[extropy-chat] Casimir Torque Project

[Hal Finney]

Adrian Tymes writes:
> Consider a boulder on top of a hill.  If its path is not blocked, it
> will roll down the hill because that would be energetically favorable
> to gravity.
>
> Now consider a boulder a meter or so away from a cliff.  Its path is
> otherwise not blocked, and it would be energetically favorable if the
> boulder fell off the cliff.  And yet it refuses to jump sideways a
> meter or so to allow that fall to happen.

The actual equation is force F is proportional to dE/dx, where E is
potential energy and x is a positional parameter.  In the case of the
boulder near the cliff, x could measure the distance along a path from
the boulder, to the cliff's edge, and then down to the ground.

Potential energy E is constant along that portion of the path where we
are approaching the cliff's edge.  Then as we turn and move down the path
to the ground, E decreases steadily.  This translates to dE/dx being
zero until we reach the edge of the cliff, then a constant downward.
That means there is no force along the portion of the path leading to
the cliff, and a net downwards force once we go over the edge, exactly
as observed.

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.

Hal