STM-D-0779Paper2017Published and peer-reviewed

Warp drive basics

Miguel Alcubierre · Francisco S. N. Lobo

Abstract and summary · read the original at the source

In one page

Miguel Alcubierre wrote the warp metric down in 1994. Here he and Francisco Lobo set out, in one chapter, what that geometry actually is. A warp drive is not a fast ship. It is a pocket of ordinary flat space carried along by a distortion that contracts distance ahead of it and expands distance behind, and the crew inside ride a geodesic — weightless, their clocks running at coordinate time whatever the bubble’s speed. José Natário’s version sharpens the point: hold the volume elements fixed and the bubble simply slides, so the thing being engineered is distance along the direction of travel, not the swelling of space. The authors then price it. The geometry calls for energy below the ambient vacuum level, arranged in a torus around the axis of motion, at any speed at all — and in the weak-field regime that bill is a real fraction of the ship’s own mass. They also lay out Sergei Krasnikov’s alternative: a tube built on the outbound leg that makes the round trip, measured at home, arbitrarily short.

Why it matters hereChapter 4 is metric engineering — you travel by changing the distance rather than by pushing on propellant — and this is the clean textbook statement of the geometry every later design is built against, written by the man who found it. It is also where the authors say plainly what a warp bubble is: a reactionless drive that moves by interacting with the geometry of spacetime instead of expending reaction mass. Alcubierre’s original 1994 letter is at /library/stm-fc5383ec73, the Pfenning and Ford energy bill it works against at /library/stm-710bf626ca, Chris van den Broeck’s bottle-shaped answer to that bill at /library/stm-3ce9e507bb, and the Lobo and Visser linearised analysis this chapter summarises at /library/stm-f84341488f.

What it claims

01The Alcubierre geometry does not move the ship through space. The metric carries a form function that equals one inside the bubble and zero outside, the volume elements expand behind the ship and contract ahead of it, and the ship’s own worldline stays timelike for any bubble velocity — its proper time equals coordinate time, so the crew feel no acceleration and age normally.Section II A, Equations 1 to 4
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02The expansion of space is not the essential ingredient. In Natário’s version of the warp drive the contraction of distance along the direction of motion is compensated by an expansion of area elements perpendicular to it, so the volume elements are preserved and the bubble simply slides through space — which shows that what the drive engineers is distance along the direction of travel.Section I, Introduction
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03The energy the geometry requires sits below the ambient vacuum level, and it is not smeared through the bubble: it is concentrated in a toroidal region around the axis of travel. The volume integral of it scales as the square of the bubble velocity times the square of the bubble radius divided by the wall thickness, so a wide, fast, thin-walled bubble is the expensive case and a small, slow, thick-walled one is the cheap case.Section II C, Equations 7 to 11
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04Treated in linearised theory, with a finite-mass ship inside the bubble instead of a test particle, the warp drive is an example of a reactionless drive: the bubble moves by interacting with the geometry of spacetime rather than by expending reaction mass, and the ship is carried along with it. Demanding that the net energy stored in the warp field stay below the ship’s own mass-energy then fixes the allowed bubble velocity.Section III, Equations 22 to 31; Section VII, Summary and Conclusion
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05A superluminal bubble carries something like an event horizon. Photons sent forward from the ship slow, relative to the bubble, until they sit at rest at the point where the form function equals one minus one over the bubble speed, so they never reach the leading wall. The crew therefore cannot raise or steer the bubble from inside; the metric has to be laid down beforehand by an observer whose forward light cone contains the whole trajectory. Krasnikov’s tube is the standard answer — a corridor built on the outbound leg, static once made, in which the round-trip time read at the starting point can be made arbitrarily short.Section IV, Equations 32 to 36; Section V, Equations 37 to 49
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06The quantum inequality bound that gives the largest warp-energy figures is itself an open question. The authors note that quantum inequalities might not be fundamental, that they are violated in the Casimir effect, that classical non-minimally coupled scalar fields already violate the null and weak energy conditions, and that the inequalities do not rule out warp drive spacetimes but only constrain the geometry — which is why the linearised analysis, which needs no assumption about the source at all, is the more general statement.Section II D; footnote 3; Section III
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Read it · abstract

Abstract

"Warp drive" spacetimes and wormhole geometries are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other issues, to precisely formulate the notion of "superluminal" travel and communication. Here we will consider the basic definition and properties of warp drive spacetimes. In particular, we will discuss the violation of the energy conditions associated with these spacetimes, as well as some other interesting properties such as the appearance of horizons for the superluminal case, and the possibility of using a warp drive to create closed timelike curves. Furthermore, due to the horizon problem, an observer in a spaceship cannot create nor control on demand a warp bubble. To contour this difficulty, we discuss a metric introduced by Krasnikov, which also possesses the interesting property in that the time for a round trip, as measured by clocks at the starting point, can be made arbitrarily short.

The way in

https://arxiv.org/abs/2103.05610LICENCE. This is the chapter ‘Warp Drive Basics’ from the Springer volume Wormholes, Warp Drives and Energy Conditions (Fundamental Theories of Physics 189, 2017), which Lobo edited; the authors posted it to arXiv as 2103.05610 on 9 March 2021 under arXiv’s non-exclusive distribution licence, which is not an open licence, so this page carries the summary, the claims and the authors’ own abstract and sends the reader to the source. The chapter runs to seventeen pages with five figures and thirty references, from the Instituto de Ciencias Nucleares at UNAM in Mexico City and the Instituto de Astrofísica e Ciências do Espaço in Lisbon. Cross-references in the text to ‘Chapter 10’ and ‘the Chapter on the Quantum Energy Inequalities’ are to sibling chapters of the same volume.

How to cite it

Miguel Alcubierre, Francisco S. N. Lobo (2017) Warp drive basics. arXiv:2103.05610

Where it sits in the curriculum

The metric, warp drives and wormholes The unified picture