Spacetime on a Chip

Better Geometry Through Chemistry

Randall D. Kamien
Science 315, p. 1083-4 (2007)

URL: http://www.sciencemag.org/cgi/content/summary/315/5815/1083

Short but sweet. In this article, Kamien describes an experimental method developed by Klein to print a metric onto a two-dimensional sheet. The idea is very simple, but the applications seem far-reaching.

By changing the spatial concentration of a chemical that contracts when heated, Klein and his colleagues can control where and how much a surface will curve.

You can make the perfect pringle. You can make the egg-crate potential that's so popular with theorists. You could reproduce the Rocky Mountains in at the molecular scale.

There are two applications that seem especially interesting to me. The first has to do with optics. You could pattern a photonic lattice as accurately as you like. You could put the defects in by hand, exactly where you want. (As a condensed matter theorist, the idea of controlling the defects in a lattice is quite appealing.) Unlike photonic lattices created with lasers, you could pattern a lattice once and use it over and over. You could make it in your lab in Europe, put it in your pocket and take it to your buddy in California to do tests on.

Another prospect that interests me is the study of Brownian motion in curved space. People probably do this already, but I'm not aware of it. If you read a popularization of general relativity, you'll undoubtedly find an analogy to a stretched rubber sheet. It's very elegant to think of marbles rolling along geodesics, following the curvature of the sheet. But what about a marble that gets a bunch of random kicks due to thermal fluctuations. You wouldn't see this kind of thing with planetary orbits, but you could certainly watch some florescent particles move around in your custom-made solar potential. Do particles with a drift velocity follow an approximate geodesic?

It's interesting to think about introducing random fluctuations to general relativity on a scale that is experimentally accessible. Maybe you could even explore "thermal foam" instead of quantum foam. Would these thermal fluctuations be analogous to quantum fluctuations of spacetime with a Planck length of a micron? It sounds sort of like another dream of Mr. Thompkins ...

I'm way off track now. In short, the ability to take your favorite 2D spacetime metric and print it on a chip could open up some interesting avenues of research.