Alastair Mayer’s T-Space Blog

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. […] 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.

— Miguel Alcubierre, Class. Quantum Grav. 11 (1994), L73-L77.

The above quote is from the Abstract of Miguel Alcubierre’s now-famous (in some circles) 1994 paper, “The Warp Drive: Hyper-Fast Travel Within General Relativity” wherein he demonstrates that spacetime itself could be “warped” such that a bubble of normal spacetime within the warp could be translated at faster than light speeds. Of course there’s a catch; as Alcubierre puts it, “exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.”

What does he mean by “exotic” matter? He’s not just talking about something like anti-matter, which is merely normal matter where the elementary particle charges are reversed (negative protons and positive electrons, or positrons). He’s probably not talking about so-called “Dark Matter” either — although since nobody knows what Dark Matter is, one might argue the case. We do know, however, what Dark Matter is not — it does not have negative mass or react negatively to gravity. Exotic matter has just this property. You see, for the math to work out (don’t worry, I’m staying away from formulas, you can check the original paper for them if you like), the warp requires “negative energy” to be created. It also requires a heck of a lot of it.

Some years later, Chris Van Den Broek revisited Alcubierre’s paper and worked out a solution that doesn’t require nearly so much energy (negative or otherwise) or exotic matter (“A ‘Warp Drive’ with More Reasonable Total Energy Requirements”). Alcubierre’s model can be compared with a water balloon — a sphere “filled” with warped spacetime. Van Den Broek calculated that by confining the warped spacetime to a thin shell surrounding a volume of normal space — like the film of liquid forming the shell of a soap bubble — a relatively small volume of warped space could be made to confine a larger volume of normal space. It’s not really bigger on the inside than it is on the outside, it just works that way. Mind you, even Broek’s solution only reduces the negative mass requirement to “on the order of a few solar masses”. Fortunately we can do better than that.

This is the starting point for the warp drive in my “Terraform Space” series of stories. One of the limitations is that for a given amount of (negative) energy, the “skin” of the bubble gets thinner and thinner as the diameter increases. Van Den Broek reasonably put the limit of this as the Planck Length; personally I’d prefer something a little thicker (and presumably more robust) if I’m going to travel inside it.

The question of what happens if something (interstellar dust, or worse) gets in the way of such a travelling warp bubble? Reasoning that the highly curved space at the edge of the bubble would be the equivalent of a very strong gravitational field with a very short equivalent radius, I figured that there’d be very high tidal forces that would shred anything of more than subatomic size and route what was left around the bubble. What little energy managed to make its way through the bubble would appear as random twinkles of light, hence my “spangled blackness”. As it turns out, I was more or less right.

In a 2006 paper by a whole laundry list of authors (Hart, Held, Hoiland, Jenks, Loup, Martins, Nyman, Pertierra, Santos, Shore, Sims, Stabno and Teage), “On the Problems of Hazardous Matter and Radiation at Faster than Light Speeds in the Warp Drive Space-time” (which begins with the monumentous understatement: “A warp driven vehicle travelling at a speed faster than light may collide with objects in front of the ship, which would be hazardous to the ship and its crew.” They first examine the behaviour of photons hitting the oncoming warp. This turns out to be somewhat hazardous as they are initially shifted to high-energy frequencies, but some tricks with the Broek geometry reduces that again. Of solid objects, they have this to say: “the gravitational gradients in Broek regions will disrupt hazardous objects in the ship’s neighborhood. This is a property of Broek space-time, any natural object will be disrupted and deflected”. Mind, they’re still working out some of the detailed mathematical modelling of this. Interestingly, they also reference a paper by Krasnikov that reduces energy requirements to the equivalent of -10kg (yes, that’s a negative sign; exotic matter, remember?).

Which isn’t to say we have any clue how to build one, even if the math, when all is said and done, does turn out to be workable. Even Broek has had second thoughts on that. The thing is, some of the equations involve making assumptions about corners of general relativity and/or quantum theory that we have zero experience of on an experimental basis, and not much better than zero from an
observational standpoint. (For example, we may have observed astronomical black holes — or rather their interaction with their surroundings — but not closely enough to say a lot about what happens at the event horizon.)

In the meantime, though, we can have a lot of fun with the idea. Yes, I make a couple of simplifying assumptions in my stories, but then I stick with the consequences. No turning corners while in warp. No faster-than-light radio. Other people have different kinds of fun with it.

Edward Halerewicz, Jr, has a fascinating web site, Advanced Warp Physics homepage, with plenty of information (local and linked) on what’s happening in warp physics, warp theory, and related topics. Take it with a grain of salt, though. Then there’s this image from a YouTube video showing the image distortion as a warp field moving in front of a planet (it’s just the image distorted, not the planet!).
Further out is Ken Wright’s Gravity Warp Drive website (warning, excessive use of color and animated GIFs). He does tend to push the sale of his e-books explaining some of the theories, but it’s all for a good cause; some of the proceeds go to help one of the survivors of the Philadelphia Experiment. Okaaay. There are some interesting links from there, too.

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