The discussion of the weight of a fly in a box has so far missed an
important point: measuring interval (which is related to resolution).
Let's consider the case of a comatose fly attached to an otherwise-massless
Ferris wheel, so that it undergoes uniform circular motion with radius R
and period P. (The Ferris-wheel model was chosen to reduce confusion among
those who don't understand aerodynamics. The aerodynamic case is similar,
with a few minor complications.)
I hope everyone agrees that this will perturb the center of mass of the
system and will cause forces on whatever is supporting the Ferris wheel.
The problem is that using a generic laboratory balance to measure a .1g bug
in a 20g box (as described at 12:42 PM 9/2/99 -0400) is certainly not a
suitable method for detecting these forces.
A typical thousand-dollar top-loading balance can plausibly provide a noise
floor of 0.01g using a measuring interval of three seconds. Reference: http://www.lehmanscientific.com/bal3csl.html
Such a noise level would be sufficient if the interval were finer, and vice
versa, but as things stand there's a big problem.
The force due to the motion is proportional to the mass, proportional to
the radius, and inversely proportional to the square of the period. If we
choose a period of six seconds (so that a half-period just matches the
measuring interval) and use the specified dimensions (a few hundred mm) the
fly is subjected to accelerations much less than one Gee. Therefore the
dynamical forces are much less than the ordinary weight of the fly, and
somewhat below the noise floor of the instrument.
If the period is shorter by a factor of N, the forces will be larger by a
factor of N squared, but there will be many cycles of motion during one
measuring period. Everything except possibly the last half-cycle will
average out, so the net gain will be only a factor of N at best. Large
values of N would require unnaturally fast motion of the fly, and would
also require implausibly skillful data-taking, to correlate tiny changes
with the behavior of the fly.
One could design a force-measuring apparatus with a greater bandwidth. The
noise floor would probably scale like the inverse square root of the
measuring interval. Since the actual force scales like the inverse square
of the period of motion, short-period experiments would be most favorable.
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Bottom line: The experiment as orignally described appears to have very
little power to discriminate between the various right and wrong notions of
dynamics that were being discussed. What's worse, if such an experiment's
vacuous result were to be misinterpreted as a high-precision null result,
it would tend to support some of the wrong notions.