A “warp drive” with more reasonable total energy requirements
Chris Van Den Broeck
Abstract and summary · read the original at the source
In one page
Chris Van Den Broeck, then at the Katholieke Universiteit Leuven, took Miguel Alcubierre’s warp geometry and changed one thing about it. Alcubierre’s bubble has to be big enough to hold a ship, and Michael Pfenning and Larry Ford had shown that quantum field theory forces the bubble wall to be extraordinarily thin, which pushes the bill for a hundred-metre bubble to roughly ten to the sixty-second kilograms of energy below the ambient vacuum level — orders of magnitude more than all the visible matter there is. Van Den Broeck’s move is to keep the outside of the bubble microscopically small, a few femtometres across, while expanding the volume of space inside it, so the pocket the ship rides in measures two hundred metres from within. With that shape the bill falls to a few solar masses, accompanied by a comparable amount of ordinary positive energy, and the quantum inequality that limits such dips is satisfied with room to spare.
Why it matters hereChapter 4 is metric engineering, and this is the paper that turned the warp drive from an impossible bill into a hard engineering one: the same geometry, priced down by more than thirty orders of magnitude by changing the shape of the pocket rather than the physics. Chapter 2 is where the currency comes from, since the whole bill is denominated in regions below the vacuum’s ambient level.
What it claims
01A minor modification of the Alcubierre geometry — multiplying the spatial part of the metric by a function that keeps the warp bubble’s outer surface area microscopically small while expanding the spatial volume inside it — dramatically improves the total energy requirements for a bubble able to transport macroscopic objects, bringing the total negative mass needed to the order of a few solar masses with a comparable amount of positive energy.Abstract; Section 2, Equation 4 and conditions 5
Published and peer-reviewed02The figure being improved on is Ford and Pfenning’s: for a bubble of radius 100 metres the quantum inequality forces the wall so thin that the total energy below the ambient vacuum level comes to at least 6.2 times ten to the sixty-second kilograms times the bubble speed, which for a speed near that of light is ten orders of magnitude larger than the total positive mass of the entire visible universe.Section 1, Equation 3
Published and peer-reviewed03The worked example takes an expansion factor of ten to the seventeenth, an inner pocket radius and transition thickness of one femtometre each, and an Alcubierre bubble radius of three femtometres, so the outermost surface of the warp bubble has the area of a sphere about three femtometres across while the inner diameter of the pocket is 200 metres; the wall itself cannot be thicker than about a hundred Planck lengths times the speed, which is the Ford and Pfenning limit.Section 3, Equations 6 and 7
Designed, not yet built04Adding up the pieces at that setting: the wall region carries about minus 6.3 times ten to the twenty-ninth kilograms times the speed, and the transition region where space is being blown up carries about minus 1.4 times ten to the thirtieth kilograms of negative energy together with 4.9 times ten to the thirtieth kilograms of positive energy — each of them a few solar masses.Section 3, Equations 9, 15 and 16
Published and peer-reviewed05The construction is checked against the Ford and Roman quantum inequality rather than assumed to pass it: choosing the expansion profile as a polynomial of degree eighty, so that its second derivative vanishes at the outer edge, gives a minimum curvature radius of 1.4 times ten to the minus thirty-fourth metres, about ten Planck lengths, and sampling on a tenth of that time the measured energy density of about minus 6.6 times ten to the ninety-third kilograms per cubic metre sits well inside the bound of about minus 9.2 times ten to the ninety-fourth.Section 3, Equations 12, 17, 20 and 22
Published and peer-reviewed06Van Den Broeck presents the result as a proof of principle about total energy rather than a realistic proposal, and names what is still open: the energy densities involved remain very large, generating energy below the ambient vacuum level in that quantity is unanswered, and the geometry still contains structure only a few orders of magnitude above the Planck scale, which he reads as generic for spacetimes allowing effective superluminal travel — while noting that the modified drive now falls in the mass bracket of a large traversable wormhole and, unlike a wormhole, has trivial topology.Section 4, Final remarks
What to watch
Read it · abstract
Abstract
I show how a minor modification of the Alcubierre geometry can dramatically improve the total energy requirements for a ‘warp bubble’ that can be used to transport macroscopic objects. A spacetime is presented for which the total negative mass needed is of the order of a few solar masses, accompanied by a comparable amount of positive energy. This puts the warp drive in the mass scale of large traversable wormholes. The new geometry satisfies the quantum inequality concerning WEC violations and has the same advantages as the original Alcubierre spacetime.
The way in
https://doi.org/10.1088/0264-9381/16/12/314Published as Classical and Quantum Gravity 16 (1999) 3973–3979, report number KUL-TF-99/18. The arXiv posting gr-qc/9905084, version 5 of 21 September 1999, carries the arXiv assumed licence for submissions of 1991 to 2003, which grants arXiv a distribution licence and is not a Creative Commons licence, so the author’s abstract stands here and the full text is read at the source. Equation numbers in the locators are the arXiv version’s. Two companion sheets are read with this one: Miguel Alcubierre’s 1994 warp metric is stm-fc5383ec73, and the Pfenning and Ford quantum-inequality bound this paper answers is stm-710bf626ca.
How to cite it
Chris Van Den Broeck (1999) A “warp drive” with more reasonable total energy requirements. doi:10.1088/0264-9381/16/12/314
Where it sits in the curriculum