The Fluctuation-Dissipation Theorem gives the connection between the power spectrum of the microscopic fluctuating motion we call thermal noise and the macroscopically-measurable real (dissipative) part of the admittance of the system of interest. At this stage of the development of gravitational wave interferometers, the linkage between microscopic and macroscopic quantities is crucial; we expect interferometer performance to start or rapidly advance to the point that thermal noise is one of the limiting terms in the noise budget, but to date no interferometer has performed at a sensitivity level comparable to those at which we expect thermal noise to dominate. (The one temporary exception, the LIGO 40-meter interferometer before October 1994, appeared to show broad-band thermal noise from its test masses, but the dissipation levels were much higher than will be used in full-scale instruments. See the more complete discussion below.) In order to trust designs of test masses and suspensions for LIGO, we rely on our belief that we understand the application of the Fluctuation-Dissipation Theorem.
The responsible thing to do in this situation was to carry out a direct test
of the theorem in a situation that includes all of the aspects of the LIGO
problem, except for the low noise levels of LIGO. Following the pioneering
work of Jones and McCombie in the 1950's,[] we chose a torsion
pendulum as a model single-degree-of-freedom system that should exhibit
thermal noise at a level whose measurement should be easily achievable. The
novel feature of this experiment would be the use of a torsion fiber whose
internal friction was large enough to be the dominant source of dissipation.
Furthermore, we planned to use a fiber in which the loss function 
was close enough to constant to enable us to test the prediction of a 1/f
spectrum.
This experiment became the Ph.D. thesis topic of Gabriela González, who
has now (after a two-year postdoc with the LIGO Project at MIT) taken a
faculty position at Penn State. She studied a variety of lossy
materials as possible torsion fiber materials, finally choosing Nylon 6 as
the most well-behaved fiber with the desired properties. Its internal
friction is large and nearly constant; the loss angle declines very
gradually from 0.02 to 0.007 over the range of frequencies from 2 mHz to
0.40 Hz. (Nylon's chief disadvantage, substantially hygroscopicity, was
solved by performing all measurements in vacuum.)
González's torsion pendulum was designed to be operated in two different modes. In the first, the complex admittance of the pendulum (especially its real part) could be measured by applying an electrostatic torque to the inertia arm of the pendulum. In the second mode, the pendulum was as free as we could make it of all external influences, so that its angular motion was dominated by thermal noise. The admittance measurement yielded, via the Fluctuation-Dissipation Theorem, a prediction of the thermal noise spectrum that could be compared with the spectrum of the free motion obtained in the second part of the experiment.
The results of these two halves of the experiment are shown in Figure 2.[6] The curve marked with the * symbols shows the thermal noise power
spectrum predicted by the Fluctuation-Dissipation Theorem, based on
measurements of the admittance of the pendulum. The curve marked with the 
symbols shows the actual measured angular motion power spectrum. The
excellent agreement between the two is a vivid demonstration of the validity
of the theorem and its interpretation in the internal friction case. Note
that there are no adjustable parameters used to optimize the agreement; the
two curves come from two separate measurements, each independently
calibrated.
For comparison, the figure also shows the prediction of the thermal noise power spectrum that would result if we made the naive and arbitrary assumption that the spectrum arose from velocity damping, normalized to the dissipation at the resonance. The contrast between the two cases is striking. Thus we have demonstrated that an essentially correct interpretation of the theorem is in hand, and that it can be important in the ``structural damping'' case.