Historical research guide · 0625 · 2021
Positive energy warp drive from hidden geometric structures
Shaun D B Fell · Lavinia Heisenberg
In one minute
Shaun Fell and Lavinia Heisenberg, at ETH Zürich, take on the objection that has followed warp drives since 1994 — that carrying a craft faster than light inside a bubble of curved space demands negative energy. They rewrite the problem. Splitting the shift vector, the part of the metric that does the moving, into a gradient piece and a swirling piece, they find that the energy measured by an observer riding with the bubble is a purely geometric quantity: it is the curvature of a single scalar potential, read off in three two-dimensional slices. Seen that way it becomes clear why Alcubierre’s original needed negative energy — it used only one component of the shift, and that choice forces the sign — and it becomes straightforward to design shapes that do not. They present one: a smooth soliton with everywhere-positive energy whose central region travels at 1.26 times the speed of light, with a total energy four orders of magnitude below the Sun’s rest mass, steered by moving energy around rather than adding any.
Connection
Chapter four is metric engineering, and this is the paper that moves the warp problem from ‘needs exotic matter’ to ‘needs the right geometry’ — the positive-energy configuration is a design target other groups can now test.
From the source
Decomposing the shift vector into a gradient part and a divergence-free part shows the Eulerian energy density is geometric: for a purely gradient shift, eight pi times the density equals the sum of the three second-order principal minors of the Hessian of the scalar potential, so the curvature of that potential in two-dimensional subspaces decides whether the energy is positive.Section 3.1, equations (8) and (9)
Any configuration built on a single component of the shift vector — the Alcubierre ansatz — has a Hamiltonian constraint that reduces to minus one half of a sum of squares, which is why the classical drives come out negative; satisfying the weak energy condition requires at least two non-zero shift components.Section 3.1, equation (5)
A smooth shift potential, at least twice differentiable, yields a soliton whose energy density is positive everywhere and finite in total, with a central shift magnitude of about 1.26 — superluminal relative to distant observers — and a direction of travel set by the shape of the energy distribution.Section 3.2, equation (11) and Figure 2
The drive is tuneable without changing its energy budget: concentrating the same total energy behind the craft and thinning it in front raises the shift where the craft sits, so speed is set by the geometry of the distribution rather than by the amount of energy — the authors call this a first of its kind.Section 3, opening; Section 3.2
With Newton’s constant and the speed of light reinstated, the example configuration needs about 9.25 times ten to the forty-third joules on an initial slice, four orders of magnitude below the Sun’s rest-mass energy of about 1.78 times ten to the forty-seventh joules; its peak density of 3.2 times ten to the twenty-sixth kilograms per cubic metre would likely collapse, which tuning the Gaussian weight is expected to fix.Section 3.4
Compact regions of the distribution still violate the weak energy condition through the principal-momenta constraints, and the strong and dominant conditions are violated as well; the authors argue horizon formation on the way from subluminal to superluminal is what would protect chronology, and name both as the work still to do.Sections 3.2 and 3.3
The way in
https://doi.org/10.1088/1361-6382/ac0e47How to cite it
Shaun D B Fell, Lavinia Heisenberg (2021) Positive energy warp drive from hidden geometric structures doi:10.1088/1361-6382/ac0e47