3 ms·

Could you convert the mechanical energy of the moving plates into electrical energy? Probably orders of magnitude too small, eh? What about at the nanoscale?

• aphyr 17y ago
  Sure. You could mechanically couple one of the plates to a generator of any type. Keep in mind though that the Casimir energy is conservative--meaning that you can't extract more energy out of it than you put in. You'd get one extremely small electrical charge... and then need to use more energy to pull the plates apart again. The plates do need to be extremely close for this to be noticable. Definitely nanoscale. :) The wavelengths of the particles are any which satisfy the boundary condition that the transverse component of the electric field is zero at the plate boundary. That's basically satisfied by any photon with wavelength above the plasma frequency. For aluminum, that's about 15 electron volts or 82 nm. (warning, back of the envelope math) Obviously the lower frequency bound depends on the distance between plates. You can indeed make springs with the Casimir force, although the force depends quartically instead of quadratically on the distance. Measuring the springy oscillation rate is how we experimentally measure the force.
  • nitrogen 17y ago
    I've always understood an inverse quadratic relationship to be related to the surface area of the sphere over which a force is distributed at a given distance. Is that correct, and if so, does an inverse quartic relationship suggest additional dimensions in which the force is propagating?
    • aphyr 17y ago
      That's an interesting idea. In this case, though, I don't think it does. In fact, many radial forces don't scale with the square law--the weak and strong nuclear forces, for example. The fourth-power scaling in the parallel plates example is strictly geometry-dependent, and doesn't apply in other circumstances. I do wonder, however, if power-law forces in general reflect some measure of the "dimension" in which the system's phase space is embedded. I vaguely remember that the zeta regularization scheme is in fact tied to the dimensionality of the quantum algebra for the system... but that's higher math than I can handle. :)