Foucault doodle

September 18 would have been the 194th birthday of Leon Foucault, a French physicist most famous for devising a pendulum that demonstrates the rotation of the Earth. I’ve learned a bit more about this experiment over the past couple years.

One of the fascinating aspects of Foucault’s pendulum is how many ways there are to reason about it. Being who I am, I usually think about this in terms of oscillator coupling. Imagine you are standing in a room looking at a Foucault pendulum moving back and forth. The motion you see could be described in terms of two different “modes”: either you would see the pendulum swing from left to right, or from front to back. Clearly, this description is somewhat arbitrary, since you could move to a different position in the same room and thus change what “left-right” and “front-back” meant to you. That is, the system is invariant under rotation about its axis. Among other things, invariance means that the modes of motion (front-back or side-side) have to generally look the same; same “shape”, same frequency, etc. When a system has two oscillations at exactly the same frequency, small perturbations from the outside world (such as gyroscopic forces due to the rotation of the earth) have the effect of transferring energy back and forth between these modes of oscillation. This appears as the precession of the line along which Foucault’s pendulum swings.

The exact same mathematics describe many different systems, each with different names attached. The hemispherical rate-integrating gyroscope is essentially a solid-wave version of Foucault’s pendulum built out of a wine glass, as is sometimes noted by those still working on such devices. The same thing works when the oscillations involve light rather than elastic waves, and this is the basis of ring laser gyroscopes. Physicists sometimes talk about geometric phase (or Berry phase) to describe this general type of perturbed oscillation.

I find it fascinating when these same concepts keep appearing in different parts of the literature under different guises.

I also learned this summer that I spent many years utterly mangling Foucault’s name.

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