The warp drive: hyper-fast travel within general relativity
Miguel Alcubierre
Abstract and summary · read the original at the source
In one page
Miguel Alcubierre, then at the University of Wales in Cardiff, published this five-page paper in Classical and Quantum Gravity in 1994, and every warp result since has been an argument with it. His move is to stop asking how to make a ship go fast and ask instead what shape space itself can take. He writes down a spacetime in which a small region — a pocket of ordinary flat space carrying the ship — has space expanding behind it and contracting in front of it. The ship never travels through its own neighbourhood. It rides a free-fall path, feels no acceleration, and its clock keeps the same time as the clocks it left behind, yet the round trip to a distant star can be made as short as you like, because the distance is what was engineered and not the speed. Alcubierre writes the bill out honestly: the wall of the pocket carries negative energy density, which ordinary matter cannot supply, and he points to the Casimir effect as the place where quantum theory already produces it.
Why it matters hereChapter 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.
What it claims
01A 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
Published and peer-reviewed02Nothing 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
Settled physics03The 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
Published and peer-reviewed04The 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
Published and peer-reviewed05Observers 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
Published and peer-reviewed06Quantum 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
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Read it · abstract
Abstract
It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the “warp drive” of science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.
The way in
https://arxiv.org/abs/gr-qc/0009013Published as Classical and Quantum Gravity 11-5, L73–L77 (1994); the arXiv posting of September 2000 carries the legacy arXiv licence assumed for submissions of 1991–2003, which grants arXiv a distribution licence and is not a Creative Commons licence, so the abstract stands here and the full text is read at the source.
How to cite it
Miguel Alcubierre (1994) The warp drive: hyper-fast travel within general relativity. doi:10.1088/0264-9381/11/5/001
Where it sits in the curriculum