Historical research guide · 0622 · 1999
On the (im)possibility of warp bubbles
Chris Van Den Broeck
In one minute
Chris Van Den Broeck — the physicist who months earlier found the trick that cut the Alcubierre warp drive’s energy bill by dozens of orders of magnitude — takes stock of what a warp bubble actually costs. He gathers the objections raised since Alcubierre’s 1994 paper and sorts them into the ones that hold and the ones that do not. The claim that quantum fluctuations must blow up at the bubble’s horizons, he argues, is questionable for a bubble that went superluminal only a finite time ago, much as a freshly formed black hole is not yet in equilibrium. The enormous negative energy the quantum inequality demands turns out to be a fact about one particular shape, not about warp drives: his own small-neck, large-pocket geometry brings the total down to stellar magnitude while respecting the bound. What survives is a question of motion — above light speed the exotic matter in the outer wall would have to outrun the local light cone. And subluminal bubbles, he says plainly, are still open.
Connection
Chapter 4 needs to know exactly which parts of the warp-drive problem are settled and which are still live, and this is the paper that separates them: the energy bill is a design variable, the horizon objection is unproven, and the honest frontier is the subluminal bubble — the same accounting continued on this site by McMonigal, Lewis and O’Byrne at /library/stm-ae326cd1a7 and by Santiago, Schuster and Visser at /library/stm-467f9a2835.
From the source
Applying Ford and Roman’s quantum inequality forces the warp bubble wall to be very thin, and Ford and Pfenning showed that a bubble of 100 metres radius would then need a total negative energy of at least about 6.2 times 10 to the 62nd multiplied by the bubble speed, in kilograms — ten orders of magnitude larger than the total positive mass of the visible universe.Section 4, unreasonably high energies, Equation 2
That figure is a property of the geometry chosen, not of warp drives as such: keeping the surface area of the bubble itself microscopically small while expanding the spatial volume inside it reduces the required total energy to stellar magnitude, in a way that satisfies the quantum inequality.Section 4, Equations 3 and 4
The price of that reduction is that the energy densities remain very large and the spacetime carries structure with sizes only a few orders of magnitude above the Planck scale.Section 4, closing paragraph
Hiscock’s argument that vacuum fluctuations diverge at the particle horizons inside a superluminal bubble was computed in one space dimension and assumes the field has reached thermal equilibrium; it is questionable whether the divergence appears at all for a bubble that went superluminal and developed its horizons a finite time in the past, the situation of a newly formed black hole.Section 3, quantum fields on an Alcubierre background
For any bubble speed above the speed of light, all the exotic matter outside a critical surface must move in a spacelike direction relative to the local light cone, which reads physically as the outer shell being unable to keep up with the rest of the bubble; a trailing tail of exotic matter might circumvent it, but probably at the cost of a naked curvature singularity at the front.Section 5, energy moving locally faster than light
Subluminal bubbles remain an open possibility and microscopic ones might even occur naturally: with no horizons there is no divergence of vacuum fluctuations and no tachyonic motion of exotic matter, the negative energy densities may be supplied partly by the curvature’s own effect on the vacuum, and the open question is whether a subluminal-warp-like spacetime can be built that needs no negative energy at all — for which no ansatz yet exists.Section 6, summary
The way in
https://arxiv.org/abs/gr-qc/9906050How to cite it
Chris Van Den Broeck (1999) On the (im)possibility of warp bubbles arXiv:gr-qc/9906050