXiv |arxiv=gr-qc/9805037 |first=Michael John |last=Pfenning |title=Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes. |pages=1692 |year=1998}}</ref> In Alcubierre's original calculations, a bubble macroscopically large enough to enclose a ship of 200 meters would require a total amount of exotic matter greater than the mass of the observable universe, and straining the exotic matter to an extremely thin band of 10<sup>−32</sup> meters is considered impractical. Similar constraints apply to [[Krasnikov tube|Krasnikov's superluminal subway]]. Chris Van den Broeck constructed a modification of Alcubierre's model that requires much less exotic matter but places the ship in a curved spacetime "bottle" whose neck is about 10<sup>−32</sup> meters.<ref name=Broeck/>