

The Casimir Effect - zacharyvoase
http://alphaprobe.com/equation.html

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aphyr
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>

~~~
fnid2
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?

~~~
aphyr
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
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
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. :)

