Historical research guide · 0574 · 2007
Warp Drive: A New Approach
Richard K. Obousy · Gerald B. Cleaver
In one minute
Obousy and Cleaver take the warp drive out of pure general relativity and hand it to quantum field theory. Earlier warp papers, beginning with Alcubierre’s in 1994, wrote down a spacetime in which space contracts ahead of a craft and expands behind it — but none of them said where such a bubble would come from. This one names a source. In models with a compact extra spatial dimension, the Casimir energy of the graviton modes trapped in that dimension is a candidate for the cosmological constant, the term that drives cosmic expansion, and it varies as the inverse fourth power of the dimension’s radius. Squeeze that radius locally and the local expansion rate rises with it: their relation is that the Hubble rate goes as one over the radius squared. They then run the numbers — a shrink by a factor of ten trillion for light-speed expansion, about ten to the forty-fifth joules for a bubble around a ten-metre craft — and label them back-of-the-envelope. What they leave open is how to move an extra dimension at all.
Connection
Chapter 4 treats propulsion as engineering the metric rather than pushing on propellant, and this paper supplies the mechanism earlier warp papers left out: the vacuum energy of chapter 2 and the expansion of space are one adjustable quantity, so a device that changes the vacuum locally changes the distance a craft has to cross.
From the source
Summing the zero-point oscillations of quantum field theory to a Planck-scale cut-off gives a vacuum energy density of order ten to the seventy-first GeV to the fourth, against an observed value of order ten to the minus forty-eighth — a mismatch of ten to the one hundred and nineteenth, which the authors call by far the worst prediction of theoretical physics.Section II; Equation (2)
The vacuum energy carried by the Kaluza–Klein graviton modes of a compact extra dimension can be calculated by dimensional and zeta-function regularisation and associated with the cosmological constant; the result varies as the inverse fourth power of that dimension’s radius.Section IV; Equations (16) and (17)
Because the Hubble rate goes as the square root of the cosmological constant, and the cosmological constant goes as the inverse fourth power of the extra dimension’s radius, the Hubble rate goes as one over that radius squared — so a technology able to increase or decrease the radius locally would locally adjust the expansion and contraction of spacetime and generate a warp bubble.Section V; Equations (17)–(19)
Independently of the quantum calculation, solving the vacuum Einstein equations in five dimensions for an empty, flat toy universe with no cosmological constant gives the Hubble rate of the three large dimensions as minus the Hubble rate of the compact one: the shear of a contracting dimension inflates the remaining dimensions.Section V; Equations (20)–(25)
On back-of-the-envelope figures the authors give, reaching light-speed local expansion requires shrinking the extra dimension by a factor of ten trillion — from the ADD model’s micrometre upper bound to about ten to the minus nineteenth metres — and injecting about ten to the forty-fifth joules into a bubble enclosing a thousand cubic metres, an amount that would drop dramatically for a thin shell of modified spacetime rather than a filled bubble.Section VI; Equations (26)–(31)
The open problem the paper hands to future work is how to manipulate an extra dimension locally at all; the authors point to string theory, in which dimensions are held compact by strings wrapping around them, and ask whether string tension or winding modes could be locally altered, with the energy cost and the resulting acceleration as the calculations to do next.Section VIII, Conclusions
The way in
https://arxiv.org/abs/0712.1649How to cite it
Richard K. Obousy, Gerald B. Cleaver (2007) Warp Drive: A New Approach arXiv:0712.1649