The Casimir Effect | Hacker News Reader

The Casimir Effect

alphaprobe.com

20 pointszacharyvoase8 comments

Nicely written article! The Casimir effect is a great example of quantum mechanics which is actually tractable without too much math (until you start getting to the weirder renormalization schemes). Bonus question: after reading, do you believe the quantum vacuum (or even "the electromagnetic field" can be said to "exist"?

I wrote my thesis on the Casimir effect last year, strangely enough. If you're hungry for a little more, it might be worth scanning. http://aphyr.com/data/journals/113/comps.pdf

An interesting thing about the Casimir force is that there is a derivation due to Lifshitz that doesn't use the concept of a quantized electromagnetic field; it uses zero-point fluctuations of the charge distribution in the plates to get the same result. So it's not clear that the casimir force is direct evidence for zero-point field fluctuations.

There was a nice paper a few years ago deriving a casimir-like force between (if I'm recalling correctly) a pair of coupled resistors/inductors. I can't find the reference right now, I'll post it later if I can.

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? Could these plates be like springs that provide motive force? What scale are these plates we are talking about? What are the wavelengths of the particles?

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.

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?

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. :)

So is it conceptually possible to imagine some kind of propulsive device being built using the reverse Casimir effect described in the article? Something that might have the propulsive power of an ion engine, where its not very powerful but can run constantly? I know next to nothing about the math behind this, other than a rough and overly simplified understanding of the physics outlines, so feel free to laugh at me with gusto.

No. The energy you get out when the plates would repel will be equal to the energy required to push the plates together in the first place. No free lunch!

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