Cloaking devices!

Via Boing Boing I see that two different papers published in Science yesterday describe how to build cloaking devices. Obviously, it’s all still at a very preliminary stage, but it’s still undeniably cool. Note, though, that there are certain caveats; for example, in the second abstract linked above the author says that “Ideal invisibility devices are impossible due to the wave nature of light”.

That’s true, but actually a bit misleading; even were it not for the wave nature of light, an ideal invisibility device would be impossible for geometric reasons elucidated by Gromov in 1983. Chris Croke (who was on my orals committee, incidentally) mentions this result (as Theorem 2.1) along with many related theorems in this chapter from Geometric Methods in Inverse Problems and PDE Control, which is slightly more readable but still probably over the head of the non-specialist. Basically it says that if you can make it appear to an outsider that light (or anything that follows a “shortest path”) is traveling in a “straight line” through a particular region of space, then it really must be traveling in a “straight line”, Of course, this presupposes that space(time) is actually Euclidean, which it isn’t, but locally it’s probably close enough for the result to still hold. Also, the scare quotes are due to the fact that I don’t really mean a straight line (since space isn’t Euclidean) but rather a geodesic, for those that know what that means. i.e. not being intercepted and re-broadcast or bent around a spaceship or any other object in the region. That doesn’t mean that you couldn’t focus all the irregularities on a very small patch of the boundary (which would only be visible by an incredible stroke of luck on the part of the observer) or make the difference from expectation smaller than the observational error threshold, this latter being the (presumable, based on what I can glean from the abstracts) methodology of the Science papers.

Anyway, the point of the above paragraph is that a perfect cloaking device (i.e. one that is completely undetectable) is impossible for purely mathematical reasons, but it’s still pretty damn cool that close approximations seem to be in the works.

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