[extropy-chat] Casimir Torque Project

[Adrian Tymes]

--- Hal Finney <hal at finney.org> wrote:
> In the case of your system, the positional parameter is the
> rotational
> position of the outer ring.  But the ring is perfectly circularly
> symmetric, so rotating the ring will not change the potential energy
> E of the system.  That means that E is a constant, so dE/dx is zero,
> so the force is zero.  Therefore there is no rotational force on the
> ring.

Only if there are no discontinuities in the system, and discontinuities
are impossible in most systems.  But they seem to exist here, and
that's the point of the system.

Break it down: over the parts of the system where the ring is exposed
to the post, E varies from one end of the part to the other (and in the
same direction with respect to rotation, i.e. always clockwise or
always counterclockwise depending on how you count it); over the parts
where the ring is not exposed, E is constant.  There are no other parts
of the system as far as the ring is concerned.  E jumps significantly
(the discontinuity) when transitioning from one part of the system to
another.

I'm aware that I may have overlooked some specific point on the system
which will provide negative torque to the ring.  Rejecting whole-system
analyses and focussing just on part of a system that produces energy is
a classic failure mode for other would-be perpetual motion arguments.
But I've checked for those, and I don't see any.

It might be useful to think of this experiment as verifying whether the
Casimir effect is indeed a conservative force, like gravity, or is a
source of energy that needs certain mechanisms to tap, like radiation
from the Sun.  (Chlorophyll and solar cells are not the simplest of
systems, and a bug that skitters towards the brightest light source but
can not fly would be stuck motionless on perfectly level ground at noon
since all reachable points nearby would be equally bright.)  Previous
efforts to tap it have indicated the former, but our current
understanding of its nature indicates the latter.