Historical research guide · 0380 · 1994
The warp drive: hyper-fast travel within general relativity
Miguel Alcubierre
In one minute
Miguel Alcubierre’s 1994 paper gives a spacetime metric for a compact region of flat local space with expansion behind it and contraction ahead. A craft inside follows a free-fall path: it does not move faster than light through its immediate surroundings, feels no proper acceleration, and keeps time with distant clocks. The engineered quantity is distance, not local speed. Alcubierre derives the stress-energy required by the metric and finds negative energy density in the bubble wall. He points to the Casimir effect as a quantum setting where negative energy densities appear. The paper supplies a geometric solution and its energy condition; it does not report a constructed bubble, a propulsion demonstration, or a measured reduction of travel distance.
Connection
Chapter 4 begins here. This is the published spine of metric engineering — the paper that put ‘the distance is the engineered quantity’ into a mainstream gravity journal and set the terms of the whole programme. What later work changed is the price and the shape: Van Den Broeck’s 1999 bottle cut the exotic-energy requirement by many orders of magnitude, Pfenning and Ford bounded how much negative energy quantum field theory will lend you, and Bobrick and Martire showed in 2021 that subluminal warp shells can be built from positive energy alone.
From the source
A purely local expansion of spacetime behind a spaceship and an opposite contraction in front of it will carry the ship between two stars in an arbitrarily short time, measured both on board and by an observer who stayed at the point of departure.Abstract; Equations 1–8; Equations 15–17
Nothing in the construction moves faster than light through its own local space: the craft stays inside its own light-cone throughout, because light is carried along by the same distortion.Opening paragraphs, p. 2; discussion following Equation 17
The ship’s world line is a geodesic on which proper time equals coordinate time, so it undergoes no proper acceleration and no time dilation however large its coordinate acceleration becomes, and tidal forces near it stay small when the pocket is comfortably larger than the ship.Equation 13 and the two paragraphs following it
The whole effect lives in the shift vector: the three-dimensional slices stay flat and the lapse function is exactly one, so spacetime is flat everywhere except within a region of radius of order R around the ship, and the volume elements expand behind it and contract ahead of it.Equations 2–5 and Equation 8; expansion in Equation 12 and Figure 1
Observers whose motion is normal to the slices measure an energy density that is negative everywhere in the wall of the pocket, so the geometry violates the weak, dominant and strong energy conditions and calls for exotic matter, exactly as traversable wormholes do.Equations 18–19 and the paragraph following
Quantum field theory already permits regions of negative energy density in special circumstances — the Casimir effect is Alcubierre’s own example — so the requirement for exotic matter does not by itself rule the geometry out.Closing discussion, p. 9
The way in
https://arxiv.org/abs/gr-qc/0009013How to cite it
Miguel Alcubierre (1994) The warp drive: hyper-fast travel within general relativity doi:10.1088/0264-9381/11/5/001