[extropy-chat] Casimir Torque Project

[Hal Finney]

I have found a good site with articles and references on Casimir
forces for different shaped cavities and arrangements.  It is
www.quantumfields.com, particularly
http://www.quantumfields.com/articles.htm .  I wasn't sure about this site
at first, it looked a little "iffy" because there are so many quack sites
selling junk perpetual motion machines based on ZPE and Casimir force,
but this one looks legit from what I can tell.  At least the articles
mostly appear to be from refereed journals.

Adrian might be especially interested in "A design manual for
micromachines using Casimir forces: preliminary considerations",
http://www.quantumfields.com/staif-2000paper.PDF , by Jordan Maclay.
This is not a journal article but it looks legit to me.  It discusses a
number of possible MEMS devices that would use or interact with Casimir
force:

> Casimir forces have been computed for only a few common geometries
> (See Table 1).  The most common one is the infinite, parallel plate
> geometry that produces an attractive force between the plates. If we
> examine the infinite parallel plate geometry more fully, and imagine
> placing perfectly conductive, metal surfaces normal to the parallel
> plates in order to enclose the volume between the plates, then there
> would be outward forces on these additional four infinitely long, narrow,
> surfaces (Brown, 1969).   For a conducting spherical shell (Milton, 1978)
> and (Boyer, 1968) have predicted outward or repulsive Casimir force.
> (Lukosz, 1971) has predicted repulsive forces for a conducting hollow
> cube. The vacuum stress on two intersecting planes is attractive. For
> conductive rectangular cavities with square cross section (1 x 1 x
> c) the Casimir energy and the forces on the cavity walls have been
> computed by (Ambjorn, 1983), (Haycan, 1993), and (Mostepanenko, 1997)
> with the result that the forces can be inward or outward depending on
> the specific dimensions. (Ambjorn , 1983) has computed the constant
> energy contours for a1 x a2 x a3 geometry for the region a2, a3 > 1.
> (Maclay, 1999) has computed the energy and force for rectangular cavities
> of arbitrary dimension.
>
> For the parallel plate, sphere, cube, and rectangular cavity expressions
> for the stress-energy tensor Tuv have been derived, giving separate
> expression for the stresses Tij and energy density T00. It is very
> important to note that for all geometries for which energy densities
> and forces have been computed, the expression for the force can also
> be obtained from the expression for the energy density by the principal
> of virtual work, which is based on the conservation of energy.  By this
> principal, the force Fx in the x-direction equals dE/dx, where E is the
> total energy in the volume.  Thus in microdevices utilizing Casimir
> forces, we expect to conserve the total energy, which includes the
> mechanical energy and the field energy.

Two key points here: first, for other geometries than infinite, parallel
plates, the Casimir force seems to be as often repulsive as attractive.
The effect is apparently quite complex and has only been computed from
first principles for a few geometries.  And second, most importantly,
it conserves energy, exactly as I have been saying.  Casimir is a
conservative force and can be calculated as the partial derivative of
the potential energy E with respect to the position coordinate x.  As I
showed, this proves that Adrian's device cannot work since the position
coordinate corresponds to the rotational position of the circular shell,
which is perfectly symmetric, hence E cannot change with that position,
hence F is zero.

Nevertheless this article, and others on the site, point to some
interesting experimental tests of Casimir forces.  From what I have
read elsewhere, current results do not match up that well with theory.
They only agree to within about 10-20%, which is not that good.  Better
experimental technique could help to show whether more theory is needed.
I would encourage Adrian to continue his experiments but base them on
realistic expectations.

BTW another paper on this site, the last one by the late Robert
Forward, may interest Mike Lorrey: "A Gedanken spacecraft that
operates using the quantum vacuum (Dynamic Casimir effect)",
http://www.quantumfields.com/gedanken%20spacecraft.pdf .  The abstract
says, "In this paper we consider another suggestion from science fiction
and explore how the quantum vacuum might be utilized in the creation
of a novel spacecraft. The spacecraft is based on the dynamic Casimir
effect, in which electromagnetic radiation is emitted when an uncharged
mirror is properly accelerated in the vacuum. The radiative reaction
produces a dissipative force on the mirror that tends to resist the
acceleration of the mirror. This force can be used to accelerate a
spacecraft attached to the mirror. We also show that, in principle,
one could obtain the power to operate the accelerated mirror in such
a spacecraft using energy extracted from the quantum vacuum using the
standard Casimir effect with a parallel plate geometry."

Sounds promising, but when you read it you find that it still obeys
the boring old laws of physics: conservation of energy, conservation
of momentum.  It uses a vibrating mirror to radiate photons, a side
effect of Casimir force.  These radiating photons propel the craft using
conservation of momentum.  And that idea of powering the ship with energy
from the vacuum?  It's a simple Casimir battery, parallel plates allowed
to fall together so that you can extract energy from them.  It's a one
shot operation that does not generate infinite power.  Too bad.

As for the larger question of whether it makes more sense for Extropians
to work on concepts and ideas that are consistent with the laws of physics
vs hoping to find that these laws are false, I still think it is obvious
that the first path is more likely to succeed and advance one's goals.

Hal