Generating a Torque From The Casimir Effect
by Adrian Tymes

This theory relies on the principle that the Casimir effect generates
an attraction between two plates of reflective metal (say, silver or
aluminum) but not between reflectors and light-absorbing blackbodies
(say, a dark insulator).  This is because photons bounce back and
forth between reflectors, but not between reflectors and absorbers.
Thus, we can use blackbody to shield (prevent) the Casimir effect in
certain regions, thus potentially generating a force between
reflectors near the edges of these regions whose vector points away
from the edges.

The accompanying figure shows one way to translate this force into
torque.  The outer circle and central square of metal are indicated by
gray, while the blackbody shields are black.  The blue and red lines
are markup.  The red line shows that a line from point A passes
through the tips of the blackbody regions to the center of the circle.
Therefore, the metal at point A itself, and on the circle immediately
clockwise from point A, is completely shielded from the Casimir effect
and experiences no torque.  The metal in the region from point A to
point B experiences Casimir attraction, but the force vectors (which
extend from points on the circle to points on the central square) all
pass to the right of the center of the circle.  That is, they can all
be broken down (as shown by the blue lines) into components which
point towards the circle's center, which produce no torque, and
components which point clockwise, which produce a clockwise torque.
No other forces necessarily act upon the system to balance this torque
out (although a real implementation would have friction opposing any
torque-generated motion, were the circle free to rotate around the
shields and square, but this could be overcome by making the
components small enough - with feature sizes, especially the
separation between circle and square, on the order of tens or hundreds
of nanometers - that the Casimir torque would be large enough to
overcome friction).

It may be that the Casimir force actually produces a repulsion between
the metal reflectors in this case, since some photon pressure will
exist between them but not between the blackbodies and the metal.  If
so, the force vectors reverse - and in this example, we get a
counterclockwise torque instead of a clockwise torque, but we still
wind up with a net torque.