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Calculating the effects of Casimir forces

In the age of tiny devices, Casimir forces have emerged as troublemakers. Discovered in 1948, these complicated quantum forces affect only objects that are very, very close together. And in micromachines like the accelerometers in the iPhone or the micromirrors in digital projectors, Casimir forces can cause tiny moving parts to stick together.

the force is with them: With this arrangement of tiny objects, the ordinarily attractive Casimir forces become repulsive.

MIT researchers have developed a powerful new tool for calculating the effects of these forces. With it, they’ve found a way to arrange tiny objects so that the ordinarily attractive forces become repulsive. If engineers can design micro­electromechanical systems (MEMS) so that the Casimir forces actually prevent their moving parts from sticking together, it could lower the failure rate of existing MEMS and new ones, such as tiny micro­fluidic devices that can perform hundreds of chemical experiments in parallel.

Casimir forces are caused by the way, in the quantum-mechanical view of the universe, subatomic particles constantly flash in and out of existence. There are so many of these particles, which might last only a few sextillionths of a second, that the forces they exert generally balance each other out. But when objects are very close together–as they must be in micro­machines–there’s little room for particles to flash into existence between them. Consequently, there are fewer transient particles between them to offset the forces exerted by the transient particles around them. The difference in pressure ends up pushing the objects toward each other.

In the 1960s, physicists developed mathematical equations that, in principle, describe the effects of Casimir forces on any number of tiny objects of any shape. But in most cases, those equations remained prohibitively hard to solve.

Associate professor of applied mathematics Steven Johnson, physics PhD students Alexander McCauley and Alejandro Rodriguez ‘07, and physics professor John Joannopoulos have mathematically demonstrated that the effects of Casimir forces on objects 100 nanometers apart can be precisely modeled using objects 100,000 times as big and 100,000 times as far apart, immersed in a fluid that conducts electricity. Instead of calculating the forces exerted by tiny particles flashing into existence around tiny objects, the researchers calculate the strength of an electromagnetic field at various points around centimeter-scale objects.

For objects with odd shapes, calculating electromagnetic-field strength in a conducting fluid is still fairly complicated. But it’s eminently feasible using off-the-shelf engineering software. “Almost any geometry you can think of has not been calculated,” says Rodriguez. With the MIT researchers’ new approach, that’s about to change.

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